Bayesian Prior Uncertainty and Surprisal Elicit Distinct Neural Patterns During Sound Localization in Dynamic Environments

19 Perception, Bayesian inference, Neural oscillations, Auditory, Localization, EEG, Prior 20 uncertainty, Surprisal 21 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint

22 Estimating the location of a stimulus is a key function in sensory processing, and widely 23 considered to result from the integration of prior information and sensory input according to 24 Bayesian principles. A deviation of sensory input from the prior elicits surprisal, depending 25 on the uncertainty of the prior. 26 While this mechanism is increasingly understood in the visual domain, much less is known 27 about its implementation in audition, especially regarding spatial localization. Here, we 28 combined human EEG with computational modeling to study auditory spatial inference in a 29 noisy, volatile environment and analyzed behavioral and neural patterns associated with prior 30 uncertainty and surprisal. 31 First, our results demonstrate that participants indeed used prior information during periods 32 of stable environmental statistics, but showed evidence of surprisal and discarded prior 33 information following environmental changes. Second, we observed distinct EEG activity 34 patterns associated with prior uncertainty and surprisal in both the time- and time-frequency 35 domain, which are in line with previous studies using visual tasks. Third, these EEG activity 36 patterns were predictive of our participants’ sound localization error, response uncertainty, 37 and prior bias on a trial-by-trial basis. 38 In summary, our work provides novel behavioral and neural evidence for Bayesian inference 39 during dynamic auditory localization. 40 41

42 43 In stable environments, perception can benefit from past experiences, especially when our 44 sensory representations are unreliable. Here, a mismatch between prior and sensory input 45

in prediction error, which can be used to update predictions and increase perceptual 46 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint accuracy. However, following an abrupt change in the environment, prior information 47 quickly becomes irrelevant or even detrimental for the perceptual decision-making process1,2. 48 One way to conceptualize optimal decision making in such dynamic environments is via 49 Bayesian inference, in which perception is based on the integration of prior knowledge and 50 new sensory observations, weighted by their reliabilities and the inferred probability of an 51 environmental change3,4. 52 In the past, many studies have examined Bayesian inference using change-point paradigms, 53 in which a non-stationary environment is simulated by pseudo-randomly changing stimulus 54 statistics throughout the experimental task4,5. In such dynamic environments, changes in the 55 environment lead to large surprisal and indicate that the prior is not relevant anymore. 56 Thereby, humans have been shown to perform similar to an ideal Bayesian observer in 57 settings such as visual spatial localization6,7, visual orientation discrimination8, and auditory 58 pitch discrimination9, although sub-optimality in decision making has also been reported10-12. 59 For instance, participants might not weight the sensory evidence and prior information 60 according to their reliabilities12, especially when the task complexity is high10. 61 At the neural level, a number of studies have found prediction signals (i.e. the prior) reflected 62 in beta-band (14 – 30 Hz)13-15 and surprisal reflected in gamma-band (40-100 Hz) oscillatory 63 activity14-16. Sedley and colleagues15 employed a pitch discrimination task to disentangle 64 neural patterns associated with surprisal and prediction precision (i.e. inverse of prior 65 uncertainty). They observed that surprisal was reflected in gamma-band oscillations starting 66 from ~250 ms post-stimulus, and prior uncertainty about the next stimulus was positively 67 correlated with alpha-band oscillations (8-12 Hz) starting from ~280 ms post-stimulus. This 68 suggests that the prior, its precision and surprisal are coded in distinct neural patterns. 69 Similarly, Chao et al.14 used a hierarchical predictive coding model to differentiate the 70 feedforward and feedback signals during a tone sequence discrimination task. They observed 71 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint feedback prediction signals in beta range oscillations during the pre-stimulus time period, and 72 feedforward prediction error signals reflected in gamma-band oscillations following stimulus 73 presentation. From a predictive coding perspective17, the above studies demonstrate that 74 surprisal (or prediction errors) and prior are coded in higher (i.e. gamma) and lower (beta) 75 frequency bands, respectively, while uncertainty associated with the prior information is 76 reflected in alpha-band oscillations. In addition to gamma-band oscillations, surprisal is 77 commonly observed to scale with the amplitude of the P3 event-related potential (ERP), 78 along with the updating of the prior information (i.e. belief update)8,18-20. Nassar and 79 colleagues8 found that the effect of P3 amplitude and surprisal on belief update was 80 dependent on the statistical context in the environment. They used a change-point paradigm 81 in which larger surprisal values would indicate a true change in the environment as well as an 82 oddball paradigm in which the oddball stimuli would trigger large surprisal responses without 83 a change in the environment. Their results showed that contrary to the change-point 84 paradigm, participants did not update their beliefs even with high surprisal values in response 85 to oddball stimuli, even though in both conditions P3 amplitude scaled with surprisal. 86 So far, evidence for a Bayesian inference mechanism comes primarily from the visual 87 domain, as well as from auditory pitch or temporal estimation tasks6,15,20. However, 88 Krishnamurthy et al.21 have provided an intriguing behavioral study on Bayesian integration 89 of prior information and sensory evidence in auditory spatial localization. In their task, 90 participants had to first predict and then estimate the actual location of a sound source, as the 91 predictability of its location varied over time. They observed that changes in stimulus 92 predictability lead to changes in the magnitude of prior-driven biases, dependent on the 93 relevance and reliability of prior expectations. In other words, periods of stable stimulus 94 statistics enhanced prior usage, while recent changes reduced it. However, their study 95 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint provided an additional visual representation for all the sounds establishing the prior, which 96 arguably leads to multisensory (i.e. audio-visual) rather than purely auditory spatial priors. 97 As humans perform better at localization of visual compared to auditory stimuli in unimodal 98 tasks22,23, vision is usually the dominant modality during multisensory localization24,25. In 99 addition, multisensory recalibration effects can transfer to subsequent unimodal tasks26 and 100 subjects trained with audio-visual stimuli are more accurate in their sound localization 101 responses compared to subjects trained using only auditory stimuli27, while, modality 102 dominance is reduced or even reversed with decreasing reliability of the visual stimuli28,29. 103 For these reasons, it is unclear to what extend the results of Krishnamurthy et al.21 104 specifically reflect Bayesian inference in auditory spatial localization, or are at least partly 105 driven by visual priors. Consequently, the aim of our present study is to expand upon the 106 literature by (1) investigating whether behavioral responses in a unimodal auditory 107 localization task adhere to the principles of Bayesian inference; (2) testing how this spatial 108 inference process is altered by the presence of additional visual priors (as in Krishnamurthy et 109 al.21); (3) study the neural patterns associated with prior uncertainty and surprisal, along with 110 their impact on subsequent behavioral responses. 