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On computational tools for Bayesian data analysis
4
TL;DR: While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures.
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Abstract: While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures. Recent innovations like Monte Carlo Markov chain, sequential Monte Carlo methods and more recently Approximate Bayesian Computation techniques have considerably increased the potential for Bayesian applications and they have also opened new avenues for Bayesian inference, first and foremost Bayesian model choice.
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Citations
Monte Carlo Methods in Bayesian Computation
TL;DR: The authors use the setting of singular perturbations, which allows them to study both weak and strong interactions among the states of the chain and give the asymptotic behavior of many controlled stochastic dynamic systems when the perturbation parameter tends to 0.
599
•Posted Content
Adaptive Multiple Importance Sampling
Christian P. Robert,Antonietta Mira,Jean-Michel Marin,Jean-Marie Cornuet +3 more
- 01 Jan 2012
TL;DR: The Adaptive Multiple Importance Sampling (AMIS) algorithm as discussed by the authors aims at an optimal recycling of past simulations in an iterated importance sampling (IS) scheme, where the importance weights of all simulated values, past as well as present, are recomputed at each iteration, following the technique of the deterministic multiple mixture estimator of Owen & Zhou.
148
•Posted Content
Bayesian Analysis of Stochastic Volatility Models
TL;DR: In this article, a Bayesian Markov Chain Monte Carlo (BMMC) algorithm was used to estimate the time varying volatility of the French financial market, and an explicit expression for the parameter's estimators was found via Monte Carlo technique.
77
Hidden Markov models
Tobias Rydén
- 01 Jan 2004
TL;DR: In this article, the authors investigate the probabilistic modelling of stochastic processes and the resulting statistical procedures and propose a forward-backward algorithm for the hidden Markov chain.
12
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Arnaud Doucet,Nando de Freitas,Neil Gordon,Adrian F. M. Smith +3 more
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Monte Carlo Statistical Methods
Christian P. Robert,George Casella +1 more
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TL;DR: This new edition contains five completely new chapters covering new developments and has sold 4300 copies worldwide of the first edition (1999).
Sampling-Based Approaches to Calculating Marginal Densities
TL;DR: In this paper, three sampling-based approaches, namely stochastic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm, are compared and contrasted in relation to various joint probability structures frequently encountered in applications.
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