Fast Bayesian Inference of Copy Number Variants using Hidden Markov Models with Wavelet Compression

By combining Haar wavelets with Bayesian Hidden Markov Models, we improve detection of genomic copy number variants (CNV) in array CGH experiments compared to the state-of-the-art, including standard Gibbs sampling. At the same time, we achieve drastically reduced running times, as the method concentrates computational effort on chromosomal segments which are difficult to call, by dynamically and adaptively recomputing consecutive blocks of observations likely to share a copy number. This makes routine diagnostic use and re-analysis of legacy data collections feasible; to this end, we also propose an effective automatic prior. An open source software implementation of our method is available at http://bioinformatics.rutgers.edu/Software/HaMMLET/ . The web supplement is at http://bioinformatics.rutgers.edu/Supplements/HaMMLET/ . Author Summary Identifying large-scale genome deletions and duplications, or copy number variants (CNV), accurately in populations or individual patients is a crucial step in indicating disease factors or diagnosing an individual patient's disease type. Hidden Markov Models (HMM) are a type of statistical model widely used for CNV detection, as well as other biological applications such as the analysis of gene expression time course data or the analysis of discrete-valued DNA and protein sequences. As with many statistical models, there are two fundamentally different inference approaches. In the frequentist framework, a single estimate of the model parameters would be used as a basis for subsequent inference, making the identification of CNV dependent on the quality of that estimate. This is an acute problem for HMM as methods for finding globally optimal parameters are not known. Alternatively, one can use a Bayesian approach and integrate over all possible parameter choices. While the latter is known to lead to significantly better results, the much—up to hundreds of times—larger computational effort prevents wide adaptation so far. Our proposed method addresses this by combining Haar wavelets and HMM. We greatly accelerate fully Bayesian HMMs, while simultaneously increasing convergence and thus the accuracy of the Gibbs sampler used for Bayesian computations, leading to substantial improvements over the state-of-the-art.