Bayesian natural selection and the evolution of perceptual systems

In recent years, there has been much interest in characterizing statistical properties of natural stimuli in order to better understand the design of perceptual systems. A fruitful approach has been to compare the processing of natural stimuli in real perceptual systems with that of ideal observers derived within the framework of Bayesian statistical decision theory. While this form of optimization theory has provided a deeper understanding of the information contained in natural stimuli as well as of the computational principles employed in perceptual systems, it does not directly consider the process of natural selection, which is ultimately responsible for design. Here we propose a formal framework for analysing how the statistics of natural stimuli and the process of natural selection interact to determine the design of perceptual systems. The framework consists of two complementary components. The first is a maximum fitness ideal observer, a standard Bayesian ideal observer with a utility function appropriate for natural selection. The second component is a formal version of natural selection based upon Bayesian statistical decision theory. Maximum fitness ideal observers and Bayesian natural selection are demonstrated in several examples. We suggest that the Bayesian approach is appropriate not only for the study of perceptual systems but also for the study of many other systems in biology.     

Parental and sib likelihoods in genealogy reconstruction

Estimation of genealogical relationships from genetic data provides an approach to answering many questions of population biology. In this estimation problem, previous work has shown that bilateral relatives such as full sibs may be more likely parents than the true parent individuals. This paper investigates the source of this paradox, and the circumstances under which it may arise. Alternative approaches to inferring parentage are proposed; these involve analysis of the distributions of log-likelihood statistics and of the bivariate distribution of sib and parent log-likelihoods. A Bayesian approach may also be superposed on the likelihood analysis, enabling any prior knowledge of the population to be incorporated.     

贝叶斯统计在QTL作图中的应用研究进展

在许多复杂情况下, 贝叶斯统计方法比经典数理统计方法能更直接解决问题, 且可有效整合部分先验信息, 但其需要高强度计算的特性曾限制了其广泛应用。近几十年来, 随着高速计算机的发展以及MCMC算法的不断提出, 贝叶斯方法已被用于群体遗传学、分子进化、连锁作图和数量遗传学等研究领域, 文章综述了数量遗传学中QTL作图的贝叶斯方法从简单到复杂的发展历程。     

Bayesian restoration of ion channel records using hidden Markov models

Hidden Markov models have been used to restore recorded signals of single ion channels buried in background noise. Parameter estimation and signal restoration are usually carried out through likelihood maximization by using variants of the Baum-Welch forward-backward procedures. This paper presents an alternative approach for dealing with this inferential task. The inferences are made by using a combination of the framework provided by Bayesian statistics and numerical methods based on Markov chain Monte Carlo stochastic simulation. The reliability of this approach is tested by using synthetic signals of known characteristics. The expectations of the model parameters estimated here are close to those calculated using the Baum-Welch algorithm, but the present methods also yield estimates of their errors. Comparisons of the results of the Bayesian Markov Chain Monte Carlo approach with those obtained by filtering and thresholding demonstrate clearly the superiority of the new methods.     

Modeling Inhibitory Interneurons in Efficient Sensory Coding Models

There is still much unknown regarding the computational role of inhibitory cells in the sensory cortex. While modeling studies could potentially shed light on the critical role played by inhibition in cortical computation, there is a gap between the simplicity of many models of sensory coding and the biological complexity of the inhibitory subpopulation. In particular, many models do not respect that inhibition must be implemented in a separate subpopulation, with those inhibitory interneurons having a diversity of tuning properties and characteristic E/I cell ratios. In this study we demonstrate a computational framework for implementing inhibition in dynamical systems models that better respects these biophysical observations about inhibitory interneurons. The main approach leverages recent work related to decomposing matrices into low-rank and sparse components via convex optimization, and explicitly exploits the fact that models and input statistics often have low-dimensional structure that can be exploited for efficient implementations. While this approach is applicable to a wide range of sensory coding models (including a family of models based on Bayesian inference in a linear generative model), for concreteness we demonstrate the approach on a network implementing sparse coding. We show that the resulting implementation stays faithful to the original coding goals while using inhibitory interneurons that are much more biophysically plausible.     

