Bayesian computation via empirical likelihood

Evaluation of spatial Bayesian Empirical Likelihood models in analysis of small area data

Bayesian empirical likelihood (BEL) models are becoming increasingly popular as an attractive alternative to fully parametric models. However, they have only recently been applied to spatial data analysis for small area estimation. This study considers the development of spatial BEL models using two popular conditional autoregressive (CAR) priors, namely BYM and Leroux priors. The performance of the proposed models is compared with their parametric counterparts and with existing spatial BEL models using independent Gaussian priors and generalised Moran basis priors. The models are applied to two benchmark spatial datasets, simulation study and COVID-19 data. The results indicate promising opportunities for these models to capture new insights into spatial data. Specifically, the spatial BEL models outperform the parametric spatial models when the underlying distributional assumptions of data appear to be violated.

Optogenetic and thermogenetic manipulation of defined neural circuits and behaviors in Drosophila

Neural network dynamics underlying flexible animal behaviors remain elusive. The fruit fly Drosophila melanogaster is considered an excellent model in behavioral neuroscience because of its simple neuroanatomical architecture and the availability of various genetic methods. Moreover, Drosophila larvae's transparent body allows investigators to use optical methods on freely moving animals, broadening research directions. Activating or inhibiting well-defined events in excitable cells with a fine temporal resolution using optogenetics and thermogenetics led to the association of functions of defined neural populations with specific behavioral outputs such as the induction of associative memory. Furthermore, combining optogenetics and thermogenetics with state-of-the-art approaches, including connectome mapping and machine learning-based behavioral quantification, might provide a complete view of the experience- and time-dependent variations of behavioral responses. These methodologies allow further understanding of the functional connections between neural circuits and behaviors such as chemosensory, motivational, courtship, and feeding behaviors and sleep, learning, and memory.

Valence opponency in peripheral olfactory processing

Are olfactory receptor neurons (ORNs) arranged in a functionally meaningful manner to facilitate information processing? Here, we address this long-standing question by uncovering a valence map in the olfactory periphery of Drosophila. Within sensory hairs, we find that neighboring ORNs antagonistically regulate behaviors: stereotypically compartmentalized large- and small-spike ORNs, recognized by their characteristic spike amplitudes, either promote or inhibit the same type of behavior, respectively. Systematic optogenetic and thermogenetic assays—covering the majority of antennal sensilla—highlight a valence-opponent organization. Critically, odor-mixture behavioral experiments show that lateral inhibition between antagonistic ORNs mediates robust behavioral decisions in response to countervailing cues. Computational modeling predicts that the robustness of behavioral output depends on odor mixture ratios.

A hallmark of complex sensory systems is the organization of neurons into functionally meaningful maps, which allow for comparison and contrast of parallel inputs via lateral inhibition. However, it is unclear whether such a map exists in olfaction. Here, we address this question by determining the organizing principle underlying the stereotyped pairing of olfactory receptor neurons (ORNs) in Drosophila sensory hairs, wherein compartmentalized neurons inhibit each other via ephaptic coupling. Systematic behavioral assays reveal that most paired ORNs antagonistically regulate the same type of behavior. Such valence opponency is relevant in critical behavioral contexts including place preference, egg laying, and courtship. Odor-mixture experiments show that ephaptic inhibition provides a peripheral means for evaluating and shaping countervailing cues relayed to higher brain centers. Furthermore, computational modeling suggests that this organization likely contributes to processing ratio information in odor mixtures. This olfactory valence map may have evolved to swiftly process ethologically meaningful odor blends without involving costly synaptic computation.

A unified Bayesian framework for exact inference of area under the receiver operating characteristic curve

The area under the receiver operating characteristic curve is a widely used measure for evaluating the performance of a diagnostic test. Common approaches for inference on area under the receiver operating characteristic curve are usually based upon approximation. For example, the normal approximation based inference tends to suffer from the problem of low accuracy for small sample size. Frequentist empirical likelihood based approaches for area under the receiver operating characteristic curve estimation may perform better, but are usually conducted through approximation in order to reduce the computational burden, thus the inference is not exact. By contrast, we proposed an exact inferential procedure by adapting the empirical likelihood into a Bayesian framework and draw inference from the posterior samples of the area under the receiver operating characteristic curve obtained via a Gibbs sampler. The full conditional distributions within the Gibbs sampler only involve empirical likelihoods with linear constraints, which greatly simplify the computation. To further enhance the applicability and flexibility of the Bayesian empirical likelihood, we extend our method to the estimation of partial area under the receiver operating characteristic curve, comparison of multiple tests, and the doubly robust estimation of area under the receiver operating characteristic curve in the presence of missing test results. Simulation studies confirm the desirable performance of the proposed methods, and a real application is presented to illustrate its usefulness.

