Abhra Sarkar

Male mice song syntax depends on social contexts and influences female preferences.

In 2005, Holy and Guo advanced the idea that male mice produce ultrasonic vocalizations (USV) with some features similar to courtship songs of songbirds. Since then, studies showed that male mice emit USV songs in different contexts (sexual and other) and possess a multisyllabic repertoire. Debate still exists for and against plasticity in their vocalizations. But the use of a multisyllabic repertoire can increase potential flexibility and information, in how elements are organized and recombined, namely syntax. In many bird species, modulating song syntax has ethological relevance for sexual behavior and mate preferences. In this study we exposed adult male mice to different social contexts and developed a new approach of analyzing their USVs based on songbird syntax analysis. We found that male mice modify their syntax, including specific sequences, length of sequence, repertoire composition, and spectral features, according to stimulus and social context. Males emit longer and simpler syllables and sequences when singing to females, but more complex syllables and sequences in response to fresh female urine. Playback experiments show that the females prefer the complex songs over the simpler ones. We propose the complex songs are to lure females in, whereas the directed simpler sequences are used for direct courtship. These results suggest that although mice have a much more limited ability of song modification, they could still be used as animal models for understanding some vocal communication features that songbirds are used for.

A Foxp2 Mutation Implicated in Human Speech Deficits Alters Sequencing of Ultrasonic Vocalizations in Adult Male Mice

Development of proficient spoken language skills is disrupted by mutations of the FOXP2 transcription factor. A heterozygous missense mutation in the KE family causes speech apraxia, involving difficulty producing words with complex learned sequences of syllables. Manipulations in songbirds have helped to elucidate the role of this gene in vocal learning, but findings in non-human mammals have been limited or inconclusive. Here, we performed a systematic study of ultrasonic vocalizations (USVs) of adult male mice carrying the KE family mutation. Using novel statistical tools, we found that Foxp2 heterozygous mice did not have detectable changes in USV syllable acoustic structure, but produced shorter sequences and did not shift to more complex syntax in social contexts where wildtype animals did. Heterozygous mice also displayed a shift in the position of their rudimentary laryngeal motor cortex (LMC) layer-5 neurons. Our findings indicate that although mouse USVs are mostly innate, the underlying contributions of FoxP2 to sequencing of vocalizations are conserved with humans.

Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors

We consider the problem of estimating the density of a random variable when precise measurements on the variable are not available, but replicated proxies contaminated with measurement error are available for sufficiently many subjects. Under the assumption of additive measurement errors this reduces to a problem of deconvolution of densities. Deconvolution methods often make restrictive and unrealistic assumptions about the density of interest and the distribution of measurement errors, for example, normality and homoscedasticity and thus independence from the variable of interest. This article relaxes these assumptions and introduces novel Bayesian semiparametric methodology based on Dirichlet process mixture models for robust deconvolution of densities in the presence of conditionally heteroscedastic measurement errors. In particular, the models can adapt to asymmetry, heavy tails, and multimodality. In simulation experiments, we show that our methods vastly outperform a recent Bayesian approach based on estimating the densities via mixtures of splines. We apply our methods to data from nutritional epidemiology. Even in the special case when the measurement errors are homoscedastic, our methodology is novel and dominates other methods that have been proposed previously. Additional simulation results, instructions on getting access to the dataset and R programs implementing our methods are included as part of online supplementary materials.

Bayesian Semiparametric Multivariate Density Deconvolution

ABSTRACT We consider the problem of multivariate density deconvolution when interest lies in estimating the distribution of a vector valued random variable X but precise measurements on X are not available, observations being contaminated by measurement errors U. The existing sparse literature on the problem assumes the density of the measurement errors to be completely known. We propose robust Bayesian semiparametric multivariate deconvolution approaches when the measurement error density of U is not known but replicated proxies are available for at least some individuals. Additionally, we allow the variability of U to depend on the associated unobserved values of X through unknown relationships, which also automatically includes the case of multivariate multiplicative measurement errors. Basic properties of finite mixture models, multivariate normal kernels, and exchangeable priors are exploited in novel ways to meet modeling and computational challenges. Theoretical results showing the flexibility of the proposed methods in capturing a wide variety of data-generating processes are provided. We illustrate the efficiency of the proposed methods in recovering the density of X through simulation experiments. The methodology is applied to estimate the joint consumption pattern of different dietary components from contaminated 24 h recalls. Supplementary materials for this article are available online.

Bayesian semiparametric regression in the presence of conditionally heteroscedastic measurement and regression errors

We consider the problem of robust estimation of the regression relationship between a response and a covariate based on sample in which precise measurements on the covariate are not available but error-prone surrogates for the unobserved covariate are available for each sampled unit. Existing methods often make restrictive and unrealistic assumptions about the density of the covariate and the densities of the regression and the measurement errors, for example, normality and, for the latter two, also homoscedasticity and thus independence from the covariate. In this article we describe Bayesian semiparametric methodology based on mixtures of B-splines and mixtures induced by Dirichlet processes that relaxes these restrictive assumptions. In particular, our models for the aforementioned densities adapt to asymmetry, heavy tails and multimodality. The models for the densities of regression and measurement errors also accommodate conditional heteroscedasticity. In simulation experiments, our method vastly outperforms existing methods. We apply our method to data from nutritional epidemiology.

