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Generalized parallel tempering on Bayesian inverse problems

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HIERARCHICAL MARKOV CHAIN MONTE CARLO METHODS FOR BAYESIAN INVERSE PROBLEMS

Juan Pablo Madrigal Cianci

This thesis is devoted to the construction, analysis, and implementation of two types of hierarchical Markov Chain Monte Carlo (MCMC) methods for the solution of large-scale Bayesian Inverse Problems (BIP).The first hierarchical method we present is based ...

EPFL2022

MATHICSE Technical Report : Generalized Parallel Tempering on Bayesian Inverse Problems

Fabio Nobile, Juan Pablo Madrigal Cianci

In the current work we present two generalizations of the Parallel Tempering algorithm, inspired by the so-called continuous-time Infinite Swapping algorithm. Such a method, found its origins in the molecular dynamics community, and can be understood as th ...

MATHICSE2020

We present an improved analysis of the Euler-Maruyama discretization of the Langevin diffusion. Our analysis does not require global contractivity, and yields polynomial dependence on the time horizon. Compared to existing approaches, we make an additional ...

2019

Approximation of Non-decaying Signals from Shift-Invariant Subspaces

Michaël Unser, Quy Ha Nguyen

In our recent work, the sampling and reconstruction of non-decaying signals, modeled as members of weighted-L-p spaces, were shown to be stable with an appropriate choice of the generating kernel for the shift-invariant reconstruction space. In this paper, ...

2019

Vase-Kite Equilibrium of Resorcin[4]arene Cavitands Investigated Using Molecular Dynamics Simulations with Ball-and-Stick Local Elevation Umbrella Sampling

Jovana Milic

A key feature of resorcin[4]arene cavitands is their ability to switch between a closed/contracted (Vase) and an open/expanded (Kite) conformation. The mechanism and dynamics of this interconversion remains, however, elusive. In the present study, the Vase ...

2019

A novel approach is presented for constructing polynomial chaos representations of scalar quantities of interest (QoI) that extends previously developed methods for adaptation in Homogeneous Chaos spaces. In this work, we develop a Bayesian formulation of ...

ROYAL SOC2018

An Ergodic Theory of Binary Operations-Part II: Applications to Polarization

Rajai Nasser

An open problem in polarization theory is to determine the binary operations that always lead to polarization (in the general multilevel sense) when they are used in Arikan style constructions. This paper, which is presented in two parts, solves this probl ...

Institute of Electrical and Electronics Engineers2017

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Martin Vetterli, Arash Amini, Mitra Fatemi

We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of

\mathds{1}_{\{p\leq0\}}

to the image plane, where

\mathds{1}

denotes the indicator function and

p

is some r ...

2016

An Ergodic Theory of Binary Operations-Part I: Key Properties

Rajai Nasser

Ieee-Inst Electrical Electronics Engineers Inc2016

Sampling-Based Nuclear Data Uncertainty Quantification for Continuous Energy Monte Carlo Codes

Ting Zhu

The goal of the present PhD research is to establish a methodology of nuclear data uncertainty quantification (NDUQ) for MCNPX, the continuous-energy Monte-Carlo (M-C) code. The high fidelity (continuous-energy treatment and flexible geometry modelling) of ...

EPFL2015

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Martin Vetterli, Arash Amini, Mitra Fatemi

We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of

\mathds{1}_{\{p\leq0\}}

to the image plane, where

\mathds{1}

denotes the indicator function and

p

is some r ...

2016