Bayesian analysis of immigration in Europe with generalized logistic regression

The number of immigrants moving to and settling in Europe has increased over the past decade, making migration one of the most topical and pressing issues in European politics. It is without a doubt that immigration has multiple impacts, in terms of economy, society and culture, on the European Union. It is fundamental to policy-makers to correctly evaluate people's attitudes towards immigration when designing integration policies. Of critical interest is to properly discriminate between subjects who are favourable towards immigration from those who are against it. Public opinions on migration are typically coded as binary responses in surveys. However, traditional methods, such as the standard logistic regression, may suffer from computational issues and are often not able to accurately model survey information. In this paper we propose an efficient Bayesian approach for modelling binary response data based on the generalized logistic regression. We show how the proposed approach provides an increased flexibility compared to traditional methods, due to its ability to capture heavy and light tails. The power of our methodology is tested through simulation studies and is illustrated using European Social Survey data on immigration collected in different European countries in 2016-2017.

Estimating the Gumbel-Barnett copula parameter of dependence

In this paper, we developed an empirical evaluation of four estimation procedures for the dependence parameter of the Gumbel-Barnett copula obtained from a Gumbel type I distribution. We used the maximum likelihood, moments and Bayesian methods and studied the performance of the estimates, assuming three dependence levels and 20 different sample sizes. For each method and scenario, a simulation study was conducted with 1000 runs and the quality of the estimator was evaluated using four different criteria. A Bayesian estimator assuming a Beta(a,b) as prior distribution, showed the best performance regardless the sample size and the dependence structure.

Accelerating Bayesian inference for evolutionary biology models

Motivation

Bayesian inference is widely used nowadays and relies largely on Markov chain Monte Carlo (MCMC) methods. Evolutionary biology has greatly benefited from the developments of MCMC methods, but the design of more complex and realistic models and the ever growing availability of novel data is pushing the limits of the current use of these methods.

Results

We present a parallel Metropolis-Hastings (M-H) framework built with a novel combination of enhancements aimed towards parameter-rich and complex models. We show on a parameter-rich macroevolutionary model increases of the sampling speed up to 35 times with 32 processors when compared to a sequential M-H process. More importantly, our framework achieves up to a twentyfold faster convergence to estimate the posterior probability of phylogenetic trees using 32 processors when compared to the well-known software MrBayes for Bayesian inference of phylogenetic trees.

Availability and Implementation

https://bitbucket.org/XavMeyer/hogan

Supplementary information

Supplementary data are available at Bioinformatics online.

Bayesian semiparametric density ratio modelling with applications to medical malpractice reform

This study examines the efficacy of tort reforms instituted throughout the country during the last decade, improving upon existing semiparametric density ratio estimation (DRE) methodologies in the process. DRE is a well-known semiparametric modelling technique that has been used for well over two decades. Although the approach has been demonstrated to be extremely useful in statistical modelling, it has suffered from one main limitation—the methodology has thus far not been capable of modelling individual-level heterogeneity. We address this issue by presenting a novel adaptation of DRE to model individual level heterogeneity. We do so by marginalizing the associated empirical likelihood function involving density ratios to provide an overall distribution of the entire population despite having extremely limited initial information about each individual in the dataset. We apply this approach to medical malpractice loss data from the previous decade to quantify the probability of changes in tort losses. Our results demonstrate the success of a number of recently implemented malpractice reforms. Comparisons to existing DRE methods, as well as standard regression methods, illustrate the efficacy of our approach.

Approximate Bayesian inference for complex ecosystems

Mathematical models have been central to ecology for nearly a century. Simple models of population dynamics have allowed us to understand fundamental aspects underlying the dynamics and stability of ecological systems. What has remained a challenge, however, is to meaningfully interpret experimental or observational data in light of mathematical models. Here, we review recent developments, notably in the growing field of approximate Bayesian computation (ABC), that allow us to calibrate mathematical models against available data. Estimating the population demographic parameters from data remains a formidable statistical challenge. Here, we attempt to give a flavor and overview of ABC and its applications in population biology and ecology and eschew a detailed technical discussion in favor of a general discussion of the advantages and potential pitfalls this framework offers to population biologists.