111 Participants listened to sequences of sounds coming from pseudorandom locations and 112 reported the location of the last sound of each trial. We conducted both an audio-visual 113 condition (as in Krishnamurthy et al.21) and a modified audio-only condition while recording 114 high density EEG, and fitted a near optimal Bayesian observer model to participants’ 115 responses. Our results reveal neural patterns reflecting prior uncertainty and surprisal for both 116 conditions in time-domain as well as the lower (i.e. alpha/beta) and higher (i.e. gamma) 117 frequency range oscillations. Critically, we observed a significant relationship between the 118 neural activity associated with prior uncertainty and surprisal and the behavioural location 119 estimation error, response uncertainty, and prior bias. In summary, our results indicate 120 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint behaviourally relevant electrophysiological patterns reflecting Bayesian inference processes 121 during both auditory-only and audio-visual spatial localization in dynamic environments. 122 123

124 Participants 125 Thirty-five participants took part in the study, in exchange for monetary compensation (10 126 Euros per hour). Our sample size is based on a previous study employing a similar auditory 127 change-point paradigm21. Three participants had a mean estimation error of > 25° during the 128 training sessions and were excluded prior to the main experiment. We excluded three 129 additional participants due to a large number of noisy EEG channels (> 10%). The remaining 130 29 participants were between 19 and 37 years old (15 females, Mage = 24.4, SDage = 3.8) and 131 right-handed. They reported no hearing impairments or neurological deficits, had normal or 132 corrected-to-normal vision, gave informed consent, and were naïve to the purpose of the 133 experiment. The study was conducted in accordance with the standards of the Declaration of 134 Helsinki (1996). We further followed the Austrian Universities Act of 2002, which states that 135 only medical universities or studies conducting applied medical research are required to 136 obtain additional approval by an ethics committee. Therefore, no additional ethical approval 137 was required for our study. 138 139 Experimental setup and procedure 140 The experiment was run using MATLAB (2018b, MathWorks, Natick, MA) and 141 Psychophysics Toolbox30. We presented visual stimuli via an LCD monitor (48 x 27 cm) with 142 a refresh rate of 60 Hz and auditory stimuli via tube earphones (ER2; Etymotic Research, Elk 143 Grove Village, IL). Individual auditory stimuli consisted of 50 ms pink noise burst (10 ms 144 on- and off-set ramps), high-pass filtered using a 4th order Butterworth filter with a 250 Hz 145 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint cut-off frequency. Each sound was rendered at a specific direction by employing each 146 participant’s head-related transfer function (HRTF, measured prior to the experimental 147 sessions, using the same approach as in Ignatiadis et al.31) using the Auditory Modeling 148 Toolbox32. 149 Low visual and auditory stimulus presentation latencies were verified via an oscilloscope (M 150 = 0 ms, SD = 4.4 ms). Participants sat at a desk in a dark and sound attenuated room, with 151 their head in a chin rest (75 cm distance to the screen) to minimize movement. 152 The experiment was divided into two sessions, conducted on separate days (less than 3 days 153 apart). The first session consisted of nine training blocks (not included in our analysis), to 154 familiarize participants with the sound localization task and response method. In the second 155 session, participants completed two further training blocks and six main task blocks. Each 156 block consisted of 50 trials, resulting in 300 trials for the main task. 157 Throughout the main task, we collected 128-channel high-density EEG (actiCAP with 158 actiCHamp; Brain Products GmbH, Gilching, Germany) and eye tracking data (EyeLink 159 1000 Plus; SR Research, Osgoode, Ontario, Canada), at a sampling rate of 1 kHz. Electrode 160 impedances were kept below 25 kΩ and the signal was recorded against ‘FCz’ as reference 161 electrode. In addition to the scalp electrodes, we recorded an auxiliary audio channel via a 162 stimulus tracking device (StimTrak, Brain Products GmbH, Gilching, Germany) to later align 163 the EEG triggers offline with the onset of sounds and ensure correct trigger timing. 164 165 Training task 166 At the beginning of each trial, participants fixated on a central dot (0.5° radius) displayed at 167 the centre of the screen. Around the fixation dot, we displayed a semi-arc (0.75° width) that 168 represented the range of azimuth angles on the frontal horizontal plane (see Figure 1). After 169 750-1000 ms of fixation, jittered on each trial, we presented a single sound from different 170 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint locations in azimuth (from 90° to -90°). 950 ms after the sound offset, a mouse cursor 171 appeared at the location of the fixation dot, which signalled participants to respond and 172 turned into a line when moved close to the semi-arc. Their task then was to indicate the 173 azimuth location of the sound, by moving the line along the semi-arc (response resolution 174 <1°) via a mouse in their right hand, and click the left mouse button at the desired location. 175 Subsequently, they indicated their level of response uncertainty by marking an 80% 176 confidence-interval around their response location. After that, feedback was provided for 500 177 ms via a red line presented on the arc at the true sound location, followed by a new trial. At 178 the end of each training block, participants received additional feedback on their mean 179 absolute error (in degrees) and the percentage of times that their marked area of response 180 uncertainty included the true sound location (goal was 80%). 181 Importantly, trials alternated between an auditory-only (A) (as described above) and an 182 audio-visual (AV) condition. In the AV condition, a line indicating the sound location 183 appeared on the arc simultaneously with the sound presentation. We added this condition to 184 the training, to help participants establish a mapping between the auditory sound location and 185 its abstract spatial representation on the visual arc on screen. 186 187 Main task 188 The main task was highly similar to the training, with the important difference that each trial 189 consisted of a sequence of sounds, with a stimulus-onset asynchrony of 500 ms. Sound 190 locations were randomly sampled from a normal distribution whose (generative) mean was 191 sampled from a uniform distribution bounded between 60 and -60 degrees, and a constant 192 standard deviation of 10° (i.e. experimental noise). Each sound of the sequence had a 1/6 193 probability of being a change-point, at which point a new generative mean was sampled from 194 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint the bounded uniform distribution (60° to -60°), thus resulting in a sudden change of the mean 195 sound location. 196 The participants’ task was to indicate the location of the last sound of the sequence (i.e. the 197 probe sound). Each sequence contained between 1 and 43 sounds and each sound had a 1/12 198 probability of being the probe sound, thus rendering the trial length unpredictable and 199 encouraging participants to pay attention to each sound location. Prior to the experiment, 200 participants were only superficially informed about the concepts of change-points and 201 experimental noise, without mentioning specific parameter values. 202 Akin to the training blocks, we presented the A and AV condition trials in alternating order. 