arXiv subjects

Kaoru Irie

Publications and source records attributed to Kaoru Irie.

At least 19 recordsLinked to original sources

arXiv2025

On non-stationarity of the Poisson gamma state space models

The Poisson-gamma state space (PGSS) models have been utilized in the analysis of non-negative integer-valued time series to sequentially obtain closed form filtering and predictive densities. In this study, we show the underlying mechanics and non-stationary properties of multi-step ahead predictive distributions for the PGSS family of models. By exploiting the non-stationary structure of the PGSS model, we establish that the predictive mean remains constant while the predictive variance diverges with the forecast horizon, a property also found in Gaussian random walk models. We show that, in the long run, the predictive distribution converges to a zero-degenerated distribution, such that both point and interval forecasts eventually converge towards zero. In doing so, we comment on the effect of hyper-parameters and the discount factor on the long-run behavior of the forecasts.

stat.ME↗

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.

stat.ME↗

arXiv2024

The Group R2D2 Shrinkage Prior for Sparse Linear Models with Grouped Covariates

Shrinkage priors are a popular Bayesian paradigm to handle sparsity in high-dimensional regression. Still limited, however, is a flexible class of shrinkage priors to handle grouped sparsity, where covariates exhibit some natural grouping structure. This paper proposes a novel extension of the $R^2$-induced Dirichlet Decomposition (R2D2) prior to accommodate grouped variable selection in linear regression models. The proposed method, called the Group R2D2 prior, employs a Dirichlet prior distribution on the coefficient of determination for each group, allowing for a flexible and adaptive shrinkage that operates at both group and individual variable levels. This approach improves the original R2D2 prior to handle grouped predictors, providing a balance between within-group dependence and group-level sparsity. We present several theoretical properties of this proposed prior distribution while also developing a Markov Chain Monte Carlo algorithm. Through simulation studies and real-data analysis, we demonstrate that our method outperforms traditional shrinkage priors in terms of both estimation accuracy, inference and prediction.

stat.ME↗

arXiv2024

Quantifying uncertainty in the numerical integration of evolution equations based on Bayesian isotonic regression

This paper presents a new Bayesian framework for quantifying discretization errors in numerical solutions of ordinary differential equations. By modelling the errors as random variables, we impose a monotonicity constraint on the variances, referred to as discretization error variances. The key to our approach is the use of a shrinkage prior for the variances coupled with variable transformations. This methodology extends existing Bayesian isotonic regression techniques to tackle the challenge of estimating the variances of a normal distribution. An additional key feature is the use of a Gaussian mixture model for the $\log$-$\chi^2_1$ distribution, enabling the development of an efficient Gibbs sampling algorithm for the corresponding posterior.

math.NA↗

arXiv2024

On the Proofs of the Predictive Synthesis Formula

Bayesian predictive synthesis is useful in synthesizing multiple predictive distributions coherently. However, the proof for the fundamental equation of the synthesized predictive density has been missing. In this technical report, we review the series of research on predictive synthesis, then fill the gap between the known results and the equation used in modern applications. We provide two proofs and clarify the structure of predictive synthesis.

stat.ME↗

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.

stat.AP↗

arXiv2024

Zero-inflated stochastic volatility model for disaggregated inflation data with exact zeros

The disaggregated time-series for the Consumer Price Index (CPI) often exhibits exact zero price changes, stemming from structural features of the data collection process. However, the currently prominent stochastic volatility model of trend-inflation is designed for aggregate measures of price inflation, where zeros rarely occur. We formulate a zero-inflated stochastic volatility model applicable to such non-stationary, real-valued, multivariate time-series data with exact zeros, which jointly specifies the dynamic zero-generating process. For posterior inference, an efficient custom P\'olya--Gamma augmented Gibbs sampler is derived. Applying the model to disaggregated CPI data in four advanced economies -- US, UK, Germany, and Japan -- we find that the zero-inflated model yields more informative estimates of time-varying trend and volatility, as it accounts for the presence of zeros and avoids underestimation. In an out-of-sample forecasting exercise, we find that the zero-inflated model delivers improved point forecasts and better calibrated interval forecasts, particularly when zero-inflation is prevalent.

