Statistical and Bayesian approaches to RNA secondary structure prediction

Prediction of RNA secondary structure is a fundamental problem in computational structural biology. For several decades, free energy minimization has been the most popular method for prediction from a single sequence. In recent years, the McCaskill algorithm for computation of partition function and base-pair probabilities has become increasingly appreciated. This paradigm-shifting work has inspired the developments of extended partition function algorithms, statistical sampling and clustering, and application of Bayesian statistical inference. The performance of thermodynamics-based methods is limited by thermodynamic rules and parameters. However, further improvements may come from statistical estimates derived from structural databases for thermodynamics parameters with weak or little experimental data. The Bayesian inference approach appears to be promising in this context.     

Detecting Genetic Association of Common Human Facial Morphological Variation Using High Density 3D Image Registration

Human facial morphology is a combination of many complex traits. Little is known about the genetic basis of common facial morphological variation. Existing association studies have largely used simple landmark-distances as surrogates for the complex morphological phenotypes of the face. However, this can result in decreased statistical power and unclear inference of shape changes. In this study, we applied a new image registration approach that automatically identified the salient landmarks and aligned the sample faces using high density pixel points. Based on this high density registration, three different phenotype data schemes were used to test the association between the common facial morphological variation and 10 candidate SNPs, and their performances were compared. The first scheme used traditional landmark-distances; the second relied on the geometric analysis of 15 landmarks and the third used geometric analysis of a dense registration of ∼30,000 3D points. We found that the two geometric approaches were highly consistent in their detection of morphological changes. The geometric method using dense registration further demonstrated superiority in the fine inference of shape changes and 3D face modeling. Several candidate SNPs showed potential associations with different facial features. In particular, one SNP, a known risk factor of non-syndromic cleft lips/palates, rs642961 in the IRF6 gene, was validated to strongly predict normal lip shape variation in female Han Chinese. This study further demonstrated that dense face registration may substantially improve the detection and characterization of genetic association in common facial variation.     

Comparing Families of Dynamic Causal Models

Mathematical models of scientific data can be formally compared using Bayesian model evidence. Previous applications in the biological sciences have mainly focussed on model selection in which one first selects the model with the highest evidence and then makes inferences based on the parameters of that model. This “best model” approach is very useful but can become brittle if there are a large number of models to compare, and if different subjects use different models. To overcome this shortcoming we propose the combination of two further approaches: (i) family level inference and (ii) Bayesian model averaging within families. Family level inference removes uncertainty about aspects of model structure other than the characteristic of interest. For example: What are the inputs to the system? Is processing serial or parallel? Is it linear or nonlinear? Is it mediated by a single, crucial connection? We apply Bayesian model averaging within families to provide inferences about parameters that are independent of further assumptions about model structure. We illustrate the methods using Dynamic Causal Models of brain imaging data.     

On the importance of being structured: instantaneous coalescence rates and human evolution—lessons for ancestral population size inference?

Most species are structured and influenced by processes that either increased or reduced gene flow between populations. However, most population genetic inference methods assume panmixia and reconstruct a history characterized by population size changes. This is potentially problematic as population structure can generate spurious signals of population size change through time. Moreover, when the model assumed for demographic inference is misspecified, genomic data will likely increase the precision of misleading if not meaningless parameters. For instance, if data were generated under an n-island model (characterized by the number of islands and migrants exchanged) inference based on a model of population size change would produce precise estimates of a bottleneck that would be meaningless. In addition, archaeological or climatic events around the bottleneck''s timing might provide a reasonable but potentially misleading scenario. In a context of model uncertainty (panmixia versus structure) genomic data may thus not necessarily lead to improved statistical inference. We consider two haploid genomes and develop a theory that explains why any demographic model with structure will necessarily be interpreted as a series of changes in population size by inference methods ignoring structure. We formalize a parameter, the inverse instantaneous coalescence rate, and show that it is equivalent to a population size only in panmictic models, and is mostly misleading for structured models. We argue that this issue affects all population genetics methods ignoring population structure which may thus infer population size changes that never took place. We apply our approach to human genomic data.     