203 In AV trials, all sounds except for the final probe sound were presented along with a 204 simultaneous visual representation of the sound location via a line on the semi-arc. To ensure 205 comparability of the two conditions, we presented identical trials in the A and AV conditions. 206 In other words, each A trial had a corresponding AV trial, which only differed in the 207 additional visual representations for the latter. The order of trials was randomized within 208 subjects, and the corresponding A and AV trials were never presented in direct succession. 209 As in the training task, participants gave localization and response uncertainty responses at 210 the end of each trial. However, they did not receive immediate feedback on the true sound 211 location after each trial, but only a summary performance feedback at the end of each block, 212 regarding their mean absolute error (in degrees) and the percentage of times that their marked 213 area of response uncertainty included the true sound location. 214 215 Bayesian model 216 We fitted a near optimal Bayesian observer model to our participants’ localization responses 217 (for modeling details see Supplement 1) to obtain two latent variables (i.e. not directly 218 observable variables, which we inferred via our model) for every stimulus with optimized 219 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint parameters for each participant. The first latent variable is the prior uncertainty (𝑃𝑈), which 220 we defined as standard deviation of the preceding posterior distribution (see Supplement 1, 221 Eq. 25). The second latent variable is the information theoretic quantity of surprisal (𝑆𝑈). 222 This is defined as the negative logarithm of the probability density of the full prior 223 distribution, evaluated at the latest observation (see Supplement 1, Eq. 26) 224 225 Behavioural analysis 226 Using the participants’ responses, we derived three behavioural metrics for each trial and 227 analysed them over two experimental factors. The behavioural metrics are: (i) the estimation 228 error, which is calculated by computing the absolute difference between the localization 229 response and the sound’s true location; .(ii) the response uncertainty, indicating the 230 confidence area (in degrees) that participants marked around their response line at the end of 231 each trial; (iii) the prior bias, computed as the estimation error on the current trial, divided 232 by the difference (in degrees) between the previous and the current sound locations: 233 Prior bias = (xresponse – x(t))/(x(t-1)- xt). 234 235 These metrics were evaluated over two main independent variables. The first one is the 236 sensory modality condition (AV vs. A), the second one is how many individual sounds had 237 been presented since the last change-point (sounds after change-point, SAC). In other words, 238 the latter is a proxy of the strength of the present prior and the expected surprise elicited by 239 the current sound. 240 To investigate how our experimental manipulations affected the behavioral variables, we 241 computed a linear mixed effect model (LMM) using the glmmTMB33 package in R (version 242 4.3.2) with Modality (AV and A) and SAC level (1 to 6) as fixed effect variables and subjects 243 as random effect variable. Single sound trials are excluded from the analyses. 244 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint 245 EEG preprocessing 246 All EEG data preprocessing and analysis was performed using EEGlab34 (version 2022.1), 247 Fieldtrip35 (version 20220827), and custom scripts. 248 First, we aligned our EEG triggers to sound onsets using the Stimtrak external channel. Next, 249 we downsampled the continuous EEG signal to 250 Hz, applied a high-pass filter with a cut-250 off frequency of 0.25 Hz (Hamming window, zero-phase finite impulse response filter) using 251 the ‘pop_eegfiltnew’ function from EEGlab and removed line noise using the ‘nt_zapline’ 252 function from NoiseTools toolbox36. We then epoched the data from -1 to 2 seconds relative 253 to the onset of each sound stimulus in the experiment, visually inspected the data and 254 excluded epochs containing excessive noise as well as eye blinks close to the stimulus onset. 255 As mentioned above, identical trials were presented in the A and AV conditions, although in 256 randomized order. To maximize comparability between the A and AV conditions, for each 257 participant, we only analyzed trial epochs that were present in both conditions after artifact 258 rejection. Therefore, if we rejected an epoch in one condition, we also rejected the 259 corresponding epoch in the other condition. 260 We then interpolated noisy channels via spherical interpolation, added the reference electrode 261 ‘FCz’ back to the dataset and re-referenced the data to the average of all electrodes. 262 Next, we performed independent component analysis (ICA) to identify and remove ocular 263 and heart-related artifacts. Particularly, in order to avoid using overlapping data segments for 264 the ICA we performed the ICA decomposition on slightly differently preprocessed data: We 265 high-pass filtered the data at 1 Hz cut-off frequency37 and extracted the epochs between 0 to 266 500 ms for each sound (thus containing no overlapping data periods between epochs). The 267 remaining preprocessing steps were identical to the original dataset. We obtained ICA 268 weights from this alternatively preprocessed dataset using the Picard algorithm with PCA 269 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint (principal component analysis) to control for data rank deficiency caused by channel 270 interpolation. Then we applied the resulting ICA weights back to the original dataset and 271 rejected ocular and heart-related components by visual inspection using the IClabel38 plugin. 272 Finally, we baseline corrected each epoch using the time period from -100 to 0 ms, relative to 273 the sound onset. 274 275 Spectral analysis 276 Prior to the spectral analysis, we subtracted the mean activity of all trials from each trial in to 277 analyze only the induced oscillatory power. For the lower frequency range (4 to 30 Hz), we 278 performed short-time fast Fourier transform, using a single Hanning taper with a window 279 length of 300 ms in steps of 16 ms and a frequency resolution of 1 Hz. For the higher 280 frequency range (40 to 100 Hz), we used the multi-taper method, with varying window length 281 of 250-100 ms (window length shortens with higher frequencies) in steps of 16 ms and a 282 frequency resolution of 2 Hz. The resulting spectral power was then expressed as relative 283 signal change to the mean of the time period from 0 to 500 ms around each sound (i.e. the 284 entire interval between the onset of the current and the next sound). 285 286 Regression analysis 287 Next, our goal was to identify neural activity patterns associated with our Bayesian model 288 latent variables PU (prior uncertainty) and SU (surprise). To do so, we performed three 289 separate ordinary least squares linear regressions with both PU and SU values as predictors 290 and EEG amplitudes as the output: one for the time-domain data (i.e. ERPs), one for the 291 lower, and one for the higher frequency range. For the time-domain data, independent 292 regressions were performed for each EEG time-point and channel, while for the time-293 frequency domain data, regressions also included the frequency domain. 294 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint Both EEG data and latent variables were z-transformed prior to the regression. We excluded 295 the final probe sounds of each sequence from this analysis, since they contain only auditory 296 stimuli in both A and AV conditions. Additionally, not including the final sounds that 297 participants responded upon in the regression analysis, allowed us to keep them as an 298 independent data set to test the behavioral relevance of the regression results (see next 299 subsection). The first sounds were also excluded from the analysis, as they do not have a 300 reliable estimate of the model latent variable values considering there are no preceding 301 sounds to form a prior. 