Bounds on the minimum number of recombination events in a sample history

Recombination is an important evolutionary factor in many organisms, including humans, and understanding its effects is an important task facing geneticists. Detecting past recombination events is thus important; this article introduces statistics that give a lower bound on the number of recombination events in the history of a sample, on the basis of the patterns of variation in the sample DNA. Such lower bounds are appropriate, since many recombination events in the history are typically undetectable, so the true number of historical recombinations is unobtainable. The statistics can be calculated quickly by computer and improve upon the earlier bound of Hudson and Kaplan 1985. A method is developed to combine bounds on local regions in the data to produce more powerful improved bounds. The method is flexible to different models of recombination occurrence. The approach gives recombination event bounds between all pairs of sites, to help identify regions with more detectable recombinations, and these bounds can be viewed graphically. Under coalescent simulations, there is a substantial improvement over the earlier method (of up to a factor of 2) in the expected number of recombination events detected by one of the new minima, across a wide range of parameter values. The method is applied to data from a region within the lipoprotein lipase gene and the amount of detected recombination is substantially increased. Further, there is strong clustering of detected recombination events in an area near the center of the region. A program implementing these statistics, which was used for this article, is available from http://www.stats.ox.ac.uk/mathgen/programs.html.     

Two-trait-locus linkage analysis: a powerful strategy for mapping complex genetic traits.

Recent advances in molecular biology have provided geneticists with ever-increasing numbers of highly polymorphic genetic markers that have made possible linkage mapping of loci responsible for many human diseases. However, nearly all diseases mapped to date follow clear Mendelian, single-locus segregation patterns. In contrast, many common familial diseases such as diabetes, psoriasis, several forms of cancer, and schizophrenia are familial and appear to have a genetic component but do not exhibit simple Mendelian transmission. More complex models are required to explain the genetics of these important diseases. In this paper, we explore two-trait-locus, two-marker-locus linkage analysis in which two trait loci are mapped simultaneously to separate genetic markers. We compare the utility of this approach to standard one-trait-locus, one-marker-locus linkage analysis with and without allowance for heterogeneity. We also compare the utility of the two-trait-locus, two-marker-locus analysis to two-trait-locus, one-marker-locus linkage analysis. For common diseases, pedigrees are often bilineal, with disease genes entering via two or more unrelated pedigree members. Since such pedigrees often are avoided in linkage studies, we also investigate the relative information content of unilineal and bilineal pedigrees. For the dominant-or-recessive and threshold models that we consider, we find that two-trait-locus, two-marker-locus linkage analysis can provide substantially more linkage information, as measured by expected maximum lod score, than standard one-trait-locus, one-marker-locus methods, even allowing for heterogeneity, while, for a dominant-or-dominant generating model, one-locus models that allow for heterogeneity extract essentially as much information as the two-trait-locus methods. For these three models, we also find that bilineal pedigrees provide sufficient linkage information to warrant their inclusion in such studies. We also discuss strategies for assessing the significance of the two linkages assumed in two-trait-locus, two-marker-locus models.     

Evidential statistics as a statistical modern synthesis to support 21st century science

During the 20th century, population ecology and science in general relied on two very different statistical paradigms to solve its inferential problems: error statistics (also referred to as classical statistics and frequentist statistics) and Bayesian statistics. A great deal of good science was done using these tools, but both schools suffer from technical and philosophical difficulties. At the turning of the 21st century (Royall in Statistical evidence: a likelihood paradigm. Chapman & Hall, London, 1997 ; Lele in The nature of scientific evidence: statistical, philosophical and empirical considerations. The University of Chicago Press, Chicago, pp 191–216, 2004a ), evidential statistics emerged as a seriously contending paradigm. Drawing on and refining elements from error statistics, likelihoodism, Bayesian statistics, information criteria, and robust methods, evidential statistics is a statistical modern synthesis that smoothly incorporates model identification, model uncertainty, model comparison, parameter estimation, parameter uncertainty, pre-data control of error, and post-data strength of evidence into a single coherent framework. We argue that evidential statistics is currently the most effective statistical paradigm to support 21st century science. Despite the power of the evidential paradigm, we think that there is no substitute for learning how to clarify scientific arguments with statistical arguments. In this paper we sketch and relate the conceptual bases of error statistics, Bayesian statistics and evidential statistics. We also discuss a number of misconceptions about the paradigms that have hindered practitioners, as well as some real problems with the error and Bayesian statistical paradigms solved by evidential statistics.     

