Bayesian semiparametric Markov renewal mixed models for vocalization syntax.

Speech and language play an important role in human vocal communication. Studies have shown that vocal disorders can result from genetic factors. In the absence of high-quality data on humans, mouse vocalization experiments in laboratory settings have been proven useful in providing valuable insights into mammalian vocal development, including especially the impact of certain genetic mutations. Such data sets usually consist of categorical syllable sequences along with continuous intersyllable interval (ISI) times for mice of different genotypes vocalizing under different contexts. ISIs are of particular importance as increased ISIs can be an indication of possible vocal impairment. Statistical methods for properly analyzing ISIs along with the transition probabilities have however been lacking. In this article, we propose a class of novel Markov renewal mixed models that capture the stochastic dynamics of both state transitions and ISI lengths. Specifically, we model the transition dynamics and the ISIs using Dirichlet and gamma mixtures, respectively, allowing the mixture probabilities in both cases to vary flexibly with fixed covariate effects as well as random individual-specific effects. We apply our model to analyze the impact of a mutation in the Foxp2 gene on mouse vocal behavior. We find that genotypes and social contexts significantly affect the length of ISIs but, compared to previous analyses, the influences of genotype and social context on the syllable transition dynamics are weaker.

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.

Bayesian Semiparametric Longitudinal Inverse-Probit Mixed Models for Category Learning.

Understanding how the adult human brain learns novel categories is an important problem in neuroscience. Drift-diffusion models are popular in such contexts for their ability to mimic the underlying neural mechanisms. One such model for gradual longitudinal learning was recently developed in Paulon et al. (J Am Stat Assoc 116:1114-1127, 2021). In practice, category response accuracies are often the only reliable measure recorded by behavioral scientists to describe human learning. Category response accuracies are, however, often the only reliable measure recorded by behavioral scientists to describe human learning. To our knowledge, however, drift-diffusion models for such scenarios have never been considered in the literature before. To address this gap, in this article, we build carefully on Paulon et al. (J Am Stat Assoc 116:1114-1127, 2021), but now with latent response times integrated out, to derive a novel biologically interpretable class of 'inverse-probit' categorical probability models for observed categories alone. However, this new marginal model presents significant identifiability and inferential challenges not encountered originally for the joint model in Paulon et al. (J Am Stat Assoc 116:1114-1127, 2021). We address these new challenges using a novel projection-based approach with a symmetry-preserving identifiability constraint that allows us to work with conjugate priors in an unconstrained space. We adapt the model for group and individual-level inference in longitudinal settings. Building again on the model's latent variable representation, we design an efficient Markov chain Monte Carlo algorithm for posterior computation. We evaluate the empirical performance of the method through simulation experiments. The practical efficacy of the method is illustrated in applications to longitudinal tone learning studies.

Functional connectivity across the human subcortical auditory system using an autoregressive matrix-Gaussian copula graphical model approach with partial correlations.

The auditory system comprises multiple subcortical brain structures that process and refine incoming acoustic signals along the primary auditory pathway. Due to technical limitations of imaging small structures deep inside the brain, most of our knowledge of the subcortical auditory system is based on research in animal models using invasive methodologies. Advances in ultrahigh-field functional magnetic resonance imaging (fMRI) acquisition have enabled novel noninvasive investigations of the human auditory subcortex, including fundamental features of auditory representation such as tonotopy and periodotopy. However, functional connectivity across subcortical networks is still underexplored in humans, with ongoing development of related methods. Traditionally, functional connectivity is estimated from fMRI data with full correlation matrices. However, partial correlations reveal the relationship between two regions after removing the effects of all other regions, reflecting more direct connectivity. Partial correlation analysis is particularly promising in the ascending auditory system, where sensory information is passed in an obligatory manner, from nucleus to nucleus up the primary auditory pathway, providing redundant but also increasingly abstract representations of auditory stimuli. While most existing methods for learning conditional dependency structures based on partial correlations assume independently and identically Gaussian distributed data, fMRI data exhibit significant deviations from Gaussianity as well as high-temporal autocorrelation. In this paper, we developed an autoregressive matrix-Gaussian copula graphical model (ARMGCGM) approach to estimate the partial correlations and thereby infer the functional connectivity patterns within the auditory system while appropriately accounting for autocorrelations between successive fMRI scans. Our results show strong positive partial correlations between successive structures in the primary auditory pathway on each side (left and right), including between auditory midbrain and thalamus, and between primary and associative auditory cortex. These results are highly stable when splitting the data in halves according to the acquisition schemes and computing partial correlations separately for each half of the data, as well as across cross-validation folds. In contrast, full correlation-based analysis identified a rich network of interconnectivity that was not specific to adjacent nodes along the pathway. Overall, our results demonstrate that unique functional connectivity patterns along the auditory pathway are recoverable using novel connectivity approaches and that our connectivity methods are reliable across multiple acquisitions.