302 For each subject, this analysis resulted in a beta coefficient per time-point, channel, and 303 frequency (for the time-frequency domain data), separately for each latent variable. 304 For group statistics, we performed a total of six cluster-corrected permutation tests39, one for 305 each combination of latent variable (PU, SU) and EEG data (time domain, low – and high 306 time-frequency domain), to compare whether the obtained beta coefficients differed 307 significantly from zero across participants. Cluster correction for multiple comparisons was 308 applied using a cluster-level alpha of .001, and permutation of the data points was performed 309 over 1000 iterations, and we only considered clusters with a duration of > 5ms length. For 310 PU, we tested the time period of -250 ms to 100 ms relative to every sound onset, as the prior 311 uncertainty should be neurally represented already pre-stimulus, and up until completion of 312 initial sensory processing. For SU, on the other hand, we ran the test for the time period of 0 313 to 500 ms around each sound onset, as meaningful neural correlates of surprisal should only 314 appear following stimulus presentation. 315 Additionally, we tested how the neural activity patterns associated with PU and SU variables 316 differed between the AV and A conditions. Again, we used a cluster-based permutation test 317 with the cluster level alpha set to .001 and permutation of the data points performed over 318 1000 iterations. 319 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint 320 Behavioral correlates of latent variable brain activation patterns 321 Finally, we were interested in whether the neural activity patterns associated with PU and SU, 322 as identified in the previous step, were predictive of the behavioral metrics on a trial-by-trial 323 basis. Therefore, within each subject, we regressed EEG activity around the final probe sound 324 of each trial against the three behavioral variables estimation error, response uncertainty, and 325 prior bias. Specifically, we averaged the EEG activity around the probe sound across all 326 constituting data points (time, channels, and frequencies) for every significant PU and SU 327 regression cluster. This resulted in a single value per trial, which we then regressed against 328 the behavioral outcome of that trial (all variables were z-transformed prior to regression). For 329 the group-level statistic, we performed one sample t-test (α = 0.05) for each regression 330 between EEG activity and behavioral outcome variables, to see whether the resulting beta 331 coefficients differed significantly from zero. Single sound trials are excluded from the 332 analyses. 333 334

335 Behavioral results 336 Figure 2 shows the behavioral and model data as a function of our two main independent 337 variables, stimulus condition (AV vs. A) and SAC level (1 to 6). For the behavioral data, the 338 linear mixed effects model revealed a smaller sound localization estimation error in the AV 339 compared to the A condition (p < .01; see Table 1 for detailed statistical outcomes), as well as 340 a larger prior bias (p < .001). In line with our expectations, these results suggest that the 341 additional visual stimulus during non-probe sounds helped establishing a prior that eventually 342 improved probe localization. Further, we observed a main effect of SAC level (p < .01) for 343 prior bias, indicating that bias was small immediately following a change-point, but increased 344 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint subsequently. No other main effects or interactions were observed for the behavioral data (p 345 > .05). 346 For the latent model variable PU, the LMM analysis revealed a main effect of Modality (p < 347 .001). This was due to larger PU values in the A compared to the AV condition, in line with 348 our expectation of a weaker prior in the former. Further, we found a main effect of SAC level 349 (p < .001), with the largest PU values at the second sound after a change-point, indicating that 350 change-points led to a transient increase in PU. 351 For the model variable SU, we found a significant main effect of Modality (p < .001), due to 352 overall larger SU values in the AV compared to the A condition. Again, this is likely a 353 consequence of a stronger prior in the former, which leads to stronger surprisal following a 354 change-point. Finally, we observed a main effect of SAC level (p < .001), due to surprisal 355 being largest directly after a change-point, and then decreasing with increasing numbers of 356 sounds after the change-point. No interactions were observed for the model variables (p > 357 .25). 358 359 EEG regression results 360 Figure 3 displays the results of the regression (i.e. beta coefficients) between the time-domain 361 EEG data and the model variables PU and SU (see Supplementary Table 2 for the cluster 362 statistics). For both the AV and A condition, there are two time periods in which PU 363 significantly predicts the EEG activity patterns. The first is between around -250 to -100 ms 364 prior to sound onset, in line with activated prior information in expectation of a stimulus. The 365 second period is between 0 and 100 ms following a sound, potentially tracking the 366 comparison between the prior and the sensory stimulus. Further, both periods are comprised 367 of a medio-central- and an occipital cluster of electrodes with opposing beta coefficient 368 values, likely due to the dipolar pattern of an underlying event-related potential. 369 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint For the regression against SU, both AV and A conditions show significantly associated EEG 370 time-domain patterns aggregated between 100 and 500 ms following a sound, in line with a 371 surprisal response to the comparison between prior and sensory input. Again, the topography 372 shows a dipolar pattern, with medio-central and occipital clusters of opposing beta 373 coefficients. In summary, the time domain regression shows large, spatially overlapping, but 374 temporally distinct EEG activity patterns associated with PU and SU. 375 In the time-frequency domain (Figure 4), regressions revealed that pre-stimulus 376 synchronization in the delta-theta range was positively associated with PU, in both AV and A 377 conditions. Only for the AV condition, PU was negatively associated with synchronization 378 around the stimulus onset in the alpha and beta frequency range. Finally, also in the AV 379 condition, pre-stimulus gamma power (~75 Hz) was positively associated with PU. 380 Several time-frequency activity patters are also significantly linked to SU values. In both the 381 AV and A condition, SU is associated with reduced low frequency activity around the initial 382 onset of the stimulus. Subsequently, however, around 200 ms, the relationship becomes 383 positive for the theta to alpha range, arguably due to enhanced processing of surprising 384 stimuli. Likewise, early post-stimulus activity also correlates positively with beta-band 385 power. During the later time period around 400 – 500 ms following the stimulus, 386 synchronization in the theta-alpha as well as in the beta range (the latter only for AV) is 387 negatively associated with SU. Lastly, gamma-band power (~70 – 90 Hz) in the AV 388 condition was positively associated with SU at around 200 ms following the stimulus, and 389 negatively associated later between 400 and 500 ms post-stimulus. 390 As in the time-domain, PU and SU had temporally distinct, but spatially and spectrally 391 overlapping associated EEG activity patterns, suggesting a processing cascade from the 392 representation of the prior to the computation of a prediction error and a subsequent surprise. 