Fine Mapping Causal Variants with an Approximate Bayesian Method Using Marginal Test Statistics

Two recently developed fine-mapping methods, CAVIAR and PAINTOR, demonstrate better performance over other fine-mapping methods. They also have the advantage of using only the marginal test statistics and the correlation among SNPs. Both methods leverage the fact that the marginal test statistics asymptotically follow a multivariate normal distribution and are likelihood based. However, their relationship with Bayesian fine mapping, such as BIMBAM, is not clear. In this study, we first show that CAVIAR and BIMBAM are actually approximately equivalent to each other. This leads to a fine-mapping method using marginal test statistics in the Bayesian framework, which we call CAVIAR Bayes factor (CAVIARBF). Another advantage of the Bayesian framework is that it can answer both association and fine-mapping questions. We also used simulations to compare CAVIARBF with other methods under different numbers of causal variants. The results showed that both CAVIARBF and BIMBAM have better performance than PAINTOR and other methods. Compared to BIMBAM, CAVIARBF has the advantage of using only marginal test statistics and takes about one-quarter to one-fifth of the running time. We applied different methods on two independent cohorts of the same phenotype. Results showed that CAVIARBF, BIMBAM, and PAINTOR selected the same top 3 SNPs; however, CAVIARBF and BIMBAM had better consistency in selecting the top 10 ranked SNPs between the two cohorts. Software is available at https://bitbucket.org/Wenan/caviarbf.     

Observing the observer (II): deciding when to decide

In a companion paper [1], we have presented a generic approach for inferring how subjects make optimal decisions under uncertainty. From a Bayesian decision theoretic perspective, uncertain representations correspond to "posterior" beliefs, which result from integrating (sensory) information with subjective "prior" beliefs. Preferences and goals are encoded through a "loss" (or "utility") function, which measures the cost incurred by making any admissible decision for any given (hidden or unknown) state of the world. By assuming that subjects make optimal decisions on the basis of updated (posterior) beliefs and utility (loss) functions, one can evaluate the likelihood of observed behaviour. In this paper, we describe a concrete implementation of this meta-Bayesian approach (i.e. a Bayesian treatment of Bayesian decision theoretic predictions) and demonstrate its utility by applying it to both simulated and empirical reaction time data from an associative learning task. Here, inter-trial variability in reaction times is modelled as reflecting the dynamics of the subjects' internal recognition process, i.e. the updating of representations (posterior densities) of hidden states over trials while subjects learn probabilistic audio-visual associations. We use this paradigm to demonstrate that our meta-Bayesian framework allows for (i) probabilistic inference on the dynamics of the subject's representation of environmental states, and for (ii) model selection to disambiguate between alternative preferences (loss functions) human subjects could employ when dealing with trade-offs, such as between speed and accuracy. Finally, we illustrate how our approach can be used to quantify subjective beliefs and preferences that underlie inter-individual differences in behaviour.     

Bayesian statistics for parasitologists

Bayesian statistical methods are increasingly being used in the analysis of parasitological data. Here, the basis of differences between the Bayesian method and the classical or frequentist approach to statistical inference is explained. This is illustrated with practical implications of Bayesian analyses using prevalence estimation of strongyloidiasis and onchocerciasis as two relevant examples. The strongyloidiasis example addresses the problem of parasitological diagnosis in the absence of a gold standard, whereas the onchocerciasis case focuses on the identification of villages warranting priority mass ivermectin treatment. The advantages and challenges faced by users of the Bayesian approach are also discussed and the readers pointed to further directions for a more in-depth exploration of the issues raised. We advocate collaboration between parasitologists and Bayesian statisticians as a fruitful and rewarding venture for advancing applied research in parasite epidemiology and the control of parasitic infections.     

Bayesian Parameter Inference and Model Selection by Population Annealing in Systems Biology

Parameter inference and model selection are very important for mathematical modeling in systems biology. Bayesian statistics can be used to conduct both parameter inference and model selection. Especially, the framework named approximate Bayesian computation is often used for parameter inference and model selection in systems biology. However, Monte Carlo methods needs to be used to compute Bayesian posterior distributions. In addition, the posterior distributions of parameters are sometimes almost uniform or very similar to their prior distributions. In such cases, it is difficult to choose one specific value of parameter with high credibility as the representative value of the distribution. To overcome the problems, we introduced one of the population Monte Carlo algorithms, population annealing. Although population annealing is usually used in statistical mechanics, we showed that population annealing can be used to compute Bayesian posterior distributions in the approximate Bayesian computation framework. To deal with un-identifiability of the representative values of parameters, we proposed to run the simulations with the parameter ensemble sampled from the posterior distribution, named “posterior parameter ensemble”. We showed that population annealing is an efficient and convenient algorithm to generate posterior parameter ensemble. We also showed that the simulations with the posterior parameter ensemble can, not only reproduce the data used for parameter inference, but also capture and predict the data which was not used for parameter inference. Lastly, we introduced the marginal likelihood in the approximate Bayesian computation framework for Bayesian model selection. We showed that population annealing enables us to compute the marginal likelihood in the approximate Bayesian computation framework and conduct model selection depending on the Bayes factor.     