Individual differences in working memory impact the trajectory of non-native speech category learning.

What is the role of working memory over the course of non-native speech category learning? Prior work has predominantly focused on how working memory might influence learning assessed at a single timepoint. Here, we substantially extend this prior work by examining the role of working memory on speech learning performance over time (i.e., over several months) and leverage a multifaceted approach that provides key insights into how working memory influences learning accuracy, maintenance of knowledge over time, generalization ability, and decision processes. We found that the role of working memory in non-native speech learning depends on the timepoint of learning and whether individuals learned the categories at all. Among learners, across all stages of learning, working memory was associated with higher accuracy as well as faster and slightly more cautious decision making. Further, while learners and non-learners did not have substantially different working memory performance, learners had faster evidence accumulation and more cautious decision thresholds throughout all sessions. Working memory may enhance learning by facilitating rapid category acquisition in initial stages and enabling faster and slightly more careful decision-making strategies that may reduce the overall effort needed to learn. Our results have important implications for developing interventions to improve learning in naturalistic language contexts.

Bayesian Semiparametric Longitudinal Drift-Diffusion Mixed Models for Tone Learning in Adults.

Understanding how adult humans learn nonnative speech categories such as tone information has shed novel insights into the mechanisms underlying experience-dependent brain plasticity. Scientists have traditionally examined these questions using longitudinal learning experiments under a multi-category decision making paradigm. Drift-diffusion processes are popular in such contexts for their ability to mimic underlying neural mechanisms. Motivated by these problems, we develop a novel Bayesian semiparametric inverse Gaussian drift-diffusion mixed model for multi-alternative decision making in longitudinal settings. We design a Markov chain Monte Carlo algorithm for posterior computation. We evaluate the method's empirical performances through synthetic experiments. Applied to our motivating longitudinal tone learning study, the method provides novel insights into how the biologically interpretable model parameters evolve with learning, differ between input-response tone combinations, and differ between well and poorly performing adults. supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Bayesian Copula Density Deconvolution for Zero-Inflated Data in Nutritional Epidemiology.

Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected in the form of 24-hour recalls of the intakes, which show marked patterns of conditional heteroscedasticity. Significantly compounding the challenges, the recalls for episodically consumed dietary components also include exact zeros. The problem of estimating the density of the latent long-time intakes from their observed measurement error contaminated proxies is then a problem of deconvolution of densities with zero-inflated data. We propose a Bayesian semiparametric solution to the problem, building on a novel hierarchical latent variable framework that translates the problem to one involving continuous surrogates only. Crucial to accommodating important aspects of the problem, we then design a copula based approach to model the involved joint distributions, adopting different modeling strategies for the marginals of the different dietary components. We design efficient Markov chain Monte Carlo algorithms for posterior inference and illustrate the efficacy of the proposed method through simulation experiments. Applied to our motivating nutritional epidemiology problems, compared to other approaches, our method provides more realistic estimates of the consumption patterns of episodically consumed dietary components.

