arXiv subjects

Yasuyuki Hamura

Publications and source records attributed to Yasuyuki Hamura.

At least 19 recordsLinked to original sources

arXiv2026

Trace-Class Results for MCMC Algorithms for Student-$t$ Regression Models

In this paper, we consider MCMC algorithms for Student-$t$ regression models. In three cases, we investigate the efficiency of Markov chains based on the algorithms in terms of whether trace-class results hold or not. First, we consider the case where the parameters follow a matrix-normal-inverse-Wishart distribution and show that the Markov operator associated with a standard data augmentation algorithm is trace-class. Second, we consider the case of an improper prior and univariate outcomes. In this case, the standard Markov operator is not trace-class but the Markov operator associated with a collapsed Gibbs algorithm is trace-class. Third, we consider the case of an improper prior and multivariate outcomes. We obtain a trace-class result for a parameter expanded data augmentation algorithm which is based on a univariate working parameter. Finally, we consider the problem of numerially estimating a convergence rate of the trace-class Markov operator in the second case.

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arXiv2025

Outlier-Robust Bayesian Multivariate Analysis with Correlation-Intact Sandwich Mixture

Handling outliers is a fundamental challenge in multivariate data analysis because outliers may distort the structures of correlation or conditional independence. Although robust Bayesian inference has been extensively studied in univariate settings, theoretical results ensuring posterior robustness in multivariate models are scarce. We propose a novel scale mixture of multivariate normals called correlation-intact sandwich mixtures, in which the scale parameters are real values and follow an unfolded log-Pareto distribution. Our theoretical results on posterior robustness in multivariate settings emphasize that the use of a symmetric, super heavy-tailed distribution for scale parameters is essential for achieving posterior robustness against element-wise contamination. The posterior inference for the proposed model is feasible using the developed efficient Gibbs sampling algorithm. The superiority of the proposed method was further illustrated further in simulation and empirical studies using graphical models and multivariate regression in the presence of complex outlier structures.

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arXiv2025

Geometric Ergodicity of Gibbs Algorithms for a Normal Model With a Global-Local Shrinkage Prior

We consider Gibbs samplers for a normal linear regression model with a global-local shrinkage prior and show that they produce geometrically ergodic Markov chains. First, under the horseshoe local prior and a three-parameter beta global prior under some assumptions, we prove geometric ergodicity for a Gibbs algorithm in which it is relatively easy to update the global shrinkage parameter. Second, we consider a more general class of global-local shrinkage priors. Under milder conditions, geometric ergodicity is proved for two- and three-stage Gibbs samplers based on rejection sampling. We also construct a practical rejection sampling method in the horseshoe case. Finally, a simulation study is performed to compare proposed and existing methods.

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arXiv2025

Robust Bayesian Inference for Censored Survival Models

This paper proposes a robust Bayesian accelerated failure time model for censored survival data. We develop a new family of life-time distributions using a scale mixture of the generalized gamma distributions, where we propose a novel super heavy-tailed distribution as a mixing density. We theoretically show that, under some conditions, the proposed method satisfies the full posterior robustness, which guarantees robustness of point estimation as well as uncertainty quantification. For posterior computation, we employ an integral expression of the proposed heavy-tailed distribution to develop an efficient posterior computation algorithm based on the Markov chain Monte Carlo. The performance of the proposed method is illustrated through numerical experiments and real data example.

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arXiv2024

State-Space Modeling of Shape-constrained Functional Time Series

Functional time series data frequently appears in econometric analyses, where the functions of interest are subject to some shape constraints, including monotonicity and convexity, as typical of the estimation of the Lorenz curve. This paper proposes a state-space model for time-varying functions to extract trends and serial dependence from functional time series while imposing the shape constraints on the estimated functions. The function of interest is modeled by a convex combination of selected basis functions to satisfy the shape constraints, where the time-varying convex weights on simplex follow the dynamic multi-logit models. To enable posterior computation by an efficient Markov chain Monte Carlo method, a novel data augmentation technique is devised for the complicated likelihood of this model. The proposed method is applied to the estimation of time-varying Lorenz curves, and its utility is illustrated through numerical experiments and analysis of panel data of household incomes in Japan.

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arXiv2024

A Short Note on the Efficiency of Markov Chains for Bayesian Linear Regression Models with Heavy-Tailed Errors

In this short note, we consider posterior simulation for a linear regression model when the error distribution is given by a scale mixture of multivariate normals. We first show that the sampler of Backlund and Hobert (2020) for the case of the conditionally conjugate normal-inverse Wishart prior continues to be geometrically ergodic even when the error density is heavier-tailed. Moreover, we prove that the ergodicity is uniform by verifying the minorization condition. In the second half of this note, we treat an improper case and show that the sampler of Section 4 of Roy and Hobert (2010) is geometrically ergodic under significantly milder conditions.