Faster mass spectrometry-based protein inference: junction trees are more efficient than sampling and marginalization by enumeration

The problem of identifying the proteins in a complex mixture using tandem mass spectrometry can be framed as an inference problem on a graph that connects peptides to proteins. Several existing protein identification methods make use of statistical inference methods for graphical models, including expectation maximization, Markov chain Monte Carlo, and full marginalization coupled with approximation heuristics. We show that, for this problem, the majority of the cost of inference usually comes from a few highly connected subgraphs. Furthermore, we evaluate three different statistical inference methods using a common graphical model, and we demonstrate that junction tree inference substantially improves rates of convergence compared to existing methods. The python code used for this paper is available at http://noble.gs.washington.edu/proj/fido.     

Phylodynamic Inference for Structured Epidemiological Models

Coalescent theory is routinely used to estimate past population dynamics and demographic parameters from genealogies. While early work in coalescent theory only considered simple demographic models, advances in theory have allowed for increasingly complex demographic scenarios to be considered. The success of this approach has lead to coalescent-based inference methods being applied to populations with rapidly changing population dynamics, including pathogens like RNA viruses. However, fitting epidemiological models to genealogies via coalescent models remains a challenging task, because pathogen populations often exhibit complex, nonlinear dynamics and are structured by multiple factors. Moreover, it often becomes necessary to consider stochastic variation in population dynamics when fitting such complex models to real data. Using recently developed structured coalescent models that accommodate complex population dynamics and population structure, we develop a statistical framework for fitting stochastic epidemiological models to genealogies. By combining particle filtering methods with Bayesian Markov chain Monte Carlo methods, we are able to fit a wide class of stochastic, nonlinear epidemiological models with different forms of population structure to genealogies. We demonstrate our framework using two structured epidemiological models: a model with disease progression between multiple stages of infection and a two-population model reflecting spatial structure. We apply the multi-stage model to HIV genealogies and show that the proposed method can be used to estimate the stage-specific transmission rates and prevalence of HIV. Finally, using the two-population model we explore how much information about population structure is contained in genealogies and what sample sizes are necessary to reliably infer parameters like migration rates.     

Simultaneous inference in general parametric models

Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth of the results. For the analyses we use the R add-on package multcomp, which provides a convenient interface to the general approach adopted here.     

Identifiability of Large Phylogenetic Mixture Models

Phylogenetic mixture models are statistical models of character evolution allowing for heterogeneity. Each of the classes in some unknown partition of the characters may evolve by different processes, or even along different trees. Such models are of increasing interest for data analysis, as they can capture the variety of evolutionary processes that may be occurring across long sequences of DNA or proteins. The fundamental question of whether parameters of such a model are identifiable is difficult to address, due to the complexity of the parameterization. Identifiability is, however, essential to their use for statistical inference.     

Bayesian model adequacy and choice in phylogenetics

Bayesian inference is becoming a common statistical approach to phylogenetic estimation because, among other reasons, it allows for rapid analysis of large data sets with complex evolutionary models. Conveniently, Bayesian phylogenetic methods use currently available stochastic models of sequence evolution. However, as with other model-based approaches, the results of Bayesian inference are conditional on the assumed model of evolution: inadequate models (models that poorly fit the data) may result in erroneous inferences. In this article, I present a Bayesian phylogenetic method that evaluates the adequacy of evolutionary models using posterior predictive distributions. By evaluating a model's posterior predictive performance, an adequate model can be selected for a Bayesian phylogenetic study. Although I present a single test statistic that assesses the overall (global) performance of a phylogenetic model, a variety of test statistics can be tailored to evaluate specific features (local performance) of evolutionary models to identify sources failure. The method presented here, unlike the likelihood-ratio test and parametric bootstrap, accounts for uncertainty in the phylogeny and model parameters.     