stat.ME↗

arXiv2023

Sequential Bayesian Predictive Synthesis

Dynamic Bayesian predictive synthesis is a formal approach to coherently synthesizing multiple predictive distributions into a single distribution. In sequential analysis, the computation of the synthesized predictive distribution has heavily relied on the repeated use of the Markov chain Monte Carlo method. The sequential Monte Carlo method in this problem has also been studied but is limited to a subclass of linear synthesis with weight constraint but no intercept. In this study, we provide a custom, Rao-Blackwellized particle filter for the linear and Gaussian synthesis, supplemented by timely interventions by the MCMC method to avoid the problem of particle degeneracy. In an example of predicting US inflation rate, where a sudden burst is observed in 2020-2022, we confirm the slow adaptation of the predictive distribution. To overcome this problem, we propose the estimation/averaging of parameters called discount factors based on the power-discounted likelihoods, which becomes feasible due to the fast computation by the proposed method.

stat.ME↗

arXiv2023

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.

stat.ME↗

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.

stat.ME↗

arXiv2022

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.

stat.ME↗

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.

stat.ME↗

arXiv2021

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.

stat.ME↗

arXiv2021

On the relationship between beta-Bartlett and Uhlig extended processes

Stochastic volatility processes are used in multivariate time-series analysis to track time-varying patterns in covariance matrices. Uhlig extended and beta-Bartlett processes are especially convenient for analyzing high-dimensional time-series because they are conjugate with Wishart likelihoods. In this article, we show that Uhlig extended and beta-Bartlett are closely related, but not equivalent: their hyperparameters can be matched so that they have the same forward-filtered posteriors and one-step ahead forecasts, but different joint (smoothed) posterior distributions. Under this circumstance, Bayes factors can't discriminate the models and alternative approaches to model comparison are needed. We illustrate these issues in a retrospective analysis of volatilities of returns of foreign exchange rates. Additionally, we provide a backward sampling algorithm for the beta-Bartlett process, for which retrospective analysis had not been developed.

math.ST↗

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.

stat.ME↗

arXiv2020

Bayesian Dynamic Fused LASSO

The new class of Markov processes is proposed to realize the flexible shrinkage effects for the dynamic models. The transition density of the new process consists of two penalty functions, similarly to Bayesian fused LASSO in its functional form, that shrink the current state variable to its previous value and zero. The normalizing constant of the density, which is not ignorable in the posterior computation, is shown to be essentially the log-geometric mixture of double-exponential densities. This process comprises the state equation of the dynamic regression models, which is shown to be conditionally Gaussian and linear in state variables and utilize the forward filtering and backward sampling in posterior computation by Gibbs sampler. The problem of overshrinkage that is inherent in lasso is moderated by considering the hierarchical extension, which can even realize the shrinkage of horseshoe priors marginally. The new prior is compared with the standard double-exponential prior in the estimation of and prediction by the dynamic linear models for illustration. It is also applied to the time-varying vector autoregressive models for the US macroeconomic data, where we examine the (dis)similarity of the additional shrinkage effect to dynamic variable selection or, specifically, the latent threshold models.

stat.ME↗

arXiv2020

On Global-local Shrinkage Priors for Count Data

Global-local shrinkage prior has been recognized as useful class of priors which can strongly shrink small signals towards prior means while keeping large signals unshrunk. Although such priors have been extensively discussed under Gaussian responses, we intensively encounter count responses in practice in which the previous knowledge of global-local shrinkage priors cannot be directly imported. In this paper, we discuss global-local shrinkage priors for analyzing sequence of counts. We provide sufficient conditions under which the posterior mean keeps the observation as it is for very large signals, known as tail robustness property. Then, we propose tractable priors to meet the derived conditions approximately or exactly and develop an efficient posterior computation algorithm for Bayesian inference. The proposed methods are free from tuning parameters, that is, all the hyperparameters are automatically estimated based on the data. We demonstrate the proposed methods through simulation and an application to a real dataset.

stat.ME↗

arXiv2020

Shrinkage with Robustness: Log-Adjusted Priors for Sparse Signals

We introduce a new class of distributions named log-adjusted shrinkage priors for the analysis of sparse signals, which extends the three parameter beta priors by multiplying an additional log-term to their densities. The proposed prior has density tails that are heavier than even those of the Cauchy distribution and realizes the tail-robustness of the Bayes estimator, while keeping the strong shrinkage effect on noises. We verify this property via the improved posterior mean squared errors in the tail. An integral representation with latent variables for the new density is available and enables fast and simple Gibbs samplers for the full posterior analysis. Our log-adjusted prior is significantly different from existing shrinkage priors with logarithms for allowing its further generalization by multiple log-terms in the density. The performance of the proposed priors is investigated through simulation studies and data analysis.

stat.ME↗