Abstract
Chromatin Immunoprecipitation followed by sequencing (ChIP-seq) is a valuable tool for epigenetic studies. Analysis of the data arising from ChIP-seq experiments often requires implicit or explicit statistical modeling of the read counts. The simple Poisson model is attractive, but does not provide a good fit to observed ChIP-seq data. Researchers therefore often either extend to a more general model (e.g., the Negative Binomial), and/or exclude regions of the genome that do not conform to the model. Since many modeling strategies employed for ChIP-seq data reduce to fitting a mixture of Poisson distributions, we explore the problem of inferring the optimal mixing distribution. We apply the Constrained Newton Method (CNM), which suggests the Negative Binomial - Negative Binomial (NB-NB) mixture model as a candidate for modeling ChIP-seq data. We illustrate fitting the NB-NB model with an accelerated EM algorithm on four data sets from three species. Zero-inflated models have been suggested as an approach to improve model fit for ChIP-seq data. We show that the NB-NB mixture model requires no zero-inflation and suggest that in some cases the need for zero inflation is driven by the model's inability to cope with both artifactual large read counts and the frequently observed very low read counts. We see that the CNM-based approach is a useful diagnostic for the assessment of model fit and inference in ChIP-seq data and beyond. Use of the suggested NB-NB mixture model will be of value not only when calling peaks or otherwise modeling ChIP-seq data, but also when simulating data or constructing blacklists de novo.
Highlights
Chromatin Immunoprecipitation followed by sequencing (ChIPseq) is an experiment for the genome-wide location of events such as transcription factor binding sites and histone modifications (Park, 2009; Cairns et al, 2013)
DISTRIBUTION RECOVERY First, we show that the Constrained Newton Method (CNM) estimate f(λ) is appropriate for our data, by demonstrating that the empirical distribution of X can be recovered from the CNM estimate according to the following procedure: 1. Calculate the empirical probability density f(x) directly, from the data
The Negative Binomial - Negative Binomial (NB-Negative Binomial (NB)) mixture is the only choice of distribution that can consistently model the higher counts
Summary
Chromatin Immunoprecipitation followed by sequencing (ChIPseq) is an experiment for the genome-wide location of events such as transcription factor binding sites and histone modifications (Park, 2009; Cairns et al, 2013). These events provide information on chromatin status, a topic of great interest in epigenetics. Consider read counts xi, where i indexes over genomic bins, for a single ChIP-seq sample When modeling these counts as independent samples from some Poisson random variable X, a common problem is overdispersion—that is, the property that the observations have greater variance than allowed for by the model. The Poisson distribution requires that mean and variance are equal, an assumption that (even when ignoring between-sample variability) is violated by ChIP-seq data, impairing model fit (Spyrou et al, 2009)
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