Recovering Genetic Regulatory Networks from Chromatin Immunoprecipitation and Steady-State Microarray Data

Recent advances in high-throughput DNA microarrays and chromatin immunoprecipitation (ChIP) assays have enabled the learning of the structure and functionality of genetic regulatory networks. In light of these heterogeneous data sets, this paper proposes a novel approach for reconstruction of genetic regulatory networks based on the posterior probabilities of gene regulations. Built within the framework of Bayesian statistics and computational Monte Carlo techniques, the proposed approach prevents the dichotomy of classifying gene interactions as either being connected or disconnected, thereby it reduces significantly the inference errors. Simulation results corroborate the superior performance of the proposed approach relative to the existing state-of-the-art algorithms. A genetic regulatory network for Saccharomyces cerevisiae is inferred based on the published real data sets, and biological meaningful results are discussed.     

A classification model for continuous responses: Identifying risk perception groups on health-related activities

In the current literature on latent variable models, much effort has been put on the development of dichotomous and polytomous cognitive diagnostic models (CDMs) for assessments. Recently, the possibility of using continuous responses in CDMs has been brought to discussion. But no Bayesian approach has been developed yet for the analysis of CDMs when responses are continuous. Our work is the first Bayesian framework for the continuous deterministic inputs, noisy, and gate (DINA) model. We also propose new interpretations for item parameters in this DINA model, which makes the analysis more interpretable than before. In addition, we have conducted several simulations to evaluate the performance of the continuous DINA model through our Bayesian approach. Then, we have applied the proposed DINA model to a real data example of risk perceptions for individuals over a range of health-related activities. The application results exemplify the high potential of the use of the proposed continuous DINA model to classify individuals in the study.     

Bayesian Estimation of Animal Movement from Archival and Satellite Tags

The reliable estimation of animal location, and its associated error is fundamental to animal ecology. There are many existing techniques for handling location error, but these are often ad hoc or are used in isolation from each other. In this study we present a Bayesian framework for determining location that uses all the data available, is flexible to all tagging techniques, and provides location estimates with built-in measures of uncertainty. Bayesian methods allow the contributions of multiple data sources to be decomposed into manageable components. We illustrate with two examples for two different location methods: satellite tracking and light level geo-location. We show that many of the problems with uncertainty involved are reduced and quantified by our approach. This approach can use any available information, such as existing knowledge of the animal''s potential range, light levels or direct location estimates, auxiliary data, and movement models. The approach provides a substantial contribution to the handling uncertainty in archival tag and satellite tracking data using readily available tools.     

Bayesian outbreak detection algorithm for monitoring reported cases of campylobacteriosis in Germany

In infectious disease epidemiology, statistical methods are an indispensable component for the automated detection of outbreaks in routinely collected surveillance data. So far, methodology in this area has been largely of frequentist nature and has increasingly been taking inspiration from statistical process control. The present work is concerned with strengthening Bayesian thinking in this field. We extend the widely used approach of Farrington et al. and Heisterkamp et al. to a modern Bayesian framework within a time series decomposition context. This approach facilitates a direct calculation of the decision‐making threshold while taking all sources of uncertainty in both prediction and estimation into account. More importantly, with the methodology it is now also possible to integrate covariate processes, e.g. weather influence, into the outbreak detection. Model inference is performed using fast and efficient integrated nested Laplace approximations, enabling the use of this method in routine surveillance at public health institutions. Performance of the algorithm was investigated by comparing simulations with existing methods as well as by analysing the time series of notified campylobacteriosis cases in Germany for the years 2002–2011, which include absolute humidity as a covariate process. Altogether, a flexible and modern surveillance algorithm is presented with an implementation available through the R package ‘surveillance’.     

