Mostrando recursos 1 - 20 de 252

  1. Variational Bayes for Functional Data Registration, Smoothing, and Prediction

    Earls, Cecilia; Hooker, Giles
    We propose a model for functional data registration that extends current inferential capabilities for unregistered data by providing a flexible probabilistic framework that 1) allows for functional prediction in the context of registration and 2) can be adapted to include smoothing and registration in one model. The proposed inferential framework is a Bayesian hierarchical model where the registered functions are modeled as Gaussian processes. To address the computational demands of inference in high-dimensional Bayesian models, we propose an adapted form of the variational Bayes algorithm for approximate inference that performs similarly to Markov Chain Monte Carlo (MCMC) sampling methods for...

  2. Data-Dependent Posterior Propriety of a Bayesian Beta-Binomial-Logit Model

    Tak, Hyungsuk; Morris, Carl N.
    A Beta-Binomial-Logit model is a Beta-Binomial model with covariate information incorporated via a logistic regression. Posterior propriety of a Bayesian Beta-Binomial-Logit model can be data-dependent for improper hyper-prior distributions. Various researchers in the literature have unknowingly used improper posterior distributions or have given incorrect statements about posterior propriety because checking posterior propriety can be challenging due to the complicated functional form of a Beta-Binomial-Logit model. We derive data-dependent necessary and sufficient conditions for posterior propriety within a class of hyper-prior distributions that encompass those used in previous studies. When a posterior is improper due to improper hyper-prior distributions, we suggest...

  3. Mixtures of $g$ -priors for analysis of variance models with a diverging number of parameters

    Wang, Min
    We consider Bayesian approaches for the hypothesis testing problem in the analysis-of-variance (ANOVA) models. With the aid of the singular value decomposition of the centered designed matrix, we reparameterize the ANOVA models with linear constraints for uniqueness into a standard linear regression model without any constraint. We derive the Bayes factors based on mixtures of $g$ -priors and study their consistency properties with a growing number of parameters. It is shown that two commonly used hyper-priors on $g$ (the Zellner-Siow prior and the beta-prime prior) yield inconsistent Bayes factors due to the presence of an inconsistency region around the null...

  4. Dynamic Chain Graph Models for Time Series Network Data

    Anacleto, Osvaldo; Queen, Catriona
    This paper introduces a new class of Bayesian dynamic models for inference and forecasting in high-dimensional time series observed on networks. The new model, called the dynamic chain graph model, is suitable for multivariate time series which exhibit symmetries within subsets of series and a causal drive mechanism between these subsets. The model can accommodate high-dimensional, non-linear and non-normal time series and enables local and parallel computation by decomposing the multivariate problem into separate, simpler sub-problems of lower dimensions. The advantages of the new model are illustrated by forecasting traffic network flows and also modelling gene expression data from transcriptional...

  5. Automated Parameter Blocking for Efficient Markov Chain Monte Carlo Sampling

    Turek, Daniel; de Valpine, Perry; Paciorek, Christopher J.; Anderson-Bergman, Clifford
    Markov chain Monte Carlo (MCMC) sampling is an important and commonly used tool for the analysis of hierarchical models. Nevertheless, practitioners generally have two options for MCMC: utilize existing software that generates a black-box “one size fits all" algorithm, or the challenging (and time consuming) task of implementing a problem-specific MCMC algorithm. Either choice may result in inefficient sampling, and hence researchers have become accustomed to MCMC runtimes on the order of days (or longer) for large models. We propose an automated procedure to determine an efficient MCMC block-sampling algorithm for a given model and computing platform. Our procedure dynamically...

  6. Bayesian Inference for Diffusion-Driven Mixed-Effects Models

    Whitaker, Gavin A.; Golightly, Andrew; Boys, Richard J.; Sherlock, Chris
    Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units, SDE driven mixed-effects models allow the quantification of both between and within individual variation. Performing Bayesian inference for such models using discrete-time data that may be incomplete and subject to measurement error is a challenging problem and is the focus of this paper. We extend a recently proposed MCMC scheme to include the SDE driven mixed-effects framework. Fundamental to our approach is the development of a novel construct that allows for...