Comparing perceptual category learning across modalities in the same individuals.

Category learning is a fundamental process in human cognition that spans the senses. However, much still remains unknown about the mechanisms supporting learning in different modalities. In the current study, we directly compared auditory and visual category learning in the same individuals. Thirty participants (22 F; 18-32 years old) completed two unidimensional rule-based category learning tasks in a single day - one with auditory stimuli and another with visual stimuli. We replicated the results in a second experiment with a larger online sample (N = 99, 45 F, 18-35 years old). The categories were identically structured in the two modalities to facilitate comparison. We compared categorization accuracy, decision processes as assessed through drift-diffusion models, and the generalizability of resulting category representation through a generalization test. We found that individuals learned auditory and visual categories to similar extents and that accuracies were highly correlated across the two tasks. Participants had similar evidence accumulation rates in later learning, but early on had slower rates for visual than auditory learning. Participants also demonstrated differences in the decision thresholds across modalities. Participants had more categorical generalizable representations for visual than auditory categories. These results suggest that some modality-general cognitive processes support category learning but also suggest that the modality of the stimuli may also affect category learning behavior and outcomes.

Polymer molecular weight-dependent unusual fluorescence probe behavior within 1-butyl-3-methylimidazolium hexafluorophosphate+poly(ethylene glycol).

Poly(ethylene glycols) (PEGs) and room-temperature ionic liquids (ILs) are both projected as possible alternatives to volatile organic compounds (VOCs). Their potential usage in chemical applications, however, is often hampered by their limited and, in some cases, undesired individual physicochemical properties. Properties of mixtures of PEG with a common IL 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6]) are assessed via responses of three fluorescence probes: pyrene (Py) and pyrene-1-carboxaldehyde (PyCHO) are the dipolarity sensing probes and 1,3-bis-(1-pyrenyl) propane (BPP) is the probe for microfluidity. All three probes demonstrate anomalous fluorescence behavior within the mixture of [bmim][PF6] with four different PEGs of average molecular weight (MW) 200, 400, 600, and 1500 g.mol(-1), respectively, across complete composition range. Cybotactic region dipolarity of the probe Py within the mixtures is observed to be higher than that expected from ideal additive behavior. PyCHO lowest energy fluorescence maxima implying the static dielectric constant around the cybotactic region shows values within the mixtures to be even higher than that in neat PEG, the component having higher static dielectric constant of the two, clearly indicating the milieu to have anomalously high dipolarity. "Hyperpolarity" inherent to the PEG+[bmim][PF6] mixture is confirmed. Intramolecular excimer-to-monomer fluorescence intensity ratio of BPP indicates the microfluidity within the mixture to be even lower than that within neat [bmim][PF6], the component with lowest microfluidity. Presence of strong solvent-solvent interactions within the mixture is proposed to be the major reason for the anomalous fluorescence probe responses. Specifically, extensive hydrogen-bonded network involving termini hydroxyls of PEGs and PF6- as well as ethoxy/hydroxyl oxygens of PEGs and the C2-H of bmim+ is proposed to be responsible for the unusual outcomes. Fluorescence probe responses are shown to be adequately predicted by a four-parameter simplified combined nearly ideal binary solvent/Redlich-Kister (CNIBS/R-K) model. Unusually altered physicochemical properties are demonstrated to be the key feature of the "hybrid green" PEG+IL systems.

Multiprobe spectroscopic investigation of molecular-level behavior within aqueous 1-butyl-3-methylimidazolium tetrafluoroborate.