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arXiv2024

An Approximate Identity Link Function for Bayesian Generalized Linear Models

In this note, we consider using a link function that has heavier tails than the usual exponential link function. We construct efficient Gibbs algorithms for Poisson and Multinomial models based on this link function by introducing gamma and inverse Gaussian latent variables and show that the algorithms generate geometrically ergodic Markov chains in simple settings. Our algorithms can be used for more complicated models with many parameters. We fit our simple Poisson model to a real dataset and confirm that the posterior distribution has similar implications to those under the usual Poisson regression model based on the exponential link function. Although less interpretable, our models are potentially more tractable or flexible from a computational point of view in some cases.

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arXiv2024

Robust Bayesian Modeling of Counts with Zero inflation and Outliers: Theoretical Robustness and Efficient Computation

Count data with zero inflation and large outliers are ubiquitous in many scientific applications. However, posterior analysis under a standard statistical model, such as Poisson or negative binomial distribution, is sensitive to such contamination. This study introduces a novel framework for Bayesian modeling of counts that is robust to both zero inflation and large outliers. In doing so, we introduce rescaled beta distribution and adopt it to absorb undesirable effects from zero and outlying counts. The proposed approach has two appealing features: the efficiency of the posterior computation via a custom Gibbs sampling algorithm and a theoretically guaranteed posterior robustness, where extreme outliers are automatically removed from the posterior distribution. We demonstrate the usefulness of the proposed method by applying it to trend filtering and spatial modeling using predictive Gaussian processes.

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arXiv2024

Posterior Robustness with Milder Conditions: Contamination Models Revisited

Robust Bayesian linear regression is a classical but essential statistical tool. Although novel robustness properties of posterior distributions have been proved recently under a certain class of error distributions, their sufficient conditions are restrictive and exclude several important situations. In this work, we revisit a classical two-component mixture model for response variables, also known as contamination model, where one component is a light-tailed regression model and the other component is heavy-tailed. The latter component is independent of the regression parameters, which is crucial in proving the posterior robustness. We obtain new sufficient conditions for posterior (non-)robustness and reveal non-trivial robustness results by using those conditions. In particular, we find that even the Student-$t$ error distribution can achieve the posterior robustness in our framework. A numerical study is performed to check the Kullback-Leibler divergence between the posterior distribution based on full data and that based on data obtained by removing outliers.

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arXiv2024

Locally Adaptive Bayesian Isotonic Regression using Half Shrinkage Priors

Isotonic regression or monotone function estimation is a problem of estimating function values under monotonicity constraints, which appears naturally in many scientific fields. This paper proposes a new Bayesian method with global-local shrinkage priors for estimating monotone function values. Specifically, we introduce half shrinkage priors for positive valued random variables and assign them for the first-order differences of function values. We also develop fast and simple Gibbs sampling algorithms for full posterior analysis. By incorporating advanced shrinkage priors, the proposed method is adaptive to local abrupt changes or jumps in target functions. We show this adaptive property theoretically by proving that the posterior mean estimators are robust to large differences and that asymptotic risk for unchanged points can be improved. Finally, we demonstrate the proposed methods through simulations and applications to a real data set.

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arXiv2023

Bayesian Shrinkage Estimation for Stratified Count Data

In this paper, we consider simultaneous estimation of Poisson parameters in situations where we can use side information in aggregated data. We use standardized squared error and entropy loss functions. Bayesian shrinkage estimators are derived based on conjugate priors. We compare the risk functions of direct estimators and Bayesian estimators with respect to different priors that are constructed based on different subsets of observations. We obtain conditions for domination and also prove minimaxity and admissibility in a simple setting.

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arXiv2023

Gibbs Sampler for Matrix Generalized Inverse Gaussian Distributions

Sampling from matrix generalized inverse Gaussian (MGIG) distributions is required in Markov Chain Monte Carlo (MCMC) algorithms for a variety of statistical models. However, an efficient sampling scheme for the MGIG distributions has not been fully developed. We here propose a novel blocked Gibbs sampler for the MGIG distributions, based on the Choleski decomposition. We show that the full conditionals of the diagonal and unit lower-triangular entries are univariate generalized inverse Gaussian and multivariate normal distributions, respectively. Several variants of the Metropolis-Hastings algorithm can also be considered for this problem, but we mathematically prove that the average acceptance rates become extremely low in particular scenarios. We demonstrate the computational efficiency of the proposed Gibbs sampler through simulation studies and data analysis.