On the Use of Bayesian Methods for Evaluating Compartmental Neural Models

Computational modeling is being used increasingly in neuroscience. In deriving such models, inference issues such as model selection, model complexity, and model comparison must be addressed constantly. In this article we present briefly the Bayesian approach to inference. Under a simple set of commonsense axioms, there exists essentially a unique way of reasoning under uncertainty by assigning a degree of confidence to any hypothesis or model, given the available data and prior information. Such degrees of confidence must obey all the rules governing probabilities and can be updated accordingly as more data becomes available. While the Bayesian methodology can be applied to any type of model, as an example we outline its use for an important, and increasingly standard, class of models in computational neuroscience—compartmental models of single neurons. Inference issues are particularly relevant for these models: their parameter spaces are typically very large, neurophysiological and neuroanatomical data are still sparse, and probabilistic aspects are often ignored. As a tutorial, we demonstrate the Bayesian approach on a class of one-compartment models with varying numbers of conductances. We then apply Bayesian methods on a compartmental model of a real neuron to determine the optimal amount of noise to add to the model to give it a level of spike time variability comparable to that found in the real cell.     

SIMULATION‐BASED LIKELIHOOD APPROACH FOR EVOLUTIONARY MODELS OF PHENOTYPIC TRAITS ON PHYLOGENY

Phylogenetic comparative methods (PCMs) have been used to test evolutionary hypotheses at phenotypic levels. The evolutionary modes commonly included in PCMs are Brownian motion (genetic drift) and the Ornstein–Uhlenbeck process (stabilizing selection), whose likelihood functions are mathematically tractable. More complicated models of evolutionary modes, such as branch‐specific directional selection, have not been used because calculations of likelihood and parameter estimates in the maximum‐likelihood framework are not straightforward. To solve this problem, we introduced a population genetics framework into a PCM, and here, we present a flexible and comprehensive framework for estimating evolutionary parameters through simulation‐based likelihood computations. The method does not require analytic likelihood computations, and evolutionary models can be used as long as simulation is possible. Our approach has many advantages: it incorporates different evolutionary modes for phenotypes into phylogeny, it takes intraspecific variation into account, it evaluates full likelihood instead of using summary statistics, and it can be used to estimate ancestral traits. We present a successful application of the method to the evolution of brain size in primates. Our method can be easily implemented in more computationally effective frameworks such as approximate Bayesian computation (ABC), which will enhance the use of computationally intensive methods in the study of phenotypic evolution.     

Building food networks from molecular data: Bayesian or fixed-number thresholds for including links

DNA metabarcoding of faeces or gut contents has greatly increased our ability to construct networks of predators and prey (food webs) by reducing the need to observe predation events directly. The possibility of both false positives and false negatives in DNA sequences, however, means that constructing food networks using DNA requires researchers to make many choices as to which DNA sequences indicate true prey for a particular predator. To date, DNA-based food networks are usually constructed by including any DNA sequence with more than a threshold number of reads. The logic used to select this threshold is often not explained, leading to somewhat arbitrary-seeming networks. As an alternative strategy, we demonstrate how to construct food networks using a simple Bayesian model to suggest which sequences correspond to true prey. The networks obtained using a well-chosen fixed cutoff and our Bayesian approach are very similar, especially when links are resolved to prey families rather than species. We therefore recommend that researchers reconstruct diet data using a Bayesian approach with well-specified assumptions rather than continuing with arbitrary fixed cutoffs. Explicitly stating assumptions within a Bayesian framework will lead to better-informed comparisons between networks constructed by different groups and facilitate drawing together individual case studies into more coherent ecological theory. Note that our approach can easily be extended to other types of ecological networks constructed by DNA metabarcoding of pollen loads, identification of parasite DNA in faeces, etc.     

Bayesian Estimation of Positively Selected Sites

In protein-coding DNA sequences, historical patterns of selection can be inferred from amino acid substitution patterns. High relative rates of nonsynonymous to synonymous changes (=d _N /d _S ) are a clear indicator of positive, or directional, selection, and several recently developed methods attempt to distinguish these sites from those under neutral or purifying selection. One method uses an empirical Bayesian framework that accounts for varying selective pressures across sites while conditioning on the parameters of the model of DNA evolution and on the phylogenetic history. We describe a method that identifies sites under diversifying selection using a fully Bayesian framework. Similar to earlier work, the method presented here allows the rate of nonsynonymous to synonymous changes to vary among sites. The significant difference in using a fully Bayesian approach lies in our ability to account for uncertainty in parameters including the tree topology, branch lengths, and the codon model of DNA substitution. We demonstrate the utility of the fully Bayesian approach by applying our method to a data set of the vertebrate -globin gene. Compared to a previous analysis of this data set, the hierarchical model found most of the same sites to be in the positive selection class, but with a few striking exceptions.