393 394 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint Neural patterns in the AV versus A condition 395 Overall, regression coefficients in both time domain and time-frequency domain were larger 396 for the AV compared to the A condition, resulting in more and larger significant clusters. In 397 the time domain, comparison of the regression coefficients associated with PU between the 398 two conditions revealed two centrally located positive clusters and four negative fronto-399 temporal clusters in the pre-stimulus time period (Figure 5). In the time-frequency domain, 400 we found an earlier positive posterior cluster (~ -250 to -50ms) in theta range and a negative 401 frontal cluster in beta range (~12-15 Hz) starting around 100 ms prior to the sound onset. No 402 significant clusters were found for PU in the higher frequency range. For SU in the time 403 domain, we found three positive and three negative clusters between ~150 to 300ms, possibly 404 reflecting larger underlying ERPs in the AV compared to the A condition. In the lower 405 frequency range, one negative fronto-central cluster in beta range (~12-14 Hz), and two 406 negative clusters and one positive occipital cluster in theta range were found for SU, similarly 407 due to the larger coefficients in AV condition. Finally, in the high frequency range we 408 observed three positive clusters (~150 to 220 ms) between ~ 66-90 Hz associated with SU, 409 indicating larger coefficient values in the AV condition. 410 411 Behavioral relevance of PU and SU related neural activity 412 After establishing the above distinct PU- and SU-related activity patterns for both the AV and 413 A conditions, we tested which of those patterns were, on a trial-by-trial level, predictive of 414 the behavioral metrics (error, response uncertainty, prior bias; see Figure 6). Importantly, as 415 detailed in the Methods section, we did so by regressing the behavioral variables against the 416 EEG data around the final probe sound of each trial. Thus, these data are independent of the 417 data used for the regression against the model variables reported above, which are taken from 418 each sound of the sequence except the final probe sound. 419 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint The participants’ estimation error in the A condition was significantly predicted by the 420 activity of a frontal, pre-stimulus time-domain cluster positively associated with PU, as well 421 as an occipital post-stimulus cluster positively associated with SU. 422 In the AV condition, estimation error was predicted by an early (0-150ms) posterior beta-423 band cluster positively associated with SU and a later (400 – 500ms) posterior beta-band 424 cluster negatively associated with SU. 425 Prior bias in the A condition was predicted by a posterior time-domain cluster (100 – 200ms) 426 positively associated with SU. In the AV condition, prior bias was predicted by a large time-427 domain cluster (150 – 300ms) negatively associated with SU. As can be seen from Figure 4, 428 topographies and time-courses are similar for both AV and A SU time-courses, yet behavioral 429 correlation with prior bias became significant for two different, consecutive time periods for 430 the two conditions, with different ERP polarities. Thus, although their association to SU is 431 oppositional, these clusters are likely part of the same process, which switches EEG 432 amplitude polarity at around 180ms. In the AV condition, prior bias was further predicted by 433 two time-frequency activity clusters. First, a large posterior cluster in the theta-alpha range 434 (350 – 500ms), in which a desynchronization was associated with more SU and eventually, 435 less prior bias. Second, a small left-posterior cluster in the gamma range (~470ms), in which 436 a desynchronization was likewise associated with more SU and eventually, less prior bias. 437 Finally, the participants’ response uncertainty ratings in the A condition were predicted by 438 two clusters in the time-domain. First, an early (~75 to 150ms) large central cluster and 439 second, a small later (~320ms) posterior cluster, in both of which negative ERP amplitudes 440 were associated with more surprisal and more response uncertainty. In the AV condition, 441 response uncertainty was associated with three clusters in the time-frequency domain: A 442 central-left cluster in the alpha-beta range (~ -50 – 100ms), in which a desynchronization was 443 associated with more PU as well as more response uncertainty; and two occipital clusters in 444 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint the gamma-range (~425 – 450ms), in which a desynchronization was associated with more 445 SU as well as less response uncertainty. 446 447

448 In the present study, we investigated behavioral and neural evidence for Bayesian inference 449 during auditory spatial localization in dynamic environments. 450 We report three main findings. First, our results show that participants continuously 451 integrated prior knowledge into their estimations, subject to dynamic changes in a volatile 452 environment. Second, these patterns of results were similar but amplified by the presence of 453 additional visual location priors. Third, we observed distinct EEG activity patterns associated 454 with Prior Uncertainty (PU) and Surprisal (SU), which are in line with previous studies using 455 visual and/or temporal or pitch-related tasks. Importantly, these EEG activity patterns were 456 predictive of the error, response uncertainty, as well as the prior bias of our participants’ 457 behavioral responses on a trial-by-trial basis. 458 459 Dynamic environmental changes impact behavioral and Bayesian model data 460 In our experiment, we used random change-points and experimental noise to simulate a noisy 461 dynamic environment with momentary changes to the reliability of prior information and 462 sensory evidence. Data from both experimental conditions showed stronger prior bias with 463 increasing SAC levels (i.e. accumulated sensory evidence). A similar effect was present for 464 PU, however with a peak at SAC level 2, as expected given the change-point at the previous 465 sound. Together, these results indicate that participants rely more on prior information, as 466 sensory evidence is accumulated during a period of stable environmental statistics and the 467 prior uncertainty decreases. 468 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint At the same time, estimation error and SU were largest at SAC level 1 (i.e. immediately 469 following a change-point). The large SU is indicative of a now irrelevant prior, which cannot 470 be used to improve the localization performance anymore, indicating a reason to update the 471 internal model. This was again similarly the case for both the AV and the A condition, 472 suggesting a comparable mechanism for visual and auditory spatial inference (see below for a 473 detailed discussion of the condition differences). 474 Our findings thus corroborate and extend the results by Krishnamurthy et al.21 who reported 475 similar effects following AV stimulation, by demonstrating Bayesian-like inference in 476 unimodal auditory settings and showing visual stimuli likely improved the sound localization 477 performance by providing a more precise prior distribution. 