Reliability of assessment of protein structure prediction methods

The reliability of ranking of protein structure modeling methods is assessed. The assessment is based on the parametric Student's t test and the nonparametric Wilcox signed rank test of statistical significance of the difference between paired samples. The approach is applied to the ranking of the comparative modeling methods tested at the fourth meeting on Critical Assessment of Techniques for Protein Structure Prediction (CASP). It is shown that the 14 CASP4 test sequences may not be sufficient to reliably distinguish between the top eight methods, given the model quality differences and their standard deviations. We suggest that CASP needs to be supplemented by an assessment of protein structure prediction methods that is automated, continuous in time, based on several criteria applied to a large number of models, and with quantitative statistical reliability assigned to each characterization.     

A comparison of strategies for Markov chain Monte Carlo computation in quantitative genetics

In quantitative genetics, Markov chain Monte Carlo (MCMC) methods are indispensable for statistical inference in non-standard models like generalized linear models with genetic random effects or models with genetically structured variance heterogeneity. A particular challenge for MCMC applications in quantitative genetics is to obtain efficient updates of the high-dimensional vectors of genetic random effects and the associated covariance parameters. We discuss various strategies to approach this problem including reparameterization, Langevin-Hastings updates, and updates based on normal approximations. The methods are compared in applications to Bayesian inference for three data sets using a model with genetically structured variance heterogeneity.     

Inferences from Genomic Models in Stratified Populations

Unaccounted population stratification can lead to spurious associations in genome-wide association studies (GWAS) and in this context several methods have been proposed to deal with this problem. An alternative line of research uses whole-genome random regression (WGRR) models that fit all markers simultaneously. Important objectives in WGRR studies are to estimate the proportion of variance accounted for by the markers, the effect of individual markers, prediction of genetic values for complex traits, and prediction of genetic risk of diseases. Proposals to account for stratification in this context are unsatisfactory. Here we address this problem and describe a reparameterization of a WGRR model, based on an eigenvalue decomposition, for simultaneous inference of parameters and unobserved population structure. This allows estimation of genomic parameters with and without inclusion of marker-derived eigenvectors that account for stratification. The method is illustrated with grain yield in wheat typed for 1279 genetic markers, and with height, HDL cholesterol and systolic blood pressure from the British 1958 cohort study typed for 1 million SNP genotypes. Both sets of data show signs of population structure but with different consequences on inferences. The method is compared to an advocated approach consisting of including eigenvectors as fixed-effect covariates in a WGRR model. We show that this approach, used in the context of WGRR models, is ill posed and illustrate the advantages of the proposed model. In summary, our method permits a unified approach to the study of population structure and inference of parameters, is computationally efficient, and is easy to implement.     

In defence of model‐based inference in phylogeography

Recent papers have promoted the view that model‐based methods in general, and those based on Approximate Bayesian Computation (ABC) in particular, are flawed in a number of ways, and are therefore inappropriate for the analysis of phylogeographic data. These papers further argue that Nested Clade Phylogeographic Analysis (NCPA) offers the best approach in statistical phylogeography. In order to remove the confusion and misconceptions introduced by these papers, we justify and explain the reasoning behind model‐based inference. We argue that ABC is a statistically valid approach, alongside other computational statistical techniques that have been successfully used to infer parameters and compare models in population genetics. We also examine the NCPA method and highlight numerous deficiencies, either when used with single or multiple loci. We further show that the ages of clades are carelessly used to infer ages of demographic events, that these ages are estimated under a simple model of panmixia and population stationarity but are then used under different and unspecified models to test hypotheses, a usage the invalidates these testing procedures. We conclude by encouraging researchers to study and use model‐based inference in population genetics.     

Morphological diversity at different spatial scales in a Neotropical bat assemblage

The morphology of species can be used to represent their ecological position and infer potential processes determining the structure of species assemblages. This ecomorphological approach has been widely applied to the study of bat assemblages which mainly focuses on a single spatial scale and particular guilds. We extended such an ecomorphological approach to a multi-scale analysis of a Neotropical bat assemblage and its constituent guilds (aerial and gleaning insectivores, frugivores, and nectarivores) to describe their structure at different spatial scales and determine the relative importance of inter-specific competition, habitat filtering, or stochastic processes shaping such structures. We measured the occupied morphological space (size) defined by wing and skull morphology independently and the nearest-neighbour distance (structure) among species within these spaces at each spatial scale. Observed patterns were compared with random expectations derived from null models for statistical inference. When controlling for species richness and regional sampling effects in the null models, we did not find a significant effect of spatial scale in the morphological structure of the studied bat assemblage and guilds. Morphological structure followed the same patterns across scales as those expected from random drawings of sample size alone. Similar results were obtained regardless of morphological complex (wing and skull) and guilds. At both the assemblage and guild levels, bat morphological structure seems to be determined by regional, abiotic processes (e.g. habitat filtering) shaping the composition and organization of the species pool.     