In this work, an array of molecular-level solvent features--including solute--solvent/solvent--solvent interactions, dipolarity, heterogeneity, dynamics, probe accessibility, and diffusion--were investigated across the entire composition of ambient mixtures containing the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate, [bmim][BF4], and pH 7.0 phosphate buffer, based on results assembled for nine different molecular probes utilized in a range of spectroscopic modes. These studies uncovered interesting and unusual solvatochromic probe behavior within this benchmark mixture. Solvatochromic absorbance probes--a water-soluble betaine dye (betaine dye 33), N,N-diethyl-4-nitroaniline, and 4-nitroaniline--were employed to determine ET (a blend of dipolarity/polarizability and hydrogen bond donor contributions) and the Kamlet-Taft indices pi* (dipolarity/polarizability), alpha (hydrogen bond donor acidity), and beta (hydrogen bond acceptor basicity) characterizing the [bmim][BF4] + phosphate buffer system. These parameters each showed a marked deviation from ideality, suggesting selective solvation of the individual probe solutes by [bmim][BF4]. Similar conclusions were derived from the responses of the fluorescent polarity-sensitive probes pyrene and pyrene-1-carboxaldehyde. Importantly, the fluorescent microfluidity probe 1,3-bis(1-pyrenyl)propane senses a microviscosity within the mixture that significantly exceeds expectations derived from simple interpolation of the behavior in the neat solvents. On the basis of results from this probe, a correlation between microviscosity and bulk viscosity was established; pronounced solvent-solvent hydrogen-bonding interactions were implicit in this behavior. The greatest deviation from ideal additive behavior for the probes studied herein was consistently observed to occur in the buffer-rich regime. Nitromethane-based fluorescence quenching of pyrene within the [bmim][BF4] + phosphate buffer system showed unusual compliance with a "sphere-of-action" quenching model, a further manifestation of the microheterogeneity of the system. Fluorescence correlation spectroscopic results for both small (BODIPY FL) and macromolecular (Texas Red-10 kDa dextran conjugate) diffusional probes provide additional evidence in support of microphase segregation inherent to aqueous [bmim] [BF4].

Functional Logistic Mixed-Effects Models for Learning Curves From Longitudinal Binary Data.

Purpose We present functional logistic mixed-effects models (FLMEMs) for estimating population and individual-level learning curves in longitudinal experiments. Method Using functional analysis tools in a Bayesian hierarchical framework, the FLMEM captures nonlinear, smoothly varying learning curves, appropriately accommodating uncertainty in various aspects of the analysis while also borrowing information across different model layers. An R package implementing our method is available as part of the Supplemental Materials . Results Application to speech learning data from Reetzke, Xie, Llanos, and Chandrasekaran (2018) and a simulation study demonstrate the utility of FLMEM and its many advantages over linear and logistic mixed-effects models. Conclusion The FLMEM is highly flexible and efficient in improving upon the practical limitations of linear models and logistic linear mixed-effects models. We expect the FLMEM to be a useful addition to the speech, language, and hearing scientist's toolkit. Supplemental Material https://doi.org/10.23641/asha.7822568.

Unusual solvatochromism within 1-butyl-3-methylimidazolium hexafluorophosphate + poly(ethylene glycol) mixtures.

Hybrid "green" solvent systems composed of room-temperature ionic liquids (ILs) and poly(ethylene glycols) (PEGs) may have enormous future potential. Solvatochromic absorbance probe behavior is used to assess the physicochemical properties of the mixture composed of IL 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF(6)]) and PEG (average molecular weights of 200, 400, 600, and 1500) at ambient conditions. Lowest energy intramolecular charge-transfer absorbance maxima of a betaine dye, i.e., E(T)(N), indicates the dipolarity/polarizability and/or hydrogen-bond donating (HBD) acidity of the [bmim][PF 6] + PEG mixtures to be even higher than that of neat [bmim][PF(6)], the solution component with higher dipolarity/polarizability and/or HBD acidity. Dipolarity/polarizability (pi*) obtained separately from the electronic absorbance response of probe N, N-diethyl-4-nitroaniline shows a trend similar to E(T)(N ) thus confirming the unusually high dipolarity/polarizability of the [bmim][PF(6)] + PEG mixtures. Similar to E(T)(N ) and pi*, the HBD acidity (alpha) of [bmim][PF(6)] + PEG mixtures is also observed to be anomalously high. Contrary to what is observed for E(T)(N ), pi*, and alpha, the hydrogen-bond accepting (HBA) basicity (beta) of the [bmim][PF(6)] + PEG mixtures is observed to be lower than that predicted from ideal additive behavior indicating diminished HBA basicity of the mixture as compared to its neat components. A four-parameter simplified combined nearly ideal binary solvent/Redlich-Kister (CNIBS/R-K) equation is shown to satisfactorily predict the solvatochromic parameters within [bmim][PF(6)] + PEG mixtures. It is demonstrated that [bmim][PF(6)] + PEG mixtures possess physicochemical properties that are superior to those of either the neat IL or the neat PEG.