478 479 Prior Uncertainty is coded around stimulus onset, and associated with localization 480 performance and response uncertainty 481 In the time-domain, the pre-stimulus neural patterns associated with PU likely reflect late 482 ERP responses to the previous stimulus, with their topography and latency suggesting a P3-483 like component. The P3 is well documented to scale with surprisal and internal model 484 updating8,18-20, which fits well with our observed positive association with subsequently 485 increased PU. In the A condition, activity in this time-period was predictive of the behavioral 486 performance, indicating that larger P3-like ERP responses (reflecting larger surprisal due to a 487 prediction error) to the previous stimulus were associated with larger estimation errors in the 488 current trial. In the post-stimulus period, the significant clusters span the time-range of early 489 sensory processing including the P1 component. These scale negatively with PU, thus, the 490 stronger the prior, the larger the resulting sensory evoked ERP. Importantly, this early PU 491 regression pattern is still independent of the prediction error and any resulting surprisal, both 492 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint of which would be expected to appear later in the time period of a P3 ERP component and 493 scale positively with the ERP response. 494 The above discussed pre-stimulus ERP likely underlies the theta-band time-frequency domain 495 result, with which it shares a similar topography and time window. Additionally, low 496 frequency oscillations have been associated with temporal expectancy of important upcoming 497 stimuli40. Considering the regular SOAs in our study (i.e. always 500 ms), their oscillatory 498 power in our results scale positively with PU, in line with stronger expectation of an 499 upcoming sensory event in times of weak prior information. 500 Further, in line with numerous previous studies14,15, we found prior uncertainty reflected in 501 adjacent alpha- and beta-band activity patterns. Generally, the expectancy for an upcoming 502 task-relevant stimulus is known to cause a decrease in alpha- and beta power, especially for 503 regular inter-stimulus intervals40. Thus, as PU increases, we would expect participants to 504 increase the weight of sensory evidence rather than the prior, with the observed decrease in 505 alpha/beta power reflecting attentional preparation of the upcoming stimulus. Moreover, a 506 post-stimulus alpha/beta range cluster was both negatively associated with PU and response 507 uncertainty, suggesting a common neural pattern underlying the prior and the resulting 508 subjective response uncertainty. 509 Interestingly, previous literature suggests a possible dissociation of neural patterns between 510 predictions and their precision, reflected in beta and alpha range oscillations, respectively13-15. 511 Presently, however, we found neural patterns associated with PU in multiple frequency bands 512 in pre-stimulus as well as post-stimulus period. A possible reason for this discrepancy is the 513 applied analysis pipeline. For instance, Sedley et al.15 partialized out the correlation between 514 predictor variables prior to their regression analysis, which might have canceled out 515 correlation in other frequency bands. Indeed, upon performing the same analysis without the 516 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint partialization, they similarly observed an effect for prior precision in delta/theta, alpha and 517 beta/gamma-bands. 518 Finally, we found a positive gamma cluster in the pre-stimulus time period for PU. 519 Considering the short SOAs in our study (500ms), this association might be related to the 520 previous stimulus processing reflecting facilitation of sensory processing and increased 521 weighting of the sensory likelihood in response to larger prior uncertainty and reduced prior 522 reliability. 523 However, the observed time-window (~250ms following the previous stimulus), the 524 broadband nature, as well as its presence predominantly in the AV condition, indicate that the 525 gamma-response might be affected by microsaccadic muscular activity41. Although we 526 diligently removed eye-related independent components, which can help to clear 527 microsaccadic artifacts from EEG data42, we are cautious to interpret the gamma response in 528 this time-period as genuinely brain-related. 529 530 Surprisal-related EEG activity evolves post-stimulus and is linked to behavioral error, 531 confidence and prior bias 532 As surprisal (SU) represents the deviation of sensory evidence from the prior, we 533 consequently expected it to be represented in post-stimulus neural activity patterns. In the 534 past, EEG studies repeatedly found P3-like responses in response to surprising events 8,18-535 20, whose amplitude scales with the amount of surprisal and subsequent internal updating, 536 and which have been interpreted as the supporting evidence for the Bayesian brain 537 hypothesis43. In line with these results, SU in our data was associated with neural activity in 538 the time range of the P3 ERP component, in both AV and A conditions. Importantly, this 539 adds to the previous literature by showing SU related responses in auditory spatial inference 540 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint tasks, despite the auditory systems inferiority regarding localization, and thus demonstrates 541 the ubiquity of the associated P3-related mechanism. 542 In both the A and AV condition, larger amplitudes in early SU-related time-domain clusters 543 (~100-300 ms) were predictive of less prior bias in behavioral responses, indicating less use 544 of prior information following stronger neural correlates of surprisal. In addition, subjective 545 response uncertainty was likewise significantly positively associated with activity in two SU-546 related time-domain clusters, although only in the A condition. As to be expected, stronger 547 activation of these patterns subsequently led to larger response uncertainty, on a trial-by-trial 548 basis. 549 Surprisal has further been related to gamma-band oscillations, possibly reflecting the 550 processing of new sensory input14-16. Indeed, in the AV condition we found several clusters in 551 the 70 – 90 Hz frequency range, associated with SU. While two of those falls into the time-552 range of 200 – 300ms and are potentially driven by microsaccadic activity (as discussed 553 above), three of the later ones between 400 and 500 ms are particularly interesting, as their 554 activity correlates with subsequent response uncertainty and bias. More specifically, larger 555 gamma-band power in these clusters is associated with less surprisal and in subsequent 556 behavior, larger prior bias and smaller response uncertainty. 557 In addition to what previous studies have reported, our data also revealed SU to be reflected 558 in lower frequency activity. The activity patterns across space, time and frequency were very 559 similar between the AV and A conditions, with overall more pronounced power changes in 560 the former. Starting from about 400ms after stimulus onset, alpha/beta-band power is 561 negatively correlated with SU. High levels of surprisal indicate change-points which render 562 the current prior irrelevant. Thus, with large SU levels alpha/beta range power decreases in 563 order to facilitate processing of the upcoming stimulus. In line with this interpretation, two 564 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint clusters in the AV condition’s alpha/beta range were predictive of the subsequent behavioral 565 estimation error and prior bias, respectively. 566 Several other clusters associated with surprisal were also predictive of behavioral outcomes. 567 Interestingly, activity in an early beta-band cluster in the AV condition scaled positively with 568 SU and subsequent localization accuracy (i.e. negatively with estimation error). The fact that 569 stronger neural correlates of SU would be associated with better performance is suggestive of 570 an attention effect, in that the appearance of a salient change-point leads to surprisal, but 571 concurrently boosts attention and improves task performance. 572 The fact that we did not find similar behaviorally relevant clusters in the A condition might 573 be due to the lower signal-to-noise ratio as well as the lower stimulus intensity following an 574 A-only compared to a combined auditory and visual stimulus44. 