Recommendations for improving statistical inference in population genomics

The field of population genomics has grown rapidly in response to the recent advent of affordable, large-scale sequencing technologies. As opposed to the situation during the majority of the 20th century, in which the development of theoretical and statistical population genetic insights outpaced the generation of data to which they could be applied, genomic data are now being produced at a far greater rate than they can be meaningfully analyzed and interpreted. With this wealth of data has come a tendency to focus on fitting specific (and often rather idiosyncratic) models to data, at the expense of a careful exploration of the range of possible underlying evolutionary processes. For example, the approach of directly investigating models of adaptive evolution in each newly sequenced population or species often neglects the fact that a thorough characterization of ubiquitous nonadaptive processes is a prerequisite for accurate inference. We here describe the perils of these tendencies, present our consensus views on current best practices in population genomic data analysis, and highlight areas of statistical inference and theory that are in need of further attention. Thereby, we argue for the importance of defining a biologically relevant baseline model tuned to the details of each new analysis, of skepticism and scrutiny in interpreting model fitting results, and of carefully defining addressable hypotheses and underlying uncertainties.

Genomic data are now being produced at a far greater rate than they can be meaningfully analyzed and interpreted, leading to some questionable use of statistical models. In this Consensus View, the authors provide recommendations for current best practices in population genomic data analysis and highlight areas of statistical inference and theory that are in need of further attention.     

Analysis and identification of stochastic compartment models in pharmacokinetics: implication for cancer chemotherapy

One of the fundamental problems in pharmacokinetics is determining the parameters of multicompartment models from the measured excretion rate and observations on one of the compartments. Since it is frequently impractical to obtain observations for all physiological compartments, and due to the inherent variations in biological systems, a stochastic approach to multicompartment analysis is suggested. The objective of this article is to consider the identification of multicompartment models from a stochastic point of view, with particular emphasis on two- and three-compartment models.The essential part of this investigation is the statistical simulation of the C-T curves of the observed compartment for different biological conditions. We then present a probabilistic characterization of the multirandom parameter family of the rate constant matrix and evaluate the statistical properties of the solution processes for the unobservable compartments.     

IS YOUR PHYLOGENY INFORMATIVE? MEASURING THE POWER OF COMPARATIVE METHODS

Phylogenetic comparative methods may fail to produce meaningful results when either the underlying model is inappropriate or the data contain insufficient information to inform the inference. The ability to measure the statistical power of these methods has become crucial to ensure that data quantity keeps pace with growing model complexity. Through simulations, we show that commonly applied model choice methods based on information criteria can have remarkably high error rates; this can be a problem because methods to estimate the uncertainty or power are not widely known or applied. Furthermore, the power of comparative methods can depend significantly on the structure of the data. We describe a Monte Carlo-based method which addresses both of these challenges, and show how this approach both quantifies and substantially reduces errors relative to information criteria. The method also produces meaningful confidence intervals for model parameters. We illustrate how the power to distinguish different models, such as varying levels of selection, varies both with number of taxa and structure of the phylogeny. We provide an open-source implementation in the pmc ("Phylogenetic Monte Carlo") package for the R programming language. We hope such power analysis becomes a routine part of model comparison in comparative methods.     

