arXiv subjects

Satoru Tokuda

Publications and source records attributed to Satoru Tokuda.

5 recordsLinked to original sources

arXiv2022

Intrinsic regularization effect in Bayesian nonlinear regression scaled by observed data

Occam's razor is a guiding principle that models should be simple enough to describe observed data. While Bayesian model selection (BMS) embodies it by the intrinsic regularization effect (IRE), how observed data scale the IRE has not been fully understood. In the nonlinear regression with conditionally independent observations, we show that the IRE is scaled by observations' fineness, defined by the amount and quality of observed data. We introduce an observable that quantifies the IRE, referred to as the Bayes specific heat, inspired by the correspondence between statistical inference and statistical physics. We derive its scaling relation to observations' fineness. We demonstrate that the optimal model chosen by the BMS changes at critical values of observations' fineness, accompanying the IRE's variation. The changes are from choosing a coarse-grained model to a fine-grained one as observations' fineness increases. Our findings expand an understanding of BMS's typicality when observed data are insufficient.

physics.data-an↗

arXiv2021

Bayesian inference of ion velocity distribution function from laser-induced fluorescence spectra

The velocity distribution function is a statistical description that connects particle kinetics and macroscopic parameters in many-body systems. Laser-induced fluorescence (LIF) spectroscopy is utilized to measure the local velocity distribution function in spatially inhomogeneous plasmas. However, the analytic form of such a function for the system of interest is not always clear under the intricate factors in non-equilibrium states. Here, we propose a novel approach to select the valid form of the velocity distribution function based on Bayesian statistics. We formulate the Bayesian inference of ion velocity distribution function and apply it to LIF spectra locally observed at several positions in a linear magnetized plasma. We demonstrate evaluating the spatial inhomogeneity by verifying each analytic form of the local velocity distribution function. Our approach is widely applicable to experimentally establish the velocity distribution function in plasmas and fluids, including gases and liquids.

physics.plasm-ph↗

arXiv2021

Unveiling quasiparticle dynamics of topological insulators through Bayesian modelling

Quasiparticle - a key concept to describe interacting particles - characterizes electron-electron interaction in metals (Fermi liquid) and electron pairing in superconductors. While this concept essentially relies on the simplification of hard-to-solve many-body problem into one-particle picture and residual effects, a difficulty in disentangling many-body effects from experimental quasiparticle signature sometimes hinders unveiling intrinsic low-energy dynamics, as highlighted by the fierce controversy on the origin of Dirac-band anomaly in graphene and dispersion kink in high-temperature superconductors. Here, we propose an approach to solve this fundamental problem - the Bayesian modelling of quasiparticles. We have chosen a topological insulator $\mathrm{TlBi(S,Se)_2}$ as a model system to formulate an inverse problem of quasiparticle spectra with semiparametric Bayesian analysis, and successfully extracted one-particle and many-body characteristics, i.e. the intrinsic energy gap and unusual lifetime in Dirac-quasiparticle bands. Our approach is widely applicable to clarify the quasiparticle dynamics of quantum materials.

cond-mat.mes-hall↗

arXiv2020

Bayesian Modelling of Pattern Formation from One Snapshot of Pattern

Partial differential equations (PDE) have been widely used to reproduce patterns in nature and to give insight into the mechanism underlying pattern formation. Although many PDE models have been proposed, they rely on the pre-request knowledge of physical laws and symmetries, and developing a model to reproduce a given desired pattern remains difficult. We propose a novel method, referred to as Bayesian modelling of PDE (BM-PDE), to estimate the best dynamical PDE for one snapshot of a target pattern under the stationary state without ground truth. We apply BM-PDE to nontrivial patterns,such as quasi-crystals (QCs), a double gyroid and Frank Kasper structures. By using the estimated parameters for the approximant of QCs, we successfully generate, for the first time,three-dimensional dodecagonal QCs from a PDE model. Our method works for noisy patterns and the pattern synthesised without the ground truth parameters, which are required for the application toward experimental data.

cond-mat.soft↗

arXiv2016

Simultaneous Estimation of Noise Variance and Number of Peaks in Bayesian Spectral Deconvolution

The heuristic identification of peaks from noisy complex spectra often leads to misunderstanding of the physical and chemical properties of matter. In this paper, we propose a framework based on Bayesian inference, which enables us to separate multipeak spectra into single peaks statistically and consists of two steps. The first step is estimating both the noise variance and the number of peaks as hyperparameters based on Bayes free energy, which generally is not analytically tractable. The second step is fitting the parameters of each peak function to the given spectrum by calculating the posterior density, which has a problem of local minima and saddles since multipeak models are nonlinear and hierarchical. Our framework enables the escape from local minima or saddles by using the exchange Monte Carlo method and calculates Bayes free energy via the multiple histogram method. We discuss a simulation demonstrating how efficient our framework is and show that estimating both the noise variance and the number of peaks prevents overfitting, overpenalizing, and misunderstanding the precision of parameter estimation.

physics.data-an↗