arXiv subjects

Fumiya Iwashige

Publications and source records attributed to Fumiya Iwashige.

4 recordsLinked to original sources

arXiv2026

Bayesian mixture modeling using a mixture of finite mixtures with normalized inverse Gaussian weights

In Bayesian inference for mixture models with an unknown number of components, a finite mixture model is usually employed that assumes prior distributions for mixing weights and the number of components. This model is called a mixture of finite mixtures (MFM). As a prior distribution for the weights, a (symmetric) Dirichlet distribution is widely used for conjugacy and computational simplicity, while the selection of the concentration parameter influences posterior inference. As a robust alternative to Dirichlet weights, we present a method based on a MFM with normalized inverse Gaussian weights. The motivation is similar to the use of normalized inverse Gaussian processes instead of Dirichlet processes in nonparametric Bayesian statistics. Introducing latent variables, the posterior computation is carried out using blocked Gibbs sampling without using the reversible jump algorithm. We also consider extensions to dynamic MFMs after clarifying the relationship with telescoping sampling. The performance of the proposed method is illustrated through some numerical experiments and real data examples, including clustering, density estimation, and community detection. Supplementary materials for this article are available online.

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arXiv2026

Bayesian Modeling of the Stochastic Block Model for Weighted Network Data with Zero-Inflated Negative Binomial Distribution

Weighted networks encode not only the presence of interactions but also their strength. Existing methods for weighted network community detection often rely on Poisson models, which can be restrictive for overdispersed data and make efficient posterior computation difficult when covariates are incorporated. We propose Bayesian stochastic block models based on the zero-inflated negative binomial distribution: ZINB-SBM without covariates and CZINB-SBM with pairwise covariates. The proposed models accommodate overdispersion, naturally account for missing interactions through zero inflation, and admit efficient Gibbs sampling. In CZINB-SBM, Pólya-Gamma data augmentation enables posterior inference for regression coefficients with uncertainty quantification. We further employ a dynamic mixture of finite mixtures, which allows the number of communities to be inferred from the data and can lead to more accurate clustering. Simulation studies show that ZINB-SBM is more robust than a zero-inflated Poisson SBM for highly overdispersed networks. Real data analysis demonstrates interpretable block specific covariate effects and substantially improved missing link prediction compared with a Poisson regression-based Bayesian SBM.

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arXiv2025

On Misspecified Error Distributions in Bayesian Functional Clustering: Consequences and Remedies

Nonparametric Bayesian approaches provide a flexible framework for clustering without pre-specifying the number of groups, yet they are well known to overestimate the number of clusters, especially for functional data. We show that a fundamental cause of this phenomenon lies in misspecification of the error structure: errors are conventionally assumed to be independent across observed points in Bayesian functional models. Through high-dimensional clustering theory, we demonstrate that ignoring the underlying correlation leads to excess clusters regardless of the flexibility of prior distributions. Guided by this theory, we propose incorporating the underlying correlation structures via Gaussian processes and also present its scalable approximation with principled hyperparameter selection. Numerical experiments illustrate that even simple clustering based on Dirichlet processes performs well once error dependence is properly modeled.

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arXiv2023

Bayesian Boundary Trend Filtering

Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This paper develops a Bayesian trend filtering for estimating the boundary trend. To this end, the truncated multivariate normal working likelihood and global-local shrinkage priors based on the scale mixtures of normal distribution are introduced. In particular, well-known horseshoe prior for difference leads to locally adaptive shrinkage estimation for boundary trend. However, the full conditional distributions of the Gibbs sampler involve high-dimensional truncated multivariate normal distribution. To overcome the difficulty of sampling, an approximation of truncated multivariate normal distribution is employed. Using the approximation, the proposed models lead to an efficient Gibbs sampling algorithm via the Pólya-Gamma data augmentation. The proposed method is also extended by considering a nearly isotonic constraint. The performance of the proposed method is illustrated through some numerical experiments and real data examples.

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