Bayesian inference for stochastic kinetic models using a diffusion approximation

This article is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a diffusion approximation (or stochastic differential equation approach) where a white noise term models stochastic behavior and the model is identified using equispaced time course data. The estimation framework involves the introduction of m- 1 latent data points between every pair of observations. MCMC methods are then used to sample the posterior distribution of the latent process and the model parameters. The methodology is applied to the estimation of parameters in a prokaryotic autoregulatory gene network.     

bgc: Software for Bayesian estimation of genomic clines

Introgression in admixed populations can be used to identify candidate loci that might underlie adaptation or reproductive isolation. The Bayesian genomic cline model provides a framework for quantifying variable introgression in admixed populations and identifying regions of the genome with extreme introgression that are potentially associated with variation in fitness. Here we describe the bgc software, which uses Markov chain Monte Carlo to estimate the joint posterior probability distribution of the parameters in the Bayesian genomic cline model and designate outlier loci. This software can be used with next‐generation sequence data, accounts for uncertainty in genotypic state, and can incorporate information from linked loci on a genetic map. Output from the analysis is written to an HDF5 file for efficient storage and manipulation. This software is written in C++ . The source code, software manual, compilation instructions and example data sets are available under the GNU Public License at http://sites.google.com/site/bgcsoftware/ .     

Bayesian phylogenetic model selection using reversible jump Markov chain Monte Carlo

A common problem in molecular phylogenetics is choosing a model of DNA substitution that does a good job of explaining the DNA sequence alignment without introducing superfluous parameters. A number of methods have been used to choose among a small set of candidate substitution models, such as the likelihood ratio test, the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and Bayes factors. Current implementations of any of these criteria suffer from the limitation that only a small set of models are examined, or that the test does not allow easy comparison of non-nested models. In this article, we expand the pool of candidate substitution models to include all possible time-reversible models. This set includes seven models that have already been described. We show how Bayes factors can be calculated for these models using reversible jump Markov chain Monte Carlo, and apply the method to 16 DNA sequence alignments. For each data set, we compare the model with the best Bayes factor to the best models chosen using AIC and BIC. We find that the best model under any of these criteria is not necessarily the most complicated one; models with an intermediate number of substitution types typically do best. Moreover, almost all of the models that are chosen as best do not constrain a transition rate to be the same as a transversion rate, suggesting that it is the transition/transversion rate bias that plays the largest role in determining which models are selected. Importantly, the reversible jump Markov chain Monte Carlo algorithm described here allows estimation of phylogeny (and other phylogenetic model parameters) to be performed while accounting for uncertainty in the model of DNA substitution.     

Bayesian coalescent inference of past population dynamics from molecular sequences

We introduce the Bayesian skyline plot, a new method for estimating past population dynamics through time from a sample of molecular sequences without dependence on a prespecified parametric model of demographic history. We describe a Markov chain Monte Carlo sampling procedure that efficiently samples a variant of the generalized skyline plot, given sequence data, and combines these plots to generate a posterior distribution of effective population size through time. We apply the Bayesian skyline plot to simulated data sets and show that it correctly reconstructs demographic history under canonical scenarios. Finally, we compare the Bayesian skyline plot model to previous coalescent approaches by analyzing two real data sets (hepatitis C virus in Egypt and mitochondrial DNA of Beringian bison) that have been previously investigated using alternative coalescent methods. In the bison analysis, we detect a severe but previously unrecognized bottleneck, estimated to have occurred 10,000 radiocarbon years ago, which coincides with both the earliest undisputed record of large numbers of humans in Alaska and the megafaunal extinctions in North America at the beginning of the Holocene.     

A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov chain Monte Carlo methods

Recent Bayesian methods for the analysis of infectious disease outbreak data using stochastic epidemic models are reviewed. These methods rely on Markov chain Monte Carlo methods. Both temporal and non-temporal data are considered. The methods are illustrated with a number of examples featuring different models and datasets.     