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arXiv2023

A Simple Proof of Posterior Robustness

Conditions for Bayesian posterior robustness have been examined in recent literature. However, many of the proofs seem to be long and complicated. In this paper, we first summarize some basic lemmas that have been applied implicitly or explicitly. Then, using them, we give a simple proof of posterior robustness. Our sufficient condition is new and practically relevant.

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arXiv2022

Sparse Bayesian inference on gamma-distributed observations using shape-scale inverse-gamma mixtures

In various applications, we deal with high-dimensional positive-valued data that often exhibits sparsity. This paper develops a new class of continuous global-local shrinkage priors tailored to analyzing gamma-distributed observations where most of the underlying means are concentrated around a certain value. Unlike existing shrinkage priors, our new prior is a shape-scale mixture of inverse-gamma distributions, which has a desirable interpretation of the form of posterior mean and admits flexible shrinkage. We show that the proposed prior has two desirable theoretical properties; Kullback-Leibler super-efficiency under sparsity and robust shrinkage rules for large observations. We propose an efficient sampling algorithm for posterior inference. The performance of the proposed method is illustrated through simulation and two real data examples, the average length of hospital stay for COVID-19 in South Korea and adaptive variance estimation of gene expression data.

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arXiv2022

On Data Augmentation for Models Involving Reciprocal Gamma Functions

In this paper, we introduce a new and efficient data augmentation approach to the posterior inference of the models with shape parameters when the reciprocal gamma function appears in full conditional densities. Our approach is to approximate full conditional densities of shape parameters by using Gauss's multiplication formula and Stirling's formula for the gamma function, where the approximation error can be made arbitrarily small. We use the techniques to construct efficient Gibbs and Metropolis-Hastings algorithms for a variety of models that involve the gamma distribution, Student's $t$-distribution, the Dirichlet distribution, the negative binomial distribution, and the Wishart distribution. The proposed sampling method is numerically demonstrated through simulation studies.

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arXiv2021

Bayesian Shrinkage Approaches to Unbalanced Problems of Estimation and Prediction on the Basis of Negative Multinomial Samples

In this paper, we treat estimation and prediction problems where negative multinomial variables are observed and in particular consider unbalanced settings. First, the problem of estimating multiple negative multinomial parameter vectors under the standardized squared error loss is treated and a new empirical Bayes estimator which dominates the UMVU estimator under suitable conditions is derived. Second, we consider estimation of the joint predictive density of several multinomial tables under the Kullback-Leibler divergence and obtain a sufficient condition under which the Bayesian predictive density with respect to a hierarchical shrinkage prior dominates the Bayesian predictive density with respect to the Jeffreys prior. Third, our proposed Bayesian estimator and predictive density give risk improvements in simulations. Finally, the problem of estimating the joint predictive density of negative multinomial variables is discussed.

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arXiv2021

Bayesian Point Estimation and Predictive Density Estimation for the Binomial Distribution with a Restricted Probability Parameter

In this paper, we consider Bayesian point estimation and predictive density estimation in the binomial case. After presenting preliminary results on these problems, we compare the risk functions of the Bayes estimators based on the truncated and untruncated beta priors and obtain dominance conditions when the probability parameter is less than or equal to a known constant. The case where there are both a lower bound restriction and an upper bound restriction is also treated. Then our problems are shown to be related to similar problems in the Poisson case. Finally, numerical studies are presented.

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arXiv2021

Log-Regularly Varying Scale Mixture of Normals for Robust Regression

Linear regression with the classical normality assumption for the error distribution may lead to an undesirable posterior inference of regression coefficients due to the potential outliers. This paper considers the finite mixture of two components with thin and heavy tails as the error distribution, which has been routinely employed in applied statistics. For the heavily-tailed component, we introduce the novel class of distributions; their densities are log-regularly varying and have heavier tails than those of Cauchy distribution, yet they are expressed as a scale mixture of normal distributions and enable the efficient posterior inference by Gibbs sampler. We prove the robustness to outliers of the posterior distributions under the proposed models with a minimal set of assumptions, which justifies the use of shrinkage priors with unbounded densities for the coefficient vector in the presence of outliers. The extensive comparison with the existing methods via simulation study shows the improved performance of our model in point and interval estimation, as well as its computational efficiency. Further, we confirm the posterior robustness of our method in the empirical study with the shrinkage priors for regression coefficients.

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