scholarly journals Weak convergence and optimal tuning of the reversible jump algorithm

2019 ◽  
Vol 161 ◽  
pp. 32-51 ◽  
Author(s):  
Philippe Gagnon ◽  
Mylène Bédard ◽  
Alain Desgagné
Keyword(s):  
Weak Convergence ◽  
Reversible Jump ◽  
Optimal Tuning ◽  
Jump Algorithm

scholarly journals Seismic tomography with the reversible jump algorithm

2009 ◽  
Vol 178 (3) ◽  
pp. 1411-1436 ◽  
Author(s):  
Thomas Bodin ◽  
Malcolm Sambridge
Keyword(s):  
Seismic Tomography ◽  
Reversible Jump ◽  
Jump Algorithm

scholarly journals A generalized multiple-try version of the Reversible Jump algorithm

2014 ◽  
Vol 72 ◽  
pp. 298-314 ◽  
Author(s):  
Silvia Pandolfi ◽  
Francesco Bartolucci ◽  
Nial Friel
Keyword(s):  
Reversible Jump ◽  
Jump Algorithm

OPTIMAL AUXILIARY PRIORS AND REVERSIBLE JUMP PROPOSALS FOR A CLASS OF VARIABLE DIMENSION MODELS

2020 ◽  
pp. 1-33
Author(s):  
Andriy Norets
Keyword(s):  
Asymptotic Variance ◽  
Variable Number ◽  
Optimal Choice ◽  
Nonparametric Model ◽  
Reversible Jump ◽  
Curve Estimation ◽  
Sample Average ◽  
Out Of Sample ◽  
Nonparametric Alternatives ◽  
Jump Algorithm

This article develops a Markov chain Monte Carlo (MCMC) method for a class of models that encompasses finite and countable mixtures of densities and mixtures of experts with a variable number of mixture components. The method is shown to maximize the expected probability of acceptance for cross-dimensional moves and to minimize the asymptotic variance of sample average estimators under certain restrictions. The method can be represented as a retrospective sampling algorithm with an optimal choice of auxiliary priors and as a reversible jump algorithm with optimal proposal distributions. The method is primarily motivated by and applied to a Bayesian nonparametric model for conditional densities based on mixtures of a variable number of experts. The mixture of experts model outperforms standard parametric and nonparametric alternatives in out of sample performance comparisons in an application to Engel curve estimation. The proposed MCMC algorithm makes estimation of this model practical.

scholarly journals Speeding up Inference of Homologous Recombination in Bacteria

2020 ◽  
Author(s):  
Felipe J Medina-Aguayo ◽  
Xavier Didelot ◽  
Richard G Everitt
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Recombination Event ◽  
Graph Model ◽  
Monte Carlo Algorithm ◽  
Reversible Jump ◽  
Ancestral Recombination Graph ◽  
Recent Developments ◽  
Different Dimensions ◽  
Jump Algorithm

AbstractBacteria reproduce clonally but most species recombine frequently, so that the ancestral process is best captured using an ancestral recombination graph. This graph model is often too complex to be used in an inferential setup, but it can be approximated for example by the ClonalOrigin model. Inference in the ClonalOrigin model is performed via a Reversible-Jump Markov Chain Monte Carlo algorithm, which attempts to jointly explore: the recombination rate, the number of recombination events, the departure and arrival points on the clonal genealogy for each recombination event, and the range of genomic sites affected by each recombination event. However, the Reversible-Jump algorithm usually performs poorly due to the complexity of the target distribution since it needs to explore spaces of different dimensions. Recent developments in Bayesian computation methodology have provided ways to improve existing methods and code, but are not well-known outside the statistics community. We show how exploiting one of these new computational methods can lead to faster inference under the ClonalOrigin model.

A novel reversible jump algorithm for generalized linear models

Biometrika ◽  
2011 ◽  
Vol 98 (1) ◽  
pp. 231-236 ◽  
Author(s):  
M. Papathomas ◽  
P. Dellaportas ◽  
V. G. S. Vasdekis
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Reversible Jump ◽  
Jump Algorithm

Common Fixed Points in Modular Spaces

2018 ◽  
pp. 502 ◽  
Author(s):  
Salwa Salman Abed ◽  
Karrar Emad Abdul Sada
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Fixed Point Theorems ◽  
Active Role ◽  
Common Fixed Points ◽  
Weakly Compact ◽  
Expansive Mapping ◽  
Modular Spaces ◽  
Opial’S Property ◽  
Common Fixed Point Theorems

     In this paper,there are   new considerations about the dual of a modular spaces and weak convergence. Two common fixed point theorems for a -non-expansive mapping defined on a star-shaped weakly compact subset are proved,  Here the conditions of affineness, demi-closedness and Opial's property play an active role in the proving our results.  

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