Bayesian Inference for the Spatio-Temporal Invasion of Alien Species

In this paper we develop a Bayesian approach to parameter estimation in a stochastic spatio-temporal model of the spread of invasive species across a landscape. To date, statistical techniques, such as logistic and autologistic regression, have outstripped stochastic spatio-temporal models in their ability to handle large numbers of covariates. Here we seek to address this problem by making use of a range of covariates describing the bio-geographical features of the landscape. Relative to regression techniques, stochastic spatio-temporal models are more transparent in their representation of biological processes. They also explicitly model temporal change, and therefore do not require the assumption that the species' distribution (or other spatial pattern) has already reached equilibrium as is often the case with standard statistical approaches. In order to illustrate the use of such techniques we apply them to the analysis of data detailing the spread of an invasive plant, Heracleum mantegazzianum, across Britain in the 20th Century using geo-referenced covariate information describing local temperature, elevation and habitat type. The use of Markov chain Monte Carlo sampling within a Bayesian framework facilitates statistical assessments of differences in the suitability of different habitat classes for H. mantegazzianum, and enables predictions of future spread to account for parametric uncertainty and system variability. Our results show that ignoring such covariate information may lead to biased estimates of key processes and implausible predictions of future distributions.     

A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci. I. Methodology

A Bayesian approach to the statistical mapping of Quantitative Trait Loci (QTLs) using single markers was implemented via Markov Chain Monte Carlo (MCMC) algorithms for parameter estimation and hypothesis testing. Parameter estimators were marginal posterior means computed using a Gibbs sampler with data augmentation. Variables sampled included the augmented data (marker-QTL genotypes, polygenic effects), an indicator variable for linkage, and the parameters (allele frequency, QTL substitution effect, recombination rate, polygenic and residual variances). Several MCMC algorithms were derived for computing Bayesian tests of linkage, which consisted of the marginal posterior probability of linkage and the marginal likelihood of the QTL variance associated with the marker.     

In silico model‐based inference: A contemporary approach for hypothesis testing in network biology

Inductive inference plays a central role in the study of biological systems where one aims to increase their understanding of the system by reasoning backwards from uncertain observations to identify causal relationships among components of the system. These causal relationships are postulated from prior knowledge as a hypothesis or simply a model. Experiments are designed to test the model. Inferential statistics are used to establish a level of confidence in how well our postulated model explains the acquired data. This iterative process, commonly referred to as the scientific method, either improves our confidence in a model or suggests that we revisit our prior knowledge to develop a new model. Advances in technology impact how we use prior knowledge and data to formulate models of biological networks and how we observe cellular behavior. However, the approach for model‐based inference has remained largely unchanged since Fisher, Neyman and Pearson developed the ideas in the early 1900s that gave rise to what is now known as classical statistical hypothesis (model) testing. Here, I will summarize conventional methods for model‐based inference and suggest a contemporary approach to aid in our quest to discover how cells dynamically interpret and transmit information for therapeutic aims that integrates ideas drawn from high performance computing, Bayesian statistics, and chemical kinetics. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 30:1247–1261, 2014     

A Bayesian joint model of recurrent events and a terminal event

Recurrent events could be stopped by a terminal event, which commonly occurs in biomedical and clinical studies. In this situation, dependent censoring is encountered because of potential dependence between these two event processes, leading to invalid inference if analyzing recurrent events alone. The joint frailty model is one of the widely used approaches to jointly model these two processes by sharing the same frailty term. One important assumption is that recurrent and terminal event processes are conditionally independent given the subject‐level frailty; however, this could be violated when the dependency may also depend on time‐varying covariates across recurrences. Furthermore, marginal correlation between two event processes based on traditional frailty modeling has no closed form solution for estimation with vague interpretation. In order to fill these gaps, we propose a novel joint frailty‐copula approach to model recurrent events and a terminal event with relaxed assumptions. Metropolis–Hastings within the Gibbs Sampler algorithm is used for parameter estimation. Extensive simulation studies are conducted to evaluate the efficiency, robustness, and predictive performance of our proposal. The simulation results show that compared with the joint frailty model, the bias and mean squared error of the proposal is smaller when the conditional independence assumption is violated. Finally, we apply our method into a real example extracted from the MarketScan database to study the association between recurrent strokes and mortality.     

