مدل مخفی مارکوف بیزی برای تقسیم بندی توالی DNA: تجزیه و تحلیل حساسیت قبل

The sensitivity to the specification of the prior in a hidden Markov model describing homogeneous segments of DNA sequences is considered. An intron from the chimpanzee αα-fetoprotein gene, which plays an important role in embryonic development in mammals, is analysed. Three main aims are considered: (i) to assess the sensitivity to prior specification in Bayesian hidden Markov models for DNA sequence segmentation; (ii) to examine the impact of replacing the standard Dirichlet prior with a mixture Dirichlet prior; and (iii) to propose and illustrate a more comprehensive approach to sensitivity analysis, using importance sampling. It is obtained that (i) the posterior estimates obtained under a Bayesian hidden Markov model are indeed sensitive to the specification of the prior distributions; (ii) compared with the standard Dirichlet prior, the mixture Dirichlet prior is more flexible, less sensitive to the choice of hyperparameters and less constraining in the analysis, thus improving posterior estimates; and (iii) importance sampling was computationally feasible, fast and effective in allowing a richer sensitivity analysis.

Many genome sequences display heterogeneity in base composition in the form of segments of similar structure. A number of statistical techniques have been developed to identify these homogeneous DNA segments, as reviewed in Braun and Müller (1998). One technique, proposed in Churchill (1989), describes DNA sequence structure using a hidden Markov model (HMM) which is, in essence, a mixture model with Markov-dependent component indicators (MacDonald and Zucchini, 1997). Sequence analysis using HMMs is now a standard approach (Durbin et al., 1998) in the comparatively young science of bioinformatics and is a fundamental component of many gene-finding algorithms which identify and delineate genes in the human and other genomes (De Fonzo et al., 2007). Bayesian inference procedures and algorithms have revolutionized the field of computational biology (Liu and Logvinenko, 2003) due to the development of computationally-intensive simulation-based methods such as Markov chain Monte Carlo (MCMC), which are available in software such as WinBUGS (Lunn et al., 2000), and has led to the adoption of increasingly complex models in many situations. A sometimes controversial aspect of the Bayesian approach is the need to specify prior distributions for the unknown parameters. In certain situations these priors may be very well defined. However, for complex models with many parameters, the choice of priors and conclusions of the subsequent Bayesian analysis are usually validated through a prior sensitivity analysis, as presented here. For DNA sequence segmentation, a DNA sequence can be thought of as the observed process which evolves independently or dependently given an unobserved Markov chain which locates the position of the segment types. The parameters in this model are the base (nucleotide) transition probabilities for the segment types and the transition matrix of segment types. Boys et al. (2000) presented a Bayesian solution to the segmentation problem using HMMs when the number of segments is known. These results were generalised in Boys and Henderson (2004) to the case in which the number of segments is unknown. In Boys et al. (2000) and Boys and Henderson (2004), the prior knowledge for base transition probabilities in each segment was weak but the prior beliefs about the transition matrix for the segment types were strong. The authors discussed briefly the sensitivity of their conclusion to the choice of prior, especially for the transition matrix for the segment types, but no details were given. Their articles raise fundamental questions about limitations in model specification and bring to the forefront the issue of how far one can refrain from making prior assumptions about a model while keeping it feasible in practice. This prompts the important question of the impact of these priors on resultant inferences. This paper has three main aims. The primary aim is to undertake a sensitivity analysis of the priors of a Bayesian hidden Markov model for DNA sequence segmentation. We employ Markov chain Monte Carlo via a short and easy-to-use program in BRuGS (“Bayesian analysis using Gibbs Sampler in R”). The sensitivity analysis includes a traditional approach, varying the prior distributions for base transition probabilities for each segment type and for the transition matrix of segment types. A sequence of Dirichlet priors is considered for the former and Dirichlet and mixture Dirichlet priors for the latter. The second aim of this paper is to introduce an alternative approach to sensitivity analysis that employs importance sampling of an MCMC chain obtained from the traditional approach. Our focus is on the feasibility and computational efficiency of this approach for comparing a large number of priors simultaneously in a more comprehensive sensitivity analysis. The results are applied to the segmentation of a benchmarking DNA sequence, intron 7 of the chimpanzee αα-fetoprotein gene.