scholarly journals Stochastic Efficiency of Bayesian Markov Chain Monte Carlo in Spatial Econometric Models: An Empirical Comparison of Exact Sampling Methods

2017 ◽  
Vol 50 (1) ◽  
pp. 97-119 ◽  
Author(s):  
Levi John Wolf ◽  
Luc Anselin ◽  
Daniel Arribas-Bel
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Sampling Methods ◽  
Econometric Models ◽  
Empirical Comparison ◽  
Spatial Econometric ◽  
Exact Sampling ◽  
Spatial Econometric Models

scholarly journals Efficiency and robustness in Monte Carlo sampling of 3-D geophysical inversions with Obsidian v0.1.2: Setting up for success

2019 ◽  
Author(s):  
Richard Scalzo ◽  
David Kohn ◽  
Hugo Olierook ◽  
Gregory Houseman ◽  
Rohitash Chandra ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Adaptive Sampling ◽  
Sampling Methods ◽  
South Australia ◽  
Monte Carlo Sampling ◽  
Dimensional Structure ◽  
High Dimensional ◽  
Dimensional Parameter

Abstract. The rigorous quantification of uncertainty in geophysical inversions is a challenging problem. Inversions are often ill-posed and the likelihood surface may be multimodal; properties of any single mode become inadequate uncertainty measures, and sampling methods become inefficient for irregular posteriors or high-dimensional parameter spaces. We explore the influences of different choices made by the practitioner on the efficiency and accuracy of Bayesian geophysical inversion methods that rely on Markov chain Monte Carlo sampling to assess uncertainty, using a multi-sensor inversion of the three-dimensional structure and composition of a region in the Cooper Basin of South Australia as a case study. The inversion is performed using an updated version of the Obsidian distributed inversion software. We find that the posterior for this inversion has complex local covariance structure, hindering the efficiency of adaptive sampling methods that adjust the proposal based on the chain history. Within the context of a parallel-tempered Markov chain Monte Carlo scheme for exploring high-dimensional multi-modal posteriors, a preconditioned Crank-Nicholson proposal outperforms more conventional forms of random walk. Aspects of the problem setup, such as priors on petrophysics or on 3-D geological structure, affect the shape and separation of posterior modes, influencing sampling performance as well as the inversion results. Use of uninformative priors on sensor noise can improve inversion results by enabling optimal weighting among multiple sensors even if noise levels are uncertain. Efficiency could be further increased by using posterior gradient information within proposals, which Obsidian does not currently support, but which could be emulated using posterior surrogates.

MCMC SAMPLING IN THE GLOBAL ANALYSIS OF SOLAR AND REACTOR NEUTRINO DATA

2013 ◽  
Vol 28 (01) ◽  
pp. 1350005
Author(s):  
W. LIU ◽  
Y. F. LI ◽  
Q. Y. LIU
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Sampling Methods ◽  
Global Analysis ◽  
Neutrino Mixing ◽  
Mcmc Sampling ◽  
Reactor Neutrino ◽  
Antineutrino Flux ◽  
Fitting Parameters

We present a global analysis of latest solar and reactor neutrino data in the three-neutrino mixing scheme by using both the simple grid scanning and the Markov Chain Monte Carlo (MCMC) sampling methods. Accuracy and efficiency of the two sampling methods are compared and advantages of the latter are discussed. The fitting results of three oscillation parameters θ12, θ13 and [Formula: see text] are provided with both old and new evaluations of the reactor antineutrino flux. Possible correlation between the fitting parameters is also discussed.

scholarly journals Efficiency and robustness in Monte Carlo sampling for 3-D geophysical inversions with Obsidian v0.1.2: setting up for success

2019 ◽  
Vol 12 (7) ◽  
pp. 2941-2960 ◽  
Author(s):  
Richard Scalzo ◽  
David Kohn ◽  
Hugo Olierook ◽  
Gregory Houseman ◽  
Rohitash Chandra ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Adaptive Sampling ◽  
Sampling Methods ◽  
South Australia ◽  
Monte Carlo Sampling ◽  
Dimensional Structure ◽  
High Dimensional ◽  
Dimensional Parameter

Abstract. The rigorous quantification of uncertainty in geophysical inversions is a challenging problem. Inversions are often ill-posed and the likelihood surface may be multi-modal; properties of any single mode become inadequate uncertainty measures, and sampling methods become inefficient for irregular posteriors or high-dimensional parameter spaces. We explore the influences of different choices made by the practitioner on the efficiency and accuracy of Bayesian geophysical inversion methods that rely on Markov chain Monte Carlo sampling to assess uncertainty using a multi-sensor inversion of the three-dimensional structure and composition of a region in the Cooper Basin of South Australia as a case study. The inversion is performed using an updated version of the Obsidian distributed inversion software. We find that the posterior for this inversion has a complex local covariance structure, hindering the efficiency of adaptive sampling methods that adjust the proposal based on the chain history. Within the context of a parallel-tempered Markov chain Monte Carlo scheme for exploring high-dimensional multi-modal posteriors, a preconditioned Crank–Nicolson proposal outperforms more conventional forms of random walk. Aspects of the problem setup, such as priors on petrophysics and on 3-D geological structure, affect the shape and separation of posterior modes, influencing sampling performance as well as the inversion results. The use of uninformative priors on sensor noise enables optimal weighting among multiple sensors even if noise levels are uncertain.

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