基于贝叶斯统计的遗传连锁分析方法

贝叶斯学派是不同于经典数理统计的一个重要学派, 其发展的贝叶斯统计方法在现代科学的许多领域已有着广泛的应用。探讨了贝叶斯统计在遗传连锁分析中的应用, 包括遗传重组率的贝叶斯估计、遗传连锁的贝叶斯因子检验和基于马尔可夫链蒙特卡罗理论的遗传连锁图谱构建。用编制的SAS/IML程序进行了模拟研究和实例分析, 验证了贝叶斯方法在遗传连锁分析中的有效性和实用性。     

Understanding mammalian evolution using Bayesian phylogenetic inference

1. Phylogenetic trees are critical in addressing evolutionary hypotheses; however, the reconstruction of a phylogeny is no easy task. This process has recently been made less arduous by using a Bayesian statistical approach. This method offers the advantage that one can determine the probability of some hypothesis (i.e. a phylogeny), conditional on the observed data (i.e. nucleotide sequences). 2. By reconstructing phylogenies using Bayes’ theorem in combination with Markov chain Monte Carlo, phylogeneticists are able to test hypotheses more quickly compared with using standard methods such as neighbour-joining, maximum likelihood or parsimony. Critics of the Bayesian approach suggest that it is not a panacea, and argue that the prior probability is too subjective and the resulting posterior probability is too liberal compared with maximum likelihood. 3. These issues are currently debated in the arena of mammalian evolution. Recently, proponents and opponents of the Bayesian approach have constructed the mammalian phylogeny using different methods under different conditions and with a variety of parameters. These analyses showed the robustness (or lack of) of the Bayesian approach. In the end, consensus suggests that Bayesian methods are robust and give essentially the same answer as maximum likelihood methods but in less time. 4. Approaches based on fossils and molecules typically agree on ordinal-level relationships among mammals but not on higher-level relationships, as Bayesian analyses recognize the African radiation, Afrotheria, and the two Laurasian radiations, Laurasiatheria and Euarchontoglires, whereas fossils did not predict Afrotheria.     

Lysogens and free viruses in fresh, brackish, and marine waters: a Bayesian analysis

A yearlong study was conducted to determine factors that affect the abundance and distribution of lysogens and free viruses at fresh-, brackish-, and saltwater stations in Newport Bay, CA. The viral and bacterial abundance were highest in the freshwater (average 1.1 × 10⁸ and 1.1 × 10⁷ mL⁻¹, respectively) and lowest in the marine water (average 0.4 × 10⁸ and 0.5 × 10⁷ mL⁻¹, respectively). Bacterial and viral counts were also several times higher during the summer than in winter. Approximately, 35% of the 141 samples were inducible in the presence of mitomycin C. The highest percentage of inducible lysogens was observed in marine waters (42%), while the lowest percentage was observed in the warmer freshwater (23%). A statistical model for the joint occurrence of lysogens and free viruses was formulated and estimated using Bayesian techniques to understand the key environmental determinants of viruses and lysogens. Our results support the existence of significant heterogeneity between the saltwater and freshwater sites. A parsimonious model that combines the two saltwater sites performs best among the specifications that were considered. Bacteria and water temperature were significant determinants of virus counts, whereas lysogen relationships are unclear. Importantly, conditional on the covariates, viruses and lysogen fractions exhibit robust negative correlation.     

Bayesian phylogeny analysis via stochastic approximation Monte Carlo

Monte Carlo methods have received much attention in the recent literature of phylogeny analysis. However, the conventional Markov chain Monte Carlo algorithms, such as the Metropolis–Hastings algorithm, tend to get trapped in a local mode in simulating from the posterior distribution of phylogenetic trees, rendering the inference ineffective. In this paper, we apply an advanced Monte Carlo algorithm, the stochastic approximation Monte Carlo algorithm, to Bayesian phylogeny analysis. Our method is compared with two popular Bayesian phylogeny software, BAMBE and MrBayes, on simulated and real datasets. The numerical results indicate that our method outperforms BAMBE and MrBayes. Among the three methods, SAMC produces the consensus trees which have the highest similarity to the true trees, and the model parameter estimates which have the smallest mean square errors, but costs the least CPU time.     

Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models

The problem of evaluating the goodness of the predictive distributionsof hierarchical Bayesian and empirical Bayes models is investigated.A Bayesian predictive information criterion is proposed as anestimator of the posterior mean of the expected loglikelihoodof the predictive distribution when the specified family ofprobability distributions does not contain the true distribution.The proposed criterion is developed by correcting the asymptoticbias of the posterior mean of the loglikelihood as an estimatorof its expected loglikelihood. In the evaluation of hierarchicalBayesian models with random effects, regardless of our parametricfocus, the proposed criterion considers the bias correctionof the posterior mean of the marginal loglikelihood becauseit requires a consistent parameter estimator. The use of thebootstrap in model evaluation is also discussed.