Overexpression of human NR2B receptor subunit in LMAN causes stuttering and song sequence changes in adult zebra finches

Zebra finches (Taeniopygia guttata) learn to produce songs in a manner reminiscent of spoken language development in humans. One candidate gene implicated in influencing learning is the N-methyl-D-aspartate (NMDA) subtype 2B glutamate receptor (NR2B). Consistent with this idea, NR2B levels are high in the song learning nucleus LMAN (lateral magnocellular nucleus of the anterior nidopallium) during juvenile vocal learning, and decreases to low levels in adults after learning is complete and the song becomes more stereotyped. To test for the role of NR2B in generating song plasticity, we manipulated NR2B expression in LMAN of adult male zebra finches by increasing its protein levels to those found in juvenile birds, using a lentivirus containing the full-length coding sequence of the human NR2B subunit. We found that increased NR2B expression in adult LMAN induced increases in song sequence diversity and slower song tempo more similar to juvenile songs, but also increased syllable repetitions similar to stuttering. We did not observe these effects in control birds with overexpression of NR2B outside of LMAN or with the green fluorescent protein (GFP) in LMAN. Our results suggest that low NR2B subunit expression in adult LMAN is important in conserving features of stereotyped adult courtship song.

Bayesian Nonparametric Modeling of Higher Order Markov Chains

ABSTRACT We consider the problem of flexible modeling of higher order Markov chains when an upper bound on the order of the chain is known but the true order and nature of the serial dependence are unknown. We propose Bayesian nonparametric methodology based on conditional tensor factorizations, which can characterize any transition probability with a specified maximal order. The methodology selects the important lags and captures higher order interactions among the lags, while also facilitating calculation of Bayes factors for a variety of hypotheses of interest. We design efficient Markov chain Monte Carlo algorithms for posterior computation, allowing for uncertainty in the set of important lags to be included and in the nature and order of the serial dependence. The methods are illustrated using simulation experiments and real world applications. Supplementary materials for this article are available online.

Bayesian Semiparametric Mixed Effects Markov Models with Application to Vocalization Syntax

ABSTRACT Studying the neurological, genetic, and evolutionary basis of human vocal communication mechanisms using animal vocalization models is an important field of neuroscience. The datasets typically comprise structured sequences of syllables or “songs” produced by animals from different genotypes under different social contexts. It has been difficult to come up with sophisticated statistical methods that appropriately model animal vocal communication syntax. We address this need by developing a novel Bayesian semiparametric framework for inference in such datasets. Our approach is built on a novel class of mixed effects Markov transition models for the songs that accommodate exogenous influences of genotype and context as well as animal-specific heterogeneity. Crucial advantages of the proposed approach include its ability to provide insights into key scientific queries related to global and local influences of the exogenous predictors on the transition dynamics via automated tests of hypotheses. The methodology is illustrated using simulation experiments and the aforementioned motivating application in neuroscience. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

A Powerful Bayesian Test for Equality of Means in High Dimensions

ABSTRACT We develop a Bayes factor-based testing procedure for comparing two population means in high-dimensional settings. In ‘large-p-small-n” settings, Bayes factors based on proper priors require eliciting a large and complex p × p covariance matrix, whereas Bayes factors based on Jeffrey’s prior suffer the same impediment as the classical Hotelling T2 test statistic as they involve inversion of ill-formed sample covariance matrices. To circumvent this limitation, we propose that the Bayes factor be based on lower dimensional random projections of the high-dimensional data vectors. We choose the prior under the alternative to maximize the power of the test for a fixed threshold level, yielding a restricted most powerful Bayesian test (RMPBT). The final test statistic is based on the ensemble of Bayes factors corresponding to multiple replications of randomly projected data. We show that the test is unbiased and, under mild conditions, is also locally consistent. We demonstrate the efficacy of the approach through simulated and real data examples. Supplementary materials for this article are available online.

Bayesian sparse covariance decomposition with a graphical structure

We consider the problem of estimating covariance matrices of a particular structure that is a summation of a low-rank component and a sparse component. This is a general covariance structure encountered in multiple statistical models including factor analysis and random effects models, where the low-rank component relates to the correlations among variables coming from the latent factors or random effects and the sparse component displays the correlations of the remaining residuals. We propose a Bayesian method for estimating the covariance matrices of such structures by representing the covariance model in the form of a factor model with an unknown number of latent factors. We introduce binary indicators for factor selection and rank estimation for the low-rank component, combined with a Bayesian lasso method for the estimation of the sparse component. Simulation studies show that our method can recover the rank as well as the sparsity of the two respective components. We further extend our method to a latent-factor Markov graphical model, with a focus on the sparse conditional graphical model of the residuals as well as selecting the number of factors. We show through simulations that our Bayesian model can successfully recover both the number of latent factors and the Markov graphical model of the residuals.