scholarly journals dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and evidences

2020 ◽  
Vol 493 (3) ◽  
pp. 3132-3158 ◽  
Author(s):  
Joshua S Speagle
Keyword(s):  
Monte Carlo ◽  
Sampling Methods ◽  
Sampling Efficiency ◽  
Nested Sampling ◽  
Marginal Likelihoods ◽  
Mcmc Algorithms ◽  
Multimodal Distributions ◽  
Posterior Estimation ◽  
Python Package ◽  
Statistical Results

ABSTRACT We present dynesty, a public, open-source, python package to estimate Bayesian posteriors and evidences (marginal likelihoods) using the dynamic nested sampling methods developed by Higson et al. By adaptively allocating samples based on posterior structure, dynamic nested sampling has the benefits of Markov chain Monte Carlo (MCMC) algorithms that focus exclusively on posterior estimation while retaining nested sampling’s ability to estimate evidences and sample from complex, multimodal distributions. We provide an overview of nested sampling, its extension to dynamic nested sampling, the algorithmic challenges involved, and the various approaches taken to solve them in this and previous work. We then examine dynesty’s performance on a variety of toy problems along with several astronomical applications. We find in particular problems dynesty can provide substantial improvements in sampling efficiency compared to popular MCMC approaches in the astronomical literature. More detailed statistical results related to nested sampling are also included in the appendix.

Geometrical Recombination Operators for Real-Coded Evolutionary MCMCs

2010 ◽  
Vol 18 (2) ◽  
pp. 157-198 ◽  
Author(s):  
Mădălina M. Drugan ◽  
Dirk Thierens
Keyword(s):  
Monte Carlo ◽  
Sampling Methods ◽  
Search Space ◽  
Computational Effort ◽  
Multivariate Normal ◽  
Linear Transformations ◽  
Proposal Distribution ◽  
Normal Distributions ◽  
Mcmc Algorithms ◽  
Sampling Process

Markov chain Monte Carlo (MCMC) algorithms are sampling methods for intractable distributions. In this paper, we propose and investigate algorithms that improve the sampling process from multi-dimensional real-coded spaces. We present MCMC algorithms that run a population of samples and apply recombination operators in order to exchange useful information and preserve commonalities in highly probable individual states. We call this class of algorithms Evolutionary MCMCs (EMCMCs). We introduce and analyze various recombination operators which generate new samples by use of linear transformations, for instance, by translation or rotation. These recombination methods discover specific structures in the search space and adapt the population samples to the proposal distribution. We investigate how to integrate recombination in the MCMC framework to sample from a desired distribution. The recombination operators generate individuals with a computational effort that scales linearly in the number of dimensions and the number of parents. We present results from experiments conducted on a mixture of multivariate normal distributions. These results show that the recombinative EMCMCs outperform the standard MCMCs for target distributions that have a nontrivial structural relationship between the dimensions.

A Distributed Computer System for Parallel Markov Chain Monte Carlo (MCMC)

2018 ◽  
Author(s):  
Michael Hynes
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Space ◽  
Heterogeneous Computing ◽  
Peer To Peer ◽  
Parallel Tempering ◽  
Single Chain ◽  
Distributed Computing Systems ◽  
Mcmc Algorithms

A ubiquitous problem in physics is to determine expectation values of observables associated with a system. This problem is typically formulated as an integration of some likelihood over a multidimensional parameter space. In Bayesian analysis, numerical Markov Chain Monte Carlo (MCMC) algorithms are employed to solve such integrals using a fixed number of samples in the Markov Chain. In general, MCMC algorithms are computationally expensive for large datasets and have difficulties sampling from multimodal parameter spaces. An MCMC implementation that is robust and inexpensive for researchers is desired. Distributed computing systems have shown the potential to act as virtual supercomputers, such as in the SETI@home project in which millions of private computers participate. We propose that a clustered peer-to-peer (P2P) computer network serves as an ideal structure to run Markovian state exchange algorithms such as Parallel Tempering (PT). PT overcomes the difficulty in sampling from multimodal distributions by running multiple chains in parallel with different target distributions andexchanging their states in a Markovian manner. To demonstrate the feasibility of peer-to-peer Parallel Tempering (P2P PT), a simple two-dimensional dataset consisting of two Gaussian signals separated by a region of low probability was used in a Bayesian parameter fitting algorithm. A small connected peer-to-peer network was constructed using separate processes on a linux kernel, and P2P PT was applied to the dataset. These sampling results were compared with those obtained from sampling the parameter space with a single chain. It was found that the single chain was unable to sample both modes effectively, while the P2P PT method explored the target distribution well, visiting both modes approximately equally. Future work will involve scaling to many dimensions and large networks, and convergence conditions with highly heterogeneous computing capabilities of members within the network.

Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography

2000 ◽  
Vol 16 (5) ◽  
pp. 1487-1522 ◽  
Author(s):  
Jari P Kaipio ◽  
Ville Kolehmainen ◽  
Erkki Somersalo ◽  
Marko Vauhkonen
Keyword(s):  
Monte Carlo ◽  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Sampling Methods ◽  
Monte Carlo Sampling ◽  
Impedance Tomography

A survey on pure sampling in quantum Monte Carlo methods

2013 ◽  
Vol 91 (7) ◽  
pp. 505-510 ◽  
Author(s):  
Stuart M. Rothstein
Keyword(s):  
Monte Carlo ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Sampling Methods ◽  
Electrical Response ◽  
Distribution Functions ◽  
Monte Carlo Algorithm ◽  
Position Operator ◽  
Trial Solution ◽  
Mixed Distribution

The most commonly employed diffusion Monte Carlo algorithm and some of its variants afford a way to sample configuration space from a so-called “mixed distribution”, the product of an input trial solution to the Schrödinger equation for the ground state and its unknown exact solution. This mixed distribution is sufficient to compute the ground state energy and other properties represented by operators that commute with the Hamiltonian. These energy-related properties are exact, save for a small bias introduced by the input trial function’s incorrect exchange nodes, the so-called “fixed-node error”. However, properties represented by operators that commute with the position operator are also of interest. When calculated by sampling from the mixed distribution, these properties are much more strongly biased by the input trial function. Our objective is to review methods that allow sampling from the desired “pure” distribution, one that is unbiased except for the exchange node error. Thereby, one accurately calculates physical properties such as the dipole and other electrical moments, electrical response properties of molecules, and particle distribution functions for clusters. We survey the results of calculations that employ pure-sampling methods through what has been published in year 2012. Our review also touches on truly exact sampling methods.

Examining improved experimental designs for wind tunnel testing using Monte Carlo sampling methods

2010 ◽  
Vol 27 (6) ◽  
pp. 795-803 ◽  
Author(s):  
Raymond R. Hill ◽  
Derek A. Leggio ◽  
Shay R. Capehart ◽  
August G. Roesener
Keyword(s):  
Monte Carlo ◽  
Wind Tunnel ◽  
Sampling Methods ◽  
Monte Carlo Sampling ◽  
Experimental Designs ◽  
Wind Tunnel Testing ◽  
Tunnel Testing

Structural Reliability Analysis With Cross Entropy and Low Discrepancy Sampling Methods

2011 ◽  
Author(s):  
K. Pugazhendhi ◽  
A. K. Dhingra
Keyword(s):  
Monte Carlo ◽  
Importance Sampling ◽  
Structural Reliability ◽  
Sampling Methods ◽  
Reliability Evaluation ◽  
Cross Entropy ◽  
Sampling Density ◽  
Quasi Monte Carlo ◽  
Importance Sampling Techniques ◽  
Optimum Sampling

In recent years quasi Monte-Carlo (QMC) techniques are gaining more popularity for reliability evaluation because of their increased accuracy over traditional Monte-Carlo simulation. A QMC technique like Low Discrepancy Sequence (LDS) combined with importance sampling is shown to be more accurate and robust in the past for the evaluation of structural reliability. However, one of the challenges in using importance sampling techniques to evaluate the structural reliability is to identify the optimum sampling density. In this article, a novel technique based on a combination of cross entropy and low discrepancy sampling methods is used for the evaluation of structural reliability. The proposed technique does not require an apriori knowledge of Most Probable Point of failure (MPP), and succeeds in adaptively identifying the optimum sampling density for the structural reliability evaluation. Several benchmark examples verify that the proposed method is as accurate as the quasi Monte-Carlo technique using low discrepancy sequence with the added advantage of being able to accomplish this without a knowledge of the MPP.

scholarly journals Weak Convergence Rates of Population Versus Single-Chain Stochastic Approximation MCMC Algorithms

2014 ◽  
Vol 46 (04) ◽  
pp. 1059-1083 ◽  
Author(s):  
Qifan Song ◽  
Mingqi Wu ◽  
Faming Liang
Keyword(s):  
Monte Carlo ◽  
Weak Convergence ◽  
Stochastic Approximation ◽  
Convergence Rates ◽  
Gain Factor ◽  
Single Chain ◽  
Practical Applications ◽  
Mcmc Algorithms ◽  
Factor Sequence ◽  
Number Of Iterations

In this paper we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation Markov chain Monte Carlo (MCMC) algorithms (SAMCMC algorithms). Based on the theory, we give an explicit ratio of convergence rates for the population SAMCMC algorithm and the single-chain SAMCMC algorithm. Our results provide a theoretic guarantee that the population SAMCMC algorithms are asymptotically more efficient than the single-chain SAMCMC algorithms when the gain factor sequence decreases slower than O(1 / t), where t indexes the number of iterations. This is of interest for practical applications.

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