Seminar on Bayesian Computation 

 Date: Monday Nov 13th

Time: 15:00 - 16:00 JST

In person location: ISM D222

Speaker: 矢野 恵佑, 統計数理研究所/ Keisuke Yano, Institute of Statistical Mathematics

Title: (i) Reconsidering robust spectral parameter estimation and (ii) differential-geometrical clustering of geodetic velocity vectors

Abstract: In this talk, I present my recent researches on the robust spectral parameter estimation and the clustering for the tangent bundle data. The first topic is the spectral parameter estimation based on the spectral R\‘{e}nyi divergence, the joint work with Tetsuya Takabatake. In this work, we study the spectral $\alpha$-R\‘{e}nyi divergences, which includes the Itakura--Saito divergence as a subset. Although the spectral R\‘{e}nyi divergence has been studied in past works, its statistical properties have not been thoroughly investigated. Our aim is to investigate these properties. We find a variational representation of spectral R\‘{e}nyi divergence, from which the minimum spectral R\’{e}nyi divergence estimator is shown to be robust against outliers in the frequency domain, unlike the minimum Itakura–Saito divergence estimator, and thus it delivers more stable estimate. The preprint for this work is https://arxiv.org/abs/2310.06902. The second topic is differential-geometrical clustering for geodetic velocity vectors,  the joint work with Atsushi Takahashi and Masayuki Kano. Dense Global Navigation Satellite System (GNSS) observation data have provided clearer pictures of plate motions and crustal blocks. Identifying these crustal blocks is important and has been utilized in earthquake disaster prevention assessments. As is widely recognized, the selection of crustal blocks heavily impacts on the results of block fault models. Recently, objective methods for identifying crustal block structures have been proposed. In this work, we propose yet another objective identification method utilizing the parallel translation of tangent vectors and the rotational motion by Euler vectors. By using the sum of the two dissimilarities based on the parallel translation and the rotational motion, we propose hierarchical clustering of GNSS velocity vectors. We checked our method by using the ITRF2008 plate model and the public data provided by Altamimi et al. (2012).

本発表は日本語で開催します．This presentation will be held in Japanese.

参加希望の方はフォームに登録をお願いします．Kindly register by using the links provided below.

Physical https://forms.gle/TsnbobZPvPAUQhHX6

Virtual https://us06web.zoom.us/meeting/register/tZ0tc-qvqTwiGdT5kDImjxYFSXMG2DjHBsMV

 Date: Monday Aug 28th

Time: 15:00 - 16:00 JST

In person location: ISM D222

Speaker: Björn Sprungk, Technische Universität Bergakademie Freiberg 

Title: Noise-level robust MCMC, pushforward Markov kernels, and sampling on the sphere

Abstract: In the first part of the talk we consider the phenomenon of noise-level robustness of Markov chain Monte Carlo methods. Motivated by Bayesian inference with highly informative data we analyze the performance of random walk-like Metropolis-Hastings algorithms for approximate sampling of increasingly concentrating target distributions. We focus on Gaussian proposals which use a Hessian-based approximation of the target covariance. By means of pushforward transition kernels we show that for Gaussian target measures the spectral gap of the corresponding Metropolis-Hastings algorithm is independent of the concentration of the posterior, i.e., the noise level in the observational data that is used for Bayesian inference. Moreover, by exploiting the convergence of the concentrating posteriors to their Laplace approximation we extend the analysis to non-Gaussian target measures which either concentrate around a single point or along a linear manifold. In particular, in that setting we show that the average acceptance rate as well as the expected squared jump distance of suitable Metropolis-Hastings Markov chains do not deteriorate as the posterior concentrates.

In the second part we further exploit the concept of pushforward Markov kernels and derive dimension-independent Markov chain Monte Carlo methods for approximate sampling of posterior measures defined on high-dimensional spheres. Such measures occur, for instance, naturally in Bayesian level set inversion. Assuming an angular central Gaussian prior which models antipodally-symmetric directional data we exploit existing dimension-independent samplers in the ambient Hilbert space such as the preconditioned Crank Nicolson Metropolis and the elliptical slice sampler and derive MCMC algorithms on the sphere, which inherit reversibility and spectral gap properties from samplers in linear spaces.

参加希望の方はフォームに登録をお願いします．Kindly register by using the links provided below.

Physical https://forms.gle/dfVETL1VDvqo79BW8

Virtual https://us06web.zoom.us/meeting/register/tZcuc-qpqT4qGNR82cN5S6RO6oVpWXxqecEG

 Date: Monday July 10th

Time: 15:00 - 16:00 JST

In person location: ISM D222

Speaker:  栗栖 大輔, 東京大学 / Daisuke Kurisu, University of Tokyo

Title: Model averaging and empirical likelihood for non-Euclidean data

Abstract:  In this talk, I talk about two topics on the statistical analysis of non-Euclidean data. First, we extend the notion of model averaging for conventional regression models to Frechet regression, which has Euclidean predictors and a non-Euclidean output. Specifically, we propose a cross-validation (CV) criterion to select model averaging weights and show its optimality in terms of the final prediction error. Simulation results demonstrate that the CV outperforms AIC- and BIC-type model averaging estimators.  

Second, we consider the problem on estimating the Frechet mean, which is a generalization of the conventional population mean. Specifically, we develop an asymptotic theory of empirical likelihood (EL) methods for the estimation and inference of the Frechet means of Manifold-valued data. As a main result, we show that the EL statistic with an empirical Frechet mean converge in distribution to a chi-square distribution. We also discuss several extensions of the main result.

参加希望の方はフォームに登録をお願いします．Kindly register by using the links provided below.

Physical https://forms.gle/muT1L8wE2RFFThTk6

Virtual https://us06web.zoom.us/meeting/register/tZErc-ygqTooEtO9Fa0JgHzZhAbEx4Ahgc38

 Date: Monday April 17th

Time: 15:00 - 16:00 JST

In person location: ISM 

Speaker: 仲北 祥悟, 東京大学 / Shogo Nakakita, University of Tokyo

Title: A non-asymptotic analysis of Langevin-type Monte Carlo methods for non-convex and non-smooth potentials

Abstract: This study introduces a theoretical guarantee for Langevin-type Monte Carlo methods for dissipative potentials whose weak gradients have bounded moduli of continuity. The main theorem gives a non-asymptotic upper bound for the 2-Wasserstein distance between the law of a stochastic gradient Langevin Monte Carlo algorithm and the Gibbs distribution. We apply this result to the analysis of the Langevin Monte Carlo algorithm for weakly smooth potentials and the proposal of Langevin-type algorithms for potentials without convexity or continuous differentiability.

参加希望の方はフォームに登録をお願いします．Kindly register by using the links provided below.

Physical https://forms.gle/8Cwuhsu9rFx8ER9r9

Virtual https://us06web.zoom.us/meeting/register/tZYsf-yvqzMtHNzl38bJggqoqmCQMq6uNPo2