  7. A Hierarchical Bayesian Setting for an Inverse Problem in Linear Parabolic PDEs with Noisy Boundary Conditions

    Ruggeri, Fabrizio; Sawlan, Zaid; Scavino, Marco; Tempone, Raul
    In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given prescribed initial condition. We show how to derive the joint likelihood function for the forward problem, given some measurements of the solution field subject to Gaussian noise. Given Gaussian priors for the time-dependent Dirichlet boundary values, we analytically marginalize the joint likelihood using the linearity of the equation. Our hierarchical Bayesian approach is fully implemented in an example that involves the heat equation. In this...

  8. Dependent Species Sampling Models for Spatial Density Estimation

    Jo, Seongil; Lee, Jaeyong; Müller, Peter; Quintana, Fernando A.; Trippa, Lorenzo
    We consider a novel Bayesian nonparametric model for density estimation with an underlying spatial structure. The model is built on a class of species sampling models, which are discrete random probability measures that can be represented as a mixture of random support points and random weights. Specifically, we construct a collection of spatially dependent species sampling models and propose a mixture model based on this collection. The key idea is the introduction of spatial dependence by modeling the weights through a conditional autoregressive model. We present an extensive simulation study to compare the performance of the proposed model with competitors....

  9. Latent Space Approaches to Community Detection in Dynamic Networks

    Sewell, Daniel K.; Chen, Yuguo
    Embedding dyadic data into a latent space has long been a popular approach to modeling networks of all kinds. While clustering has been done using this approach for static networks, this paper gives two methods of community detection within dynamic network data, building upon the distance and projection models previously proposed in the literature. Our proposed approaches capture the time-varying aspect of the data, can model directed or undirected edges, inherently incorporate transitivity and account for each actor’s individual propensity to form edges. We provide Bayesian estimation algorithms, and apply these methods to a ranked dynamic friendship network and world...

  10. Bayesian Functional Data Modeling for Heterogeneous Volatility

    Zhu, Bin; Dunson, David B.
    Although there are many methods for functional data analysis, less emphasis is put on characterizing variability among volatilities of individual functions. In particular, certain individuals exhibit erratic swings in their trajectory while other individuals have more stable trajectories. There is evidence of such volatility heterogeneity in blood pressure trajectories during pregnancy, for example, and reason to suspect that volatility is a biologically important feature. Most functional data analysis models implicitly assume similar or identical smoothness of the individual functions, and hence can lead to misleading inferences on volatility and an inadequate representation of the functions. We propose a novel class...

  11. Bayesian Estimation of Principal Components for Functional Data

    Suarez, Adam J.; Ghosal, Subhashis
    The area of principal components analysis (PCA) has seen relatively few contributions from the Bayesian school of inference. In this paper, we propose a Bayesian method for PCA in the case of functional data observed with error. We suggest modeling the covariance function by use of an approximate spectral decomposition, leading to easily interpretable parameters. We perform model selection, both over the number of principal components and the number of basis functions used in the approximation. We study in depth the choice of using the implied distributions arising from the inverse Wishart prior and prove a convergence theorem for the...

  12. Adapting the ABC Distance Function

    Prangle, Dennis
    Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are close enough to the observations. There has been much progress on deciding which summary statistics of the data should be used to judge closeness, but less work on how to weight them. Typically weights are chosen at the start of the algorithm which normalise the summary statistics to vary on similar scales. However these may not be appropriate in iterative ABC algorithms, where the distribution from which the parameters...

  13. Estimating the Marginal Likelihood Using the Arithmetic Mean Identity

    Pajor, Anna
    In this paper we propose a conceptually straightforward method to estimate the marginal data density value (also called the marginal likelihood). We show that the marginal likelihood is equal to the prior mean of the conditional density of the data given the vector of parameters restricted to a certain subset of the parameter space, $A$ , times the reciprocal of the posterior probability of the subset $A$ . This identity motivates one to use Arithmetic Mean estimator based on simulation from the prior distribution restricted to any (but reasonable) subset of the space of parameters. By trimming this space, regions...