Multiprobe spectroscopic evidence for "hyperpolarity" within 1-butyl-3-methylimidazolium hexafluorophosphate mixtures with tetraethylene glycol.

A hybrid, potentially green solvent system composed of tetraethylene glycol (TEG) and the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF(6)]) was investigated across all mole fractions with regard to the solvent properties of the mixture. For this purpose, a suite of absorbance- and fluorescence-based solvatochromic probes were utilized to explore solute-solvent and solvent-solvent interactions existing within the [bmim][PF(6)] + TEG system. These studies revealed an interesting and unusual synergistic solvent effect. In particular, a remarkable "hyperpolarity" was observed in which the E(T) value, comprising dipolarity/polarizability and hydrogen bond donor (HBD) acidity contributions, at intermediate mole fractions of the binary mixture well exceeded that of the most polar pure component (i.e., [bmim][PF(6)]). Independently determined dipolarity/polarizability (pi*) and HBD acidity (alpha) Kamlet-Taft values for the [bmim][PF(6)] + TEG mixtures were also observed to be anomalously high at intermediate mole fractions, whereas hydrogen bond acceptor (HBA) basicities (beta values) were much more in line with the ideal arithmetic values predicted on a mole fraction basis. Two well-established fluorescent polarity probes (pyrene and pyrene-1-carboxaldehyde) further illustrated notable hyperpolarity within [bmim][PF(6)] + TEG mixtures. Moreover, the steady-state fluorescence anisotropy of the molecular rotor rhodamine 6G and the excimer-to-monomer fluorescence ratio exhibited by the fluidity probe 1,3-bis-(1-pyrenyl)propane demonstrated that solute rotation and microfluidity within the [bmim][PF(6)] + TEG mixture were significantly reduced compared with expectations based on simple solvent mixing. A solvent ordering via formation of HBD/HBA complexes involving the C-2 proton of the [bmim(+)] cation and oxygen atoms of TEG, as well as interactions between [PF(6)(-)] and the terminal hydroxyl groups of TEG, is proposed to account for the observed behavior. Further spectroscopic evidence of strong intersolvent interactions occurring within the [bmim][PF(6)] + TEG mixture was provided, inter alia, by substantial frequency shifts in the [PF(6)(-)] asymmetric stretching mode observed in the infrared spectra as TEG was incrementally added to [bmim][PF(6)]. Overall, our observations contribute to a growing literature advocating the notion that ionic liquids and certain organic solvents form ordered, nanostructured, or microsegregated phases upon mixing.

A Powerful Bayesian Test for Equality of Means in High Dimensions.

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 T 2 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.

Bayesian Semiparametric Multivariate Density Deconvolution.

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 hour recalls. Supplementary Material presents substantive additional details.

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.

Efficient precipitation of dyes from dilute aqueous solutions of ionic liquids.

The addition of only approximately 1.7 wt% (approximately 0.06 M) ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate to aqueous solutions of six popular cationic dyes resulted in the precipitation of almost all of the dye from the solution.

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.

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.

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, e.g., 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 data set and R programs implementing our methods are included as part of online supplemental materials.