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Questions tagged [reversible-jump]

Reversible jump MCMC is a Markov chain Monte Carlo method designed to move between spaces of different dimensions while preserving the intended target distribution.

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Reversible-jump MCMC and Poisson processes

Suppose we have a time interval $t \in [0, T]$ in which events occur as a Poisson process with some arbitrary time-dependent rate $\lambda(t)$. These events occur at times $Y=(Y_1, Y_2, \dotso, Y_M)$ ...
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Jacobian and proposal ratio of Birth/death step in RJMCMC of Gaussian mixture model

I am asking questions regarding RJMCMC several times in this site. Some of my questions are answered and some are unanswered. It didn't clarify all of my unclear points but I am glad that I have ...
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Trying to understand Reversible Jump MCMC

As stated in the foundational Biometrika paper of Green (1995) 'Reversible Jump Monte Carlo Calculation and model discrimination' I am researching the inversion of the data in Geophysics and MCMC is ...
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Reversible-jump MCMC for knot selection

Let $\{Z(\boldsymbol s):\boldsymbol s\in\mathcal D\}$ denote the Gaussian spatial random field on a spatial domain $\mathcal D\subset\mathbb R^2$. Suppose that at $N$ locations, we have observations $\...
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Model Comparison within Bayesian Gaussian Mixture Model framework

Suppose that we conduct a simulation study, and the model that generated the data is the following Gaussian Mixture Model. $$f(x)=\pi_{1}N(x;\mu_{1},\sigma_{1}^{2})+\pi_{2}N(x;\mu_{2},\sigma_{2}^{2})+\...
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2 answers
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Simple alternative to reversible jump for nested models?

Suppose that we have a model such that $p(y\mid k, \theta_1,\dots,\theta_{k_\text{max}})$ depends only on $k,\theta_1,\dots,\theta_k$. Hence, as $k$ assumes the values $1,\dots,k_\text{max}$, we have ...
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BMA and RJMCMC predictive performance

We have a family of statistical models, with parameter spaces of different dimensions, which we aggregated through standard Bayesian Model Averaging (BMA). Experiments using training and test sets ...
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3 votes
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Reversible Jump for normal mixtures in R^d

I'm reading the article "Multivariate mixtures of normals with unknown number of components" (Dellaportas and Papageorgiou 2006). In this article they describe in great details how to ...
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How to calculate the MH ratio in a birth-death Reversible Jump MCMC?

I know the formula and think I understand it, but I must be doing something wrong. Assume $J\sim po(\lambda)$ and $X_J=(U_1, \dots, U_J)$ and $U_i\sim U(0,w)$. Then I want to sample from the ...
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A question about the choice and interpretation of the jumping distribution in Metropolis-Hastings algorithm

In order to implement the MH algorithm you need a proposal density or jumping distribution $q(⋅|⋅)$, from which it is easy to sample. If you want to sample from a distribution $f(⋅)$, the MH algorithm ...
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Gibbs sampling with mixed prior using a Metropolis-Hastings step

My questions are about a sampling procedure for fitting a Bayesian hierarchical model where one of the priors is a mixture distribution of discrete and continuous parts. The model is not my own but I ...
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