scholarly journals Fast Bayesian Deconvolution Using Simple Reversible Jump Moves

2021 ◽  
Vol 90 (3) ◽  
pp. 034001
Author(s):  
Koki Okajima ◽  
Kenji Nagata ◽  
Masato Okada
Keyword(s):  
2008 ◽  
Vol 35 (4) ◽  
pp. 677-690 ◽  
Author(s):  
RICARDO S. EHLERS ◽  
STEPHEN P. BROOKS

2008 ◽  
Vol 19 (4) ◽  
pp. 409-421 ◽  
Author(s):  
Y. Fan ◽  
G. W. Peters ◽  
S. A. Sisson

2015 ◽  
Vol 9 (2) ◽  
pp. 304-321 ◽  
Author(s):  
Garfield O. Brown ◽  
Winston S. Buckley

AbstractWe propose a Poisson mixture model for count data to determine the number of groups in a Group Life insurance portfolio consisting of claim numbers or deaths. We take a non-parametric Bayesian approach to modelling this mixture distribution using a Dirichlet process prior and use reversible jump Markov chain Monte Carlo to estimate the number of components in the mixture. Unlike Haastrup, we show that the assumption of identical heterogeneity for all groups may not hold as 88% of the posterior probability is assigned to models with two or three components, and 11% to models with four or five components, whereas models with one component are never visited. Our major contribution is showing how to account for both model uncertainty and parameter estimation within a single framework.


Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. R293-R305 ◽  
Author(s):  
Sireesh Dadi ◽  
Richard Gibson ◽  
Kainan Wang

Upscaling log measurements acquired at high frequencies and correlating them with corresponding low-frequency values from surface seismic and vertical seismic profile data is a challenging task. We have applied a sampling technique called the reversible jump Markov chain Monte Carlo (RJMCMC) method to this problem. A key property of our approach is that it treats the number of unknowns itself as a parameter to be determined. Specifically, we have considered upscaling as an inverse problem in which we considered the number of coarse layers, layer boundary depths, and material properties as the unknowns. The method applies Bayesian inversion, with RJMCMC sampling and uses simulated annealing to guide the optimization. At each iteration, the algorithm will randomly move a boundary in the current model, add a new boundary, or delete an existing boundary. In each case, a random perturbation is applied to Backus-average values. We have developed examples showing that the mismatch between seismograms computed from the upscaled model and log velocities improves by 89% compared to the case in which the algorithm is allowed to move boundaries only. The layer boundary distributions after running the RJMCMC algorithm can represent sharp and gradual changes in lithology. The maximum deviation of upscaled velocities from Backus-average values is less than 10% with most of the values close to zero.


2016 ◽  
Vol 9 (9) ◽  
pp. 3213-3229 ◽  
Author(s):  
Mark F. Lunt ◽  
Matt Rigby ◽  
Anita L. Ganesan ◽  
Alistair J. Manning

Abstract. Atmospheric trace gas inversions often attempt to attribute fluxes to a high-dimensional grid using observations. To make this problem computationally feasible, and to reduce the degree of under-determination, some form of dimension reduction is usually performed. Here, we present an objective method for reducing the spatial dimension of the parameter space in atmospheric trace gas inversions. In addition to solving for a set of unknowns that govern emissions of a trace gas, we set out a framework that considers the number of unknowns to itself be an unknown. We rely on the well-established reversible-jump Markov chain Monte Carlo algorithm to use the data to determine the dimension of the parameter space. This framework provides a single-step process that solves for both the resolution of the inversion grid, as well as the magnitude of fluxes from this grid. Therefore, the uncertainty that surrounds the choice of aggregation is accounted for in the posterior parameter distribution. The posterior distribution of this transdimensional Markov chain provides a naturally smoothed solution, formed from an ensemble of coarser partitions of the spatial domain. We describe the form of the reversible-jump algorithm and how it may be applied to trace gas inversions. We build the system into a hierarchical Bayesian framework in which other unknown factors, such as the magnitude of the model uncertainty, can also be explored. A pseudo-data example is used to show the usefulness of this approach when compared to a subjectively chosen partitioning of a spatial domain. An inversion using real data is also shown to illustrate the scales at which the data allow for methane emissions over north-west Europe to be resolved.


Webology ◽  
2021 ◽  
Vol 18 (Special Issue 04) ◽  
pp. 1045-1055
Author(s):  
Sup arman ◽  
Yahya Hairun ◽  
Idrus Alhaddad ◽  
Tedy Machmud ◽  
Hery Suharna ◽  
...  

The application of the Bootstrap-Metropolis-Hastings algorithm is limited to fixed dimension models. In various fields, data often has a variable dimension model. The Laplacian autoregressive (AR) model includes a variable dimension model so that the Bootstrap-Metropolis-Hasting algorithm cannot be applied. This article aims to develop a Bootstrap reversible jump Markov Chain Monte Carlo (MCMC) algorithm to estimate the Laplacian AR model. The parameters of the Laplacian AR model were estimated using a Bayesian approach. The posterior distribution has a complex structure so that the Bayesian estimator cannot be calculated analytically. The Bootstrap-reversible jump MCMC algorithm was applied to calculate the Bayes estimator. This study provides a procedure for estimating the parameters of the Laplacian AR model. Algorithm performance was tested using simulation studies. Furthermore, the algorithm is applied to the finance sector to predict stock price on the stock market. In general, this study can be useful for decision makers in predicting future events. The novelty of this study is the triangulation between the bootstrap algorithm and the reversible jump MCMC algorithm. The Bootstrap-reversible jump MCMC algorithm is useful especially when the data is large and the data has a variable dimension model. The study can be extended to the Laplacian Autoregressive Moving Average (ARMA) model.


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