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Massively Parallel Signature Sequencing (MPSS) is a high-throughput, counting-based technology available for gene expression profiling. It produces output that is similar to Serial Analysis of Gene Expression and is ideal for building complex relational databases for gene expression. Our goal is to compare the in vivo global gene expression profiles of tissues infected with different Strains of Salmonella obtained using the MPSS technology. In this article, we develop an exact ANOVA type model for this count data using a zero-inflated Poisson distribution, different from existing methods that assume continuous densities. We adopt two Bayesian hierarchical models--one parametric and the other semiparametric with a Dirichlet process prior that has the ability to 'borrow strength' across related signatures, where a signature is a specific arrangement of the nucleotides, usually 16-21 base pairs long. We utilize the discreteness of Dirichlet process prior to cluster signatures that exhibit similar differential expression profiles. Tests for differential expression are carried out using nonparametric approaches, while controlling the false discovery rate. We identify several differentially expressed genes that have important biological significance and conclude with a summary of the biological discoveries. This article has supplementary materials online. KEY WORDS: Bayesian semiparametric modeling; Dirichlet process mixture; Markov chain Monte Carlo; Zero-inflated Poisson.

Proteins have two types of regions: linker regions that connect active domains and nonlinker regions, which include domains and terminal residues. It is important to try to distinguish these regions using information in the sequence of amino acids that, when folded, form the protein. In this article we develop a nonstationary hidden Markov model to infer region boundaries. The approach is based on a latent variable defined on the sequence: this variable is a continuous index of the region type and affects the probabilities that specific amino acids will appear. We develop an efficient Bayesian estimate of the model using Markov chain Monte Carlo methods, particularly Gibbs sampling, to simulate the parameters from the posteriors. We apply our method to protein sequences with domains and interdomain linkers delineated using the Pfam-A database. The prediction results are superior to simpler methods. Importantly, our method estimates the probability that each amino acid belongs to a linker region, giving insight into the properties of interdomain linkers. KEY WORDS: Bayesian model; Interdomain linker; Markov chain Monte Carlo; Nonstationary hidden Markov model; Protein structure prediction.

We propose Bayesian parametric and semiparametric partially linear regression methods to analyze the outcome-dependent follow-up data when the random time of a follow-up measurement of an individual depends on the history of both observed longitudinal outcomes and previous measurement times. We begin with the investigation of the simplifying assumptions of Lipsitz, Fitzmaurice, Ibrahim, Gelber, and Lipshultz, and present a new model for analyzing such data by allowing subject-specific correlations for the longitudinal response and by introducing a subject-specific latent variable to accommodate the association between the longitudinal measurements and the follow-up times. An extensive simulation study shows that our Bayesian partially linear regression method facilitates accurate estimation of the true regression line and the regression parameters. We illustrate our new methodology using data from a longitudinal observational study. KEY WORDS: Bayesian cubic smoothing spline; Latent variable; Partially linear model.

We propose classification models for binary and multicategory data where the predictor is a random function. We use Bayesian modeling with wavelet basis functions that have nice approximation properties over a large class of functional spaces and can accommodate a wide variety of functional forms observed in real life applications. We develop an unified hierarchical model to encompass both the adaptive wavelet-based function estimation model and the logistic classification model. We couple together these two models are to borrow strengths from each other in a unified hierarchical framework. The use of Gibbs sampling with conjugate priors for posterior inference makes the method computationally feasible. We compare the performance of the proposed model with other classification methods, such as the existing naive plug-in methods, by analyzing simulated and real data sets. KEY WORDS: Functional data; Logit link; Markov chain Monte Carlo; Wavelet transformation.

In many problems in geostatistics the response variable of interest is strongly related to the underlying geology of the spatial location. In these situations there is often little correlation in the responses found in different rock strata, so the underlying covariance structure shows sharp changes at the boundaries of the rock types. Conventional stationary and nonstationary spatial methods are inappropriate, because they typically assume that the covariance between points is a smooth function of distance. In this article we propose a generic method for the analysis of spatial data with sharp changes in the underlying covariance structure. Our method works by automatically decomposing the spatial domain into disjoint regions within which the process is assumed to be stationary, but the data are assumed independent across regions. Uncertainty in the number of disjoint regions, their shapes, and the model within regions is dealt with in a fully Bayesian fashion. We illustrate our approach on a previously unpublished dataset relating to soil permeability of the Schneider Buda oil field in Wood County, Texas. KEY WORDS: Bayes factor: Kriging: Model averaging: Reversible-jump Markov chain Monte Carlo; Voronoi tessellation.

This article considers Bayesian analysis of matched case-control problems when one of the covariates is partially missing. Within the likelihood context, the standard approach to this problem is to posit a fully parametric model among the controls for the partially missing covariate as a function of the covariates in the model and the variables making up the strata. Sometimes the strata effects are ignored at this stage. Our approach differs not only in that it is Bayesian, but, far more importantly, in the manner in which it treats the strata effects. We assume a Dirichlet process prior with a normal base measure for the stratum effects and estimate all of the parameters in a Bayesian framework. Three matched case-control examples and a simulation study are considered to illustrate our methods and the computing scheme. KEY WORDS: Case-control studies; Conditional inference; Dirichlet process; Endometrial cancer; Equine epidemiology; Exponential family; Low birth weight study; Matching; Metropolis-Hastings; Missing data; Retrospective studies.

The mode of allocating a plant's biomass to reproductive and other life processes is examined using a truncated regression model. Information from 542 goldenrod plants are used for the statistical analysis. Results show that reproductive threshold for siblings tend to be larger than that for clones. In addition, it was found that flowering can only happen if reproductive mass is achieved., 1. INTRODUCTION Biological variables are often constrained to a limited range; for example, in most organisms size measurements are positive but can not increase indefinitely. Moreover, in studying the regression [...]

The characterization of expert opinions in a decision-making framework is explored. Specifically, a supra Bayesian approach is used to collect opinion on a univariate unknown, theta. The opinion is modelled as a partial probabilistic specification and viewed as data to obtain probability densities. The latter is derived via the 'transformation of random mixtures of beta distributions' after which they are converted into likelihoods., 1. INTRODUCTION Expert opinion is often sought with regard to unknowns in a decision-making setting to improve the quality of the decision-making process. We presume that this opinion pertains to [...]

In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets under-utilized in determining the joint dependency structure. In this article, we consider a Bayesian approach to model undirected graphs underlying heterogeneous multivariate observations with additional assistance from covariates. Building on product partition models, we propose a novel covariate-dependent Gaussian graphical model that allows graphs to vary with covariates so that observations whose covariates are similar share a similar undirected graph. To efficiently embed Gaussian graphical models into our proposed framework, we explore both Gaussian likelihood and pseudo-likelihood functions. For Gaussian likelihood, a G-Wishart distribution is used as a natural conjugate prior, and for the pseudo-likelihood, a product of Gaussianconditionals is used. Moreover, the proposed model has large prior support and is flexible to approximate any v -Hölder conditional variance-covariance matrices with v ∈ ( 0,1 ] . We further show that based on the theory of fractional likelihood, the rate of posterior contraction is minimax optimal assuming the true density to be a Gaussian mixture with a known number of components. The efficacy of the approach is demonstrated via simulation studies and an analysis of a protein network for a breast cancer dataset assisted by mRNA gene expression as covariates., Competing Interests: Conflict of Interest There are no conflict of interests to declare.

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.

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.

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.

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data.