  14. Towards a Multidimensional Approach to Bayesian Disease Mapping

    Martinez-Beneito, Miguel A.; Botella-Rocamora, Paloma; Banerjee, Sudipto
    Multivariate disease mapping enriches traditional disease mapping studies by analysing several diseases jointly. This yields improved estimates of the geographical distribution of risk from the diseases by enabling borrowing of information across diseases. Beyond multivariate smoothing for several diseases, several other variables, such as sex, age group, race, time period, and so on, could also be jointly considered to derive multivariate estimates. The resulting multivariate structures should induce an appropriate covariance model for the data. In this paper, we introduce a formal framework for the analysis of multivariate data arising from the combination of more than two variables (geographical units...

  15. Adaptive Empirical Bayesian Smoothing Splines

    Serra, Paulo; Krivobokova, Tatyana
    In this paper we develop and study adaptive empirical Bayesian smoothing splines. These are smoothing splines with both smoothing parameter and penalty order determined via the empirical Bayes method from the marginal likelihood of the model. The selected order and smoothing parameter are used to construct adaptive credible sets with good frequentist coverage for the underlying regression function. We use these credible sets as a proxy to show the superior performance of adaptive empirical Bayesian smoothing splines compared to frequentist smoothing splines.

  16. Bayesian Detection of Abnormal Segments in Multiple Time Series

    Bardwell, Lawrence; Fearnhead, Paul
    We present a novel Bayesian approach to analysing multiple time-series with the aim of detecting abnormal regions. These are regions where the properties of the data change from some normal or baseline behaviour. We allow for the possibility that such changes will only be present in a, potentially small, subset of the time-series. We develop a general model for this problem, and show how it is possible to accurately and efficiently perform Bayesian inference, based upon recursions that enable independent sampling from the posterior distribution. A motivating application for this problem comes from detecting copy number variation (CNVs), using data...

  17. Bayesian Endogenous Tobit Quantile Regression

    Kobayashi, Genya
    This study proposes $p$ -th Tobit quantile regression models with endogenous variables. In the first stage regression of the endogenous variable on the exogenous variables, the assumption that the $\alpha$ -th quantile of the error term is zero is introduced. Then, the residual of this regression model is included in the $p$ -th quantile regression model in such a way that the $p$ -th conditional quantile of the new error term is zero. The error distribution of the first stage regression is modelled around the zero $\alpha$ -th quantile assumption by using parametric and semiparametric approaches. Since the value of...

  18. Hierarchical Shrinkage Priors for Regression Models

    Griffin, Jim; Brown, Phil
    In some linear models, such as those with interactions, it is natural to include the relationship between the regression coefficients in the analysis. In this paper, we consider how robust hierarchical continuous prior distributions can be used to express dependence between the size but not the sign of the regression coefficients. For example, to include ideas of heredity in the analysis of linear models with interactions. We develop a simple method for controlling the shrinkage of regression effects to zero at different levels of the hierarchy by considering the behaviour of the continuous prior at zero. Applications to linear models...

  19. The General Projected Normal Distribution of Arbitrary Dimension: Modeling and Bayesian Inference

    Hernandez-Stumpfhauser, Daniel; Breidt, F. Jay; van der Woerd, Mark J.
    The general projected normal distribution is a simple and intuitive model for directional data in any dimension: a multivariate normal random vector divided by its length is the projection of that vector onto the surface of the unit hypersphere. Observed data consist of the projections, but not the lengths. Inference for this model has been restricted to the two-dimensional (circular) case, using Bayesian methods with data augmentation to generate the latent lengths and a Metropolis-within-Gibbs algorithm to sample from the posterior. We describe a new parameterization of the general projected normal distribution that makes inference in any dimension tractable, including...

  20. Bayesian Nonparametric Tests via Sliced Inverse Modeling

    Jiang, Bo; Ye, Chao; Liu, Jun S.
    We study the problem of independence and conditional independence tests between categorical covariates and a continuous response variable, which has an immediate application in genetics. Instead of estimating the conditional distribution of the response given values of covariates, we model the conditional distribution of covariates given the discretized response (aka “slices”). By assigning a prior probability to each possible discretization scheme, we can compute efficiently a Bayes factor (BF)-statistic for the independence (or conditional independence) test using a dynamic programming algorithm. Asymptotic and finite-sample properties such as power and null distribution of the BF statistic are studied, and a stepwise...

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