575 576 Behavioral and neural tokens of Bayesian inference are more pronounced following AV 577 compared to A stimulation 578 Overall, the location estimation performance was better for the AV compared to the A 579 condition, despite the identical probe sounds (both audio-only), in line with previous 580 studies22,23. In part, this result likely reflects differences in the intrinsic sensory reliability of 581 visual and auditory spatial information28,29. Additionally, A condition was particularly 582 challenging due to the auditory-to-visual response mapping. Despite this difference, both 583 conditions showed response bias towards the prior stimulus locations, indicating participants 584 indeed kept track of the previous locations. 585 However, the higher sensory noise in the A-only condition led to larger PU and therefore less 586 prior bias during sound localization. In the AV condition, formation of the prior information 587 relies on both senses and as a result, participants relied on their audio-visual prior more than 588 the noisy audio-only sensory evidence provided by the probe sound. Similarly, a more precise 589 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint prior in the AV condition potentially led to larger SU values for the AV compared to the A 590 condition. 591 Overall, our behavioral results indicate similar mechanism for integration of prior and 592 sensory likelihood following unimodal A and bimodal AV stimulation, that complies with 593 Bayesian inference in a modality and task independent manner. 594 Likewise, the comparison of the neural activity associated with PU and SU between the 595 conditions revealed largely similar patterns. In both time- and time-frequency domain, the 596 observed differences were most likely due to the larger and more extensive regression 597 coefficient patterns for the AV compared to the A condition, due to stronger sensory 598 activations and consequently a higher signal-to-noise ratio in the former. 599 For PU, the comparison of the two conditions in the time domain revealed clusters in the pre-600 stimulus time period due to a more pronounced PU representation in the AV compared to the 601 A condition. In the time-frequency domain, the two conditions have spatially more distinct 602 PU patterns in theta range, reflected by a significant occipital cluster in comparison analysis, 603 that likely stems from the additional visual prior representation in the AV condition. 604 Comparison analysis revealed similar results for SU, mainly reflecting differences in strength 605 of the correlations between the two conditions. Additionally, these differences might partly 606 also be driven by SU itself, which showed larger variation in the AV compared to the A 607 condition. In the time domain, the differences are in the time range of ~200-300 ms due to 608 more pronounced regression patterns in the AV compared to the A condition. Similarly, in 609 lower frequency range, the differences between the two conditions are mainly in the theta 610 range and limited to occipital electrodes, possibly due to sensory specific processing of the 611 visual stimulus in the AV condition. Finally, the difference in the gamma range clusters fall 612 into the period of potential microsaccadic activity, and thus are likely driven by larger 613 artifacts in the AV condition due to the occurrence of an additional visual stimulus. 614 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint Taken together, these results suggest that auditory spatial localization in both AV and A 615 conditions is based on highly similar Bayesian inference mechanisms, which in the former 616 are additionally informed by the visual stimulus. Importantly, our data thus provide novel 617 evidence for auditory spatial localization according to Bayesian inference, while suggesting 618 that the results following audio-visual priors previously reported by Krishnamurthy et al.21 619 are similarly applicable to true auditory-only settings. 620 621

622 Perception commonly relies on both sensory input and prior information. In the present study, 623 we provide novel evidence that behavioral and neural responses during unimodal auditory 624 localization indeed conform with Bayesian inference principles. We demonstrate the impact 625 of dynamic changes in the environment on the weighting of prior knowledge and current 626 sensory evidence, and show that the resulting behavioral performance, model metrics and 627 neural patterns associated with PU and SU are in line with findings from other domains. 628 Moreover, these patterns are intensified yet structurally similar following additional visual 629 priors. 630 Taken together, despite the auditory system’s inferiority regarding spatial localization, our 631 data suggest that it employs similar mechanisms as previously observed in visual processing 632 or more domain appropriate-tasks such as auditory pitch and temporal discrimination, 633 supporting Bayesian inference as a general principle in human perceptual decision making. 634 635 Acknowledgments 636 This research was supported by an Austrian Science Fund (FWF) Young Independent 637 Researchers Group (Grant-DOI: 10.55776/ZK66) to Michelle Spierings, Ulrich Pomper, and 638 Robert Baumgartner. 639 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint 640 Author Contributions 641 Burcu Bayram Data curation; formal analysis; visualization; writing-original draft 642 David Meijer Data curation; formal analysis; writing-original draft 643 Roberto Barumerli Formal analysis; writing- review and editing 644 Michelle Spierings Conceptualization; funding acquisition; project administration; 645 resources; writing- review and editing 646 Robert Baumgartner Conceptualization; funding acquisition; project administration; 647 resources; writing- review and editing 648 Ulrich Pomper Conceptualization; funding acquisition; project administration; resources; 649 supervision; writing-original draft 650 651 Conflict of Interest 652 The authors declare no competing financial or non-financial interests. 653 654 Data Availability Statement 655 Data are available upon request. 656 657

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Neuroimage, 62–788 248(2), 1230–1233. https://doi.org/10.1016/j.neuroimage.2011.10.004 789 [44] Busch, N. A., Debener, S., Kranczioch, C., Engel, A. K., & Herrmann, C. S. (2004). Size 790 matters: Effects of stimulus size, duration and eccentricity on the visual gamma-band 791 response. Clinical Neurophysiology: Official Journal of the International Federation of 792 Clinical Neurophysiology, 115(8), 1810–1820. https://doi.org/10.1016/j.clinph.2004.03.015 793 794 Figure legends 795 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint 796 797 Figure 1. Experimental design. Left part: An exemplary trial depicted for both audio-visual 798 (AV) and audio-only (A) conditions. Each trial starts with a fixation period followed by a 799 sequence of sounds. In the A condition, only auditory stimuli are presented. In the AV 800 condition, the respective sound location is simultaneously shown via a line on the semi-arc 801 (for all sounds except for the final probe sound). At the end of the sequence, participants 802 indicate the location of the probe sound by rotating the response line on the semi-arc. 803 Subsequently, they mark an 80% confidence interval around the response line. Right part: 804 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint Depiction of the sampling of sound locations for an exemplary trial. Sound locations are 805 sampled from a Gaussian distribution with standard deviation of 10° (i.e. experimental noise). 806 Along with each change-point sound (turquoise circle), a new mean sound location is 807 sampled. Four sounds are presented following the last change-point in the sequence and 808 therefore, the trial has a stimulus-after-change-point (SAC) level of 4. 