The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform

Minghui Chen - One of the best experts on this subject based on the ideXlab platform.

  • partition weighted approach for estimating the Marginal Posterior density with applications
    Journal of Computational and Graphical Statistics, 2019
    Co-Authors: Yubo Wang, Minghui Chen, Paul O. Lewis
    Abstract:

    The computation of Marginal Posterior density in Bayesian analysis is essential in that it can provide complete information about parameters of interest. Furthermore, the Marginal Posterior density can be used for computing Bayes factors, Posterior model probabilities, and diagnostic measures. The conditional Marginal density estimator (CMDE) is theoretically the best for Marginal density estimation but requires the closed-form expression of the conditional Posterior density, which is often not available in many applications. We develop the partition weighted Marginal density estimator (PWMDE) to realize the CMDE. This unbiased estimator requires only a single MCMC output from the joint Posterior distribution and the known unnormalized Posterior density. The theoretical properties and various applications of the We carry out simulation studies to investigate the empirical performance of the PWMDE and further demonstrate the desirable features of the proposed method with two real data sets from a study of dissociative identity disorder patients and a prostate cancer study, respectively.

  • Partition Weighted Approach For Estimating the Marginal Posterior Density With Applications
    2019
    Co-Authors: Yubo Wang, Minghui Chen, Lynn Kuo, Paul O. Lewis
    Abstract:

    The computation of Marginal Posterior density in Bayesian analysis is essential in that it can provide complete information about parameters of interest. Furthermore, the Marginal Posterior density can be used for computing Bayes factors, Posterior model probabilities, and diagnostic measures. The conditional Marginal density estimator (CMDE) is theoretically the best for Marginal density estimation but requires the closed-form expression of the conditional Posterior density, which is often not available in many applications. We develop the partition weighted Marginal density estimator (PWMDE) to realize the CMDE. This unbiased estimator requires only a single Markov chain Monte Carlo output from the joint Posterior distribution and the known unnormalized Posterior density. The theoretical properties and various applications of the PWMDE are examined in detail. The PWMDE method is also extended to the estimation of conditional Posterior densities. We carry out simulation studies to investigate the empirical performance of the PWMDE and further demonstrate the desirable features of the proposed method with two real data sets from a study of dissociative identity disorder patients and a prostate cancer study, respectively. Supplementary materials for this article are available online.

  • bayesian computation from Posterior densities to bayes factors Marginal likelihoods and Posterior model probabilities
    Handbook of Statistics, 2005
    Co-Authors: Minghui Chen
    Abstract:

    Publisher Summary This chapter deals with the Bayesian computation. In Bayesian inference, a joint Posterior distribution is available through the likelihood function and a prior distribution. One way to summarize a Posterior distribution is to calculate and display Marginal Posterior densities because the Marginal Posterior densities provide complete information about parameters of interest. This chapter summarizes the current state of the art in the area of estimating Marginal and full Posterior densities and various applications of the Posterior density estimation in computing Bayes factors, Marginal likelihoods, and Posterior model probabilities. This chapter provides a most updated overview on various Monte Carlo methods for computing Marginal or full Posterior densities, including the kernel density estimation, the conditional Marginal density estimator (CMDE) the importance weighted Marginal density estimation (IWMDE), the Gibbs stopper approach, and an approach based on the Metropolis–Hastings output. Finally, the development of an efficient and practically useful Monte Carlo method for this problem is a very challenging and important future project.

  • estimating Marginal Posterior densities
    2000
    Co-Authors: Minghui Chen, Qiman Shao, Joseph G Ibrahim
    Abstract:

    In Bayesian inference, a joint Posterior distribution is available through the likelihood function and a prior distribution. One purpose of Bayesian inference is to calculate and display Marginal Posterior densities because the Marginal Posterior densities provide complete information about parameters of interest. As shown in Chapter 2, a Markov chain Monte Carlo (MCMC) sampling algorithm, such as the Gibbs sampler or a Metropolis-Hastings algorithm, can be used to draw MCMC samples from the Posterior distribution. Chapter 3 also demonstrates how we can easily obtain Posterior quantities such as Posterior means, Posterior standard deviations, and other Posterior quantities from MCMC samples. However, when a Bayesian model becomes complicated, it may be difficult to obtain a reliable estimator of a Marginal Posterior density based on the MCMC sample. A traditional method for estimating Marginal Posterior densities is kernel density estimation. Since the kernel density estimator is nonparametric, it may not be efficient. On the other hand, the kernel density estimator may not be applicable for some complicated Bayesian models. In the context of Bayesian inference, the joint Posterior density is typically known up to a normalizing constant. Using the structure of a Posterior density, a number of authors (e.g., Gelfand, Smith, and Lee 1992; Johnson 1992; Chen 1993 and 1994; Chen and Shao 1997c; Chib 1995; Verdinelli and Wasserman 1995) propose parametric Marginal Posterior density estimators based on the MCMC sample. In this chapter, we present several available Monte Carlo (MC) methods for computing Marginal Posterior density estimators, and we also discuss how well Marginal Posterior density estimation works using the Kullback—Leibler (K—L) divergence as a performance measure.

  • monte carlo estimation of bayesian credible and hpd intervals
    Journal of Computational and Graphical Statistics, 1999
    Co-Authors: Minghui Chen, Qiman Shao
    Abstract:

    Abstract This article considers how to estimate Bayesian credible and highest probability density (HPD) intervals for parameters of interest and provides a simple Monte Carlo approach to approximate these Bayesian intervals when a sample of the relevant parameters can be generated from their respective Marginal Posterior distribution using a Markov chain Monte Carlo (MCMC) sampling algorithm. We also develop a Monte Carlo method to compute HPD intervals for the parameters of interest from the desired Posterior distribution using a sample from an importance sampling distribution. We apply our methodology to a Bayesian hierarchical model that has a Posterior density containing analytically intractable integrals that depend on the (hyper) parameters. We further show that our methods are useful not only for calculating the HPD intervals for the parameters of interest but also for computing the HPD intervals for functions of the parameters. Necessary theory is developed and illustrative examples—including a si...

