State-dependent swap strategies and automatic reduction of number of temperatures in adaptive parallel tempering algorithm

źącki, Mateusz Krzysztof; Miasojedow, Błażej

doi:10.1007/s11222-015-9579-0

Cited by 14 publications

(16 citation statements)

References 29 publications

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“…To illustrate the properties of RAmPART, we considered two established benchmark problems: Gaussian mixture distributions ( Łącki and Miasojedow, 2016 ) and blurred rings ( Kramer, 2016 ). We studied a 20-dimensional Gaussian mixture distribution with two modes,

and a 20-dimensional blurred ring,

with

.…”

Section: Resultsmentioning

confidence: 99%

“…PT algorithms construct a Markov-chain on a product space

where L is the number of temperature levels ( Łącki and Miasojedow, 2016 ; Vousden et al , 2016 ). The target distribution on the product space is defined as the product of tempered posterior distributions,

with temperatures

, such that

.…”

Section: Methodsmentioning

confidence: 99%

“…In principle, different approaches could be employed to determine such regions, including the use of information obtained in a preceding multi-start local optimization. RAmPART runs an PT algorithm ( Ballnus et al , 2017 ; Łącki and Miasojedow, 2016 ; Vousden et al , 2016 ), which uses an adaptive Gaussian proposal for the random walk steps ( Fig. 1a ), an adjacent proposal for random swaps and temperature adaptation following ( Vousden et al , 2016 ).…”

Section: Methodsmentioning

confidence: 99%

“…For

updates of local mean and covariance are given by

with adaptation strength

, with

, and initial value obtained computed in the warm-up phase,

. The scaling factors for regional and global covariance are adapted to achieve an acceptance rate of 23.4% ( Haario et al , 2001 ; Łącki and Miasojedow, 2016 ):

with

.…”

Section: Methodsmentioning

confidence: 99%

“…All of these different concepts boosted the sampling performance of MCMC methods, but the auto-correlation for posteriors with multiple modes usually remains high ( Ballnus et al , 2017 ). To address this, multi-chain algorithms such as Parallel Tempering (PT; Łącki and Miasojedow, 2016 ; Miasojedow et al , 2013 ; Sambridge, 2013 ; Vousden et al , 2016 ) and Parallel Hierarchical Sampling ( Hug et al , 2013 ; Rigat and Mira, 2012 ) have been introduced. These algorithms aim to improve mixing by increasing the frequency of jumps between modes and the exploration of tails.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian parameter estimation for biochemical reaction networks using region-based adaptive parallel tempering

et al. 2018

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MotivationMathematical models have become standard tools for the investigation of cellular processes and the unraveling of signal processing mechanisms. The parameters of these models are usually derived from the available data using optimization and sampling methods. However, the efficiency of these methods is limited by the properties of the mathematical model, e.g. non-identifiabilities, and the resulting posterior distribution. In particular, multi-modal distributions with long valleys or pronounced tails are difficult to optimize and sample. Thus, the developement or improvement of optimization and sampling methods is subject to ongoing research.ResultsWe suggest a region-based adaptive parallel tempering algorithm which adapts to the problem-specific posterior distributions, i.e. modes and valleys. The algorithm combines several established algorithms to overcome their individual shortcomings and to improve sampling efficiency. We assessed its properties for established benchmark problems and two ordinary differential equation models of biochemical reaction networks. The proposed algorithm outperformed state-of-the-art methods in terms of calculation efficiency and mixing. Since the algorithm does not rely on a specific problem structure, but adapts to the posterior distribution, it is suitable for a variety of model classes.Availability and implementationThe code is available both as Supplementary Material and in a Git repository written in MATLAB.Supplementary information Supplementary data are available at Bioinformatics online.

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and a 20-dimensional blurred ring,

with

.…”

Section: Resultsmentioning

confidence: 99%

“…PT algorithms construct a Markov-chain on a product space

with temperatures

, such that

.…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…For

updates of local mean and covariance are given by

with adaptation strength

, with

, and initial value obtained computed in the warm-up phase,

. The scaling factors for regional and global covariance are adapted to achieve an acceptance rate of 23.4% ( Haario et al , 2001 ; Łącki and Miasojedow, 2016 ):

with

.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian parameter estimation for biochemical reaction networks using region-based adaptive parallel tempering

et al. 2018

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Ergonomic and Reliable Bayesian Inference with Adaptive Markov Chain Monte Carlo

Vihola¹

2020

Wiley StatsRef: Statistics Reference Online

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Adaptive Markov chain Monte Carlo (MCMC) methods provide an ergonomic way to perform Bayesian inference, imposing mild modeling constraints and requiring little user specification. The aim of this section is to provide a practical introduction to selected set of adaptive MCMC methods and to suggest guidelines for choosing appropriate methods for certain classes of models. We consider simple unimodal targets with random‐walk‐based methods, multimodal target distributions with parallel tempering, and Bayesian hidden Markov models using particle MCMC. The section is complemented by an easy‐to‐use open‐source implementation of the presented methods in Julia, with examples.

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Generalized parallel tempering on Bayesian inverse problems

et al. 2021

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In the current work we present two generalizations of the Parallel Tempering algorithm in the context of discrete-time Markov chain Monte Carlo methods for Bayesian inverse problems. These generalizations use state-dependent swapping rates, inspired by the so-called continuous time Infinite Swapping algorithm presented in Plattner et al. (J Chem Phys 135(13):134111, 2011). We analyze the reversibility and ergodicity properties of our generalized PT algorithms. Numerical results on sampling from different target distributions, show that the proposed methods significantly improve sampling efficiency over more traditional sampling algorithms such as Random Walk Metropolis, preconditioned Crank–Nicolson, and (standard) Parallel Tempering.

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State-dependent swap strategies and automatic reduction of number of temperatures in adaptive parallel tempering algorithm

Cited by 14 publications

References 29 publications

Bayesian parameter estimation for biochemical reaction networks using region-based adaptive parallel tempering

Bayesian parameter estimation for biochemical reaction networks using region-based adaptive parallel tempering

Ergonomic and Reliable Bayesian Inference with Adaptive Markov Chain Monte Carlo

Generalized parallel tempering on Bayesian inverse problems

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