Path Models of Vocal Emotion Communication

We propose to use a comprehensive path model of vocal emotion communication, encompassing encoding, transmission, and decoding processes, to empirically model data sets on emotion expression and recognition. The utility of the approach is demonstrated for two data sets from two different cultures and languages, based on corpora of vocal emotion enactment by professional actors and emotion inference by naïve listeners. Lens model equations, hierarchical regression, and multivariate path analysis are used to compare the relative contributions of objectively measured acoustic cues in the enacted expressions and subjective voice cues as perceived by listeners to the variance in emotion inference from vocal expressions for four emotion families (fear, anger, happiness, and sadness). While the results confirm the central role of arousal in vocal emotion communication, the utility of applying an extended path modeling framework is demonstrated by the identification of unique combinations of distal cues and proximal percepts carrying information about specific emotion families, independent of arousal. The statistical models generated show that more sophisticated acoustic parameters need to be developed to explain the distal underpinnings of subjective voice quality percepts that account for much of the variance in emotion inference, in particular voice instability and roughness. The general approach advocated here, as well as the specific results, open up new research strategies for work in psychology (specifically emotion and social perception research) and engineering and computer science (specifically research and development in the domain of affective computing, particularly on automatic emotion detection and synthetic emotion expression in avatars).     

A self-organizing state-space-model approach for parameter estimation in hodgkin-huxley-type models of single neurons

Traditional approaches to the problem of parameter estimation in biophysical models of neurons and neural networks usually adopt a global search algorithm (for example, an evolutionary algorithm), often in combination with a local search method (such as gradient descent) in order to minimize the value of a cost function, which measures the discrepancy between various features of the available experimental data and model output. In this study, we approach the problem of parameter estimation in conductance-based models of single neurons from a different perspective. By adopting a hidden-dynamical-systems formalism, we expressed parameter estimation as an inference problem in these systems, which can then be tackled using a range of well-established statistical inference methods. The particular method we used was Kitagawa's self-organizing state-space model, which was applied on a number of Hodgkin-Huxley-type models using simulated or actual electrophysiological data. We showed that the algorithm can be used to estimate a large number of parameters, including maximal conductances, reversal potentials, kinetics of ionic currents, measurement and intrinsic noise, based on low-dimensional experimental data and sufficiently informative priors in the form of pre-defined constraints imposed on model parameters. The algorithm remained operational even when very noisy experimental data were used. Importantly, by combining the self-organizing state-space model with an adaptive sampling algorithm akin to the Covariance Matrix Adaptation Evolution Strategy, we achieved a significant reduction in the variance of parameter estimates. The algorithm did not require the explicit formulation of a cost function and it was straightforward to apply on compartmental models and multiple data sets. Overall, the proposed methodology is particularly suitable for resolving high-dimensional inference problems based on noisy electrophysiological data and, therefore, a potentially useful tool in the construction of biophysical neuron models.     

Successful Reconstruction of a Physiological Circuit with Known Connectivity from Spiking Activity Alone

Identifying the structure and dynamics of synaptic interactions between neurons is the first step to understanding neural network dynamics. The presence of synaptic connections is traditionally inferred through the use of targeted stimulation and paired recordings or by post-hoc histology. More recently, causal network inference algorithms have been proposed to deduce connectivity directly from electrophysiological signals, such as extracellularly recorded spiking activity. Usually, these algorithms have not been validated on a neurophysiological data set for which the actual circuitry is known. Recent work has shown that traditional network inference algorithms based on linear models typically fail to identify the correct coupling of a small central pattern generating circuit in the stomatogastric ganglion of the crab Cancer borealis. In this work, we show that point process models of observed spike trains can guide inference of relative connectivity estimates that match the known physiological connectivity of the central pattern generator up to a choice of threshold. We elucidate the necessary steps to derive faithful connectivity estimates from a model that incorporates the spike train nature of the data. We then apply the model to measure changes in the effective connectivity pattern in response to two pharmacological interventions, which affect both intrinsic neural dynamics and synaptic transmission. Our results provide the first successful application of a network inference algorithm to a circuit for which the actual physiological synapses between neurons are known. The point process methodology presented here generalizes well to larger networks and can describe the statistics of neural populations. In general we show that advanced statistical models allow for the characterization of effective network structure, deciphering underlying network dynamics and estimating information-processing capabilities.