Siddhartha Chib - One of the best experts on this subject based on the ideXlab platform.

  • bayes inference via gibbs sampling of autoregressive time series subject to markov mean and variance shifts
    Journal of Business & Economic Statistics, 1993
    Co-Authors: Jim Albert, Siddhartha Chib
    Abstract:

    We examine autoregressive time series models that are subject to regime switching. These shifts are determined by the outcome of an unobserved two-state indicator variable that follows a Markov process with unknown transition probabilities. A Bayesian framework is developed in which the unobserved states, one for each time point, are treated as missing data and then analyzed via the simulation tool of Gibbs sampling. This method is expedient because the conditional Posterior distribution of the parameters, given the states, and the conditional Posterior distribution of the states, given the parameters, all have a form amenable to Monte Carlo sampling. The approach is straightforward and generates Marginal Posterior distributions for all parameters of interest. Posterior distributions of the states, future observations, and the residuals, averaged over the parameter space are also obtained. Several examples with real and artificial data sets and weak prior information illustrate the usefulness of the metho...

Christopher K Wikle - One of the best experts on this subject based on the ideXlab platform.

  • a bayesian adaptive ensemble kalman filter for sequential state and parameter estimation
    Monthly Weather Review, 2017
    Co-Authors: Jonathan R Stroud, Matthias Katzfuss, Christopher K Wikle
    Abstract:

    AbstractThis paper proposes new methodology for sequential state and parameter estimation within the ensemble Kalman filter. The method is fully Bayesian and propagates the joint Posterior distribution of states and parameters over time. To implement the method, the authors consider three representations of the Marginal Posterior distribution of the parameters: a grid-based approach, a Gaussian approximation, and a sequential importance sampling (SIR) approach with kernel resampling. In contrast to existing online parameter estimation algorithms, the new method explicitly accounts for parameter uncertainty and provides a formal way to combine information about the parameters from data at different time periods. The method is illustrated and compared to existing approaches using simulated and real data.

  • a bayesian adaptive ensemble kalman filter for sequential state and parameter estimation
    arXiv: Methodology, 2016
    Co-Authors: Jonathan R Stroud, Matthias Katzfuss, Christopher K Wikle
    Abstract:

    This paper proposes new methodology for sequential state and parameter estimation within the ensemble Kalman filter. The method is fully Bayesian and propagates the joint Posterior density of states and parameters over time. In order to implement the method we consider two representations of the Marginal Posterior distribution of the parameters: a grid-based approach and a Gaussian approximation. Contrary to existing algorithms, the new method explicitly accounts for parameter uncertainty and provides a formal way to combine information about the parameters from data at different time periods. The method is illustrated and compared to existing approaches using simulated and real data.

Daniel Gianola - One of the best experts on this subject based on the ideXlab platform.

  • Marginal inferences about variance components in a mixed linear model using gibbs sampling
    Genetics Selection Evolution, 1993
    Co-Authors: C S Wang, J J Rutledge, Daniel Gianola
    Abstract:

    Summary - Arguing from a Bayesian viewpoint, Gianola and Foulley (1990) derived a new method for estimation of variance components in a mixed linear model: variance estimation from integrated likelihoods (VEIL). Inference is based on the Marginal Posterior distribution of each of the variance components. Exact analysis requires numerical integration. In this paper, the Gibbs sampler, a numerical procedure for generating Marginal distributions from conditional distributions, is employed to obtain Marginal inferences about variance components in a general univariate mixed linear model. All needed conditional Posterior distributions are derived. Examples based on simulated data sets containing varying amounts of information are presented for a one-way sire model. Estimates of the Marginal densities of the variance components and of functions thereof are obtained, and the corresponding distributions are plotted. Numerical results with a balanced sire model suggest that convergence to the Marginal Posterior distributions is achieved with a Gibbs sequence length of 20, and that Gibbs sample sizes ranging from 300 - 3 000 may be needed to appropriately characterize the Marginal distributions. variance components / linear models / Bayesian methods / Marginalization / Gibbs sampler

J Chiang - One of the best experts on this subject based on the ideXlab platform.

  • studies in astronomical time series analysis vi bayesian block representations
    The Astrophysical Journal, 2013
    Co-Authors: Jeffrey D Scargle, J P Norris, Brad Jackson, J Chiang
    Abstract:

    This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors. We present a simple nonparametric modeling technique and an algorithm implementing it—an improved and generalized version of Bayesian Blocks [Scargle 1998]—that finds the optimal segmentation of the data in the observation interval. The structure of the algorithm allows it to be used in either a real-time trigger mode, or a retrospective mode. Maximum likelihood or Marginal Posterior functions to measure model fitness are presented for events, binned counts, and measurements at arbitrary times with known error distributions. Problems addressed include those connected with data gaps, variable exposure, extension to piecewise linear and piecewise exponential representations, multi-variate time series data, analysis of variance, data on the circle, other data modes, and dispersed data. Simulations provide evidence that the detection efficiency for weak signals is close to a theoretical asymptotic limit derived by [Arias-Castro, Donoho and Huo 2003]. In the spirit of Reproducible Research [Donoho et al. (2008)] all of the code and data necessary to reproduce all of the figures in this paper are included as auxiliary material.