809 810 811 Figure 2. Behavioral and modeling results. A) Mean of the behavioral outcomes estimation 812 error, prior bias, and response uncertainty, per sound-after-changepoint (SAC) level, for both 813 audio-visual and auditory conditions. Error bars indicate the standard error of the mean. B) 814 Median of the Prior Uncertainty1 (PU) and Surprisal (SU) values. Single subjects’ PU and SU 815 values are z-scored. Note, that the SEM is particularly small (mean = .59) for PU in the AV 816 condition. This is due to the fact, that while we fitted the sensory noise individually for each 817 participant for the A condition, we fixed the sensory noise at one degree for the AV 818 condition. Furthermore, we used the same set of trials for all participants, resulting in no 819 variation across the trial sets. Hence, for a particular stimulus, our model predicts the same 820 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint PU for every participant. The only remaining variation stems from the random sensory noise 821 of the AV stimuli. 822 823 824 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint 825 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint Figure 3. Event-related responses associated with Prior Uncertainty (PU) and Surprisal (SU). 826 Left column: Time-domain representations of clusters (numbered) of regression coefficients 827 between EEG amplitudes and model latent variables, significant at the group-level. Data are 828 shown separately for the audio-visual (AV) and auditory (A) conditions, as well as for PU 829 and SU variables. Each line shows beta coefficients averaged over channels and time points 830 of each significant cluster, obtained via permutation testing. Significant time points are 831 marked in bold colors. Right column: Topographical plots of each significant cluster, as 832 numbered on the left side as. Significant channels are marked with asterisks. Behaviorally 833 relevant clusters (see Figure 5A) are highlighted via a purple square in the background. Small 834 clusters (< 2 datapoints) are not shown, unless they are behaviorally relevant. 835 836 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint 837 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint 838 Figure 4. A) Time-frequency responses (lower frequency range, 4-30 Hz) associated with 839 Prior Uncertainty (PU) and Surprisal (SU). Left column: Time-frequency representations of 840 regression coefficients between EEG amplitudes and model latent variables, averaged over all 841 significant channels obtained via permutation testing. Significant clusters at the group-level 842 are highlighted and numbered. Data are shown separately for the audio-visual (AV) and 843 auditory (A) conditions, as well as for PU and SU variables. Right column: Topography plots 844 of each significant cluster, as numbered on the left side as. Significant channels of the 845 clusters are marked with asterisks. Behaviorally relevant clusters (see Figure 6B) are 846 highlighted via a purple square in the background. B) Same as A, for higher frequency range 847 (i.e. 40-100 Hz). Small clusters (< 2 datapoints) are not shown, unless they are behaviorally 848 relevant. 849 850 851 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint 852 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint Figure 5. Differences in Prior Uncertainty (PU) and Surprisal (SU) related activity between 853 the audio-visual (AV) and auditory (A) conditions. All data represent the difference of 854 regression coefficients (between the EEG data and the PU and SU latent variables, see 855 Figures 4 and 5) between the AV and A conditions. A) Left column: Time-domain 856 representations of regression coefficient differences. Data are shown separately for the PU 857 and SU variables. Each line shows beta coefficient differences averaged over channels and 858 time points of each significant cluster, obtained via permutation testing. Significant time 859 points are marked in bold colors. Right column: Topographical plots of each significant 860 cluster, as numbered on the left side as. Significant channels are marked with asterisks. 861 B) Left column: Time-frequency (4 – 30 Hz) domain representations of regression coefficient 862 differences. Data are shown separately for the PU and SU variables. Significant clusters at the 863 group-level are highlighted and numbered. Data are shown separately for the PU and S 864 variables. Right column: Topography plots of each significant cluster, as numbered on the 865 left side as. Significant channels of the clusters are marked with asterisks. C) Same as B, for 866 the 40-100 Hz time-frequency domain. Small clusters (< 2 datapoints) are not shown. 867 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint 868 869 Figure 6. Model latent variable components predict behavior. A) Results of the regression 870 analysis between time-domain EEG data averaged over the dimensions of significant 871 regression clusters (see Figure 4) and the behavioral estimation error (EE), response 872 uncertainty (RU), and prior bias (PB) variables. Each circle in the violin plots represents 873 single subject beta coefficients. Grey bars represent the median, interquartile range and 1.5 874 times the interquartile range. Respective topoplots of the significant clusters are shown on top 875 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint of the violin plots (same as the highlighted clusters in Figures 4). B) Same as A), for the 4-30 876 Hz time-frequency domain clusters (see Figure 5). C) Same as B), for the 40-100 Hz time-877 frequency domain clusters (see Figure 6). 878 879 TABLES 880 881 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint Table 1. Behavioral results Statistical results obtained using linear mixed-effect modeling. A. Estimation error Formula: Error ~ 1 + SAC * Modality * +(1 | Subjects) Fixed effects coefficients Estimate SE z Pr(>|z|) (Intercept) -1.37 0.82 -1.69 0.09 . SAC 0.2 0.17 1.17 0.24 Modality=AV 2.56 0.89 2.88 |z|) (Intercept) 49.52 2.44 20.29 <2e-16 *** SAC -0.09 0.14 -0.63 0.53 Modality=AV -1.06 0.76 -1.4 0.16 SAC:Modality=AV -0.35 0.2 -1.71 0.09 C. Prior bias Formula: Bias ~ 1 + SAC * Modality * +(1 | Subjects) Fixed effects coefficients Estimate SE z Pr(>|z|) (Intercept) 0.12 0.05 2.64 8.22e-3 ** SAC 0.02 0.01 3.38 7.2e-4 *** Modality=AV 0.2 0.04 5.23 1.65e-07 *** SAC:Modality=AV |z|) (Intercept) 16.57 0.3 54.37 <2e-16 *** SAC -0.37 0.02 -15.21 <2e-16 *** Modality=AV -7.64 0.13 -59.52 |z|) (Intercept) 5.83 0.1 57.74 <2e-16 *** SAC -0.17 0.01 -13.86 <2e-16 *** Modality=AV 0.3 0.07 4.49 7.02e-06 *** SAC:Modality=AV -0.01 0.08 -0.5 0.62 882 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint 883 Table 2. Cluster p-values obtained from regression analysis A. Time domain regression clusters C1 C2 C3 C4 C5 C6 C7 AV PU 0.001 0.001 0.001 0.001 A PU 0.001 0.001 0.001 0.001 0.017 0.006 AV SU 0.012 0.005 0.001 0.001 0.007 0.013 0.011 A SU 0.004 0.002 0.001 0.002 0.002 0.017 0.004 B. Time-frequency domain lower frequency range (4-30 Hz) regression clusters C1 C2 C3 C4 C5 C6 C7 AV PU 0.001 0.001 0.001 0.002 A PU 0.001 0.023 0.024 AV SU 0.014 0.018 0.001 0.001 0.001 0.001 0.006 A SU 0.001 0.001 0.001 0.001 0.013 C. Time-frequency domain higher frequency range (40-100 Hz) regression clusters C1 C2 C3 C4 C5 C6 C7 AV PU 0.001 AV SU 0.001 0.002 0.001 0.003 0.023 0.001 0.005 884 Table 3. Cluster p-values obtained from condition comparison analysis A. Time domain regression clusters C1 C2 C3 C4 C5 C6 C7 AV-A PU 0.004 0.001 0.001 0.001 0.005 0.022 AV-A SU 0.007 0.002 0.006 0.002 0.001 0.014 B. Time-frequency domain lower frequency range (4-30 Hz) regression clusters C1 C2 C3 C4 C5 C6 C7 AV-A PU 0.002 0.013 AV-A SU 0.001 0.004 0.001 0.015 C. Time-frequency domain higher frequency range (40-100 Hz) regression clusters C1 C2 C3 C4 C5 C6 C7 AV-A SU 0.002 0.001 0.004 885 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted July 23, 2024. ; https://doi.org/10.1101/2024.07.22.604566doi: bioRxiv preprint