# Questions tagged [markov-chain-montecarlo]

Markov Chain Monte Carlo (MCMC) refers to a class of simulation methods for generating samples from a complex target distribution by generating random numbers from a Markov Chain whose stationary distribution is the target distribution. MCMC methods are typically used when more direct methods for random number generation (e.g. inversion method) are infeasible. The very first MCMC method was the Metropolis (et al.) algorithm, later expanded by Hastings.

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### MCMCglmm package [closed]

the summary() for my ordinal model isn't returning all of my cutpoints. There are four levels in my response variable but I'm only getting two cut points. Does anyone know why?
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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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### Using mcmc to estimate parameters of Dirichlet distribution

We have a probabilistic model with two parameters, $\theta$ and $\eta$, both of which are uniformly distributed between 0 and 1. The model has five possible outcomes, and the probability of each ...
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### Calculate acceptance ratio of Jacobian of split-merge RJMCMC

I am keep studying the RJMCMC and want to ask question regarding the acceptance ratio of split/merge step of RJMCMC The split/merge step, suggested by Richardson and Green (1997) is following for w_j, ...
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### Assumptions and setting for bayesian mixture model (for RJMCMC)

I want to understand about Bayesian mixture model discussed in RJMCMC paper (Richardson and Green, 1997) (https://academic.oup.com/jrsssb/article/59/4/731/7083042) I also posted similar question ...
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### Meaning and importance of 'Gibbs update' in MCMC

I am studying MCMC by "Handbook of Markov Chain Monte Carlo" by Brooks, Gelman This book is nice to explaining many fundamental concepts regarding MCMC. Especially in first chapter, they ...
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### Terms and assumptions in trans-dimensional MCMC (RJ-MCMC) for Green 1995 paper

I want to use Trans-dimensional MCMC in my research and for fundamental understanding, I am trying to learn from Green (1995) paper, which is foundation of RJ-MCMC. In part of 3.3 'switching between ...
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### Adaptive Metropolis For Multidimensional Parameter

Hi recently I want to implement the adaptive Metropolis algorithm. However I dont know how to deal with multidimensional parameters. The normal step of the adaptive MCMC is to update the covariance ...
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### Which method should be used to determine the class ID of multiple SVM models?

I'm using Support Vector Machine(SVM) with image classification. Each SVM model results a linear model $$y = wx + b$$ Where $w$ and $b$ is the SVM parameters. If I have multiple SVM models, I will get ...
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### Estimation with Random Walk 2 Priors

In (https://becarioprecario.bitbucket.io/inla-gitbook/ch-smoothing.html#sec:smoothterms), they show an example of a Random Walk 2 (RW2) prior being used on the LIDAR dataset. For the model set-up, we ...
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### How can I sample a multivariate normal vector that satisfies a linear equality constraint?

Let $X \sim N_n(\mu, \Sigma)$, such that $AX=b$ where $A$ is a ($p \times n$) matrix, with $p \ll n$. How can I efficiently sample from this distribution? I've seen techniques using elliptical slice ...
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### In Bayesian linear regression Advantages of predictive posterior compared to posterior of model coefficients

In Bayesian linear regression, if we want to get confidence intervals for predictions of a new observation. I was thinking of the following two options. Use the quantiles from samples sampled from ...
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### Subtilities of MCMC method and more generally about covariance matrix and Samplers

i have difficulties to better understand about what we commonly called a sampler, especially how to produce a covariance matrix between parameters during a MCMC code run. In MCM, I know that we start ...
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### Is it possible to increase the Hastings ratio by combining and mixing elementary kernels?

Let's say I am working with a state $X$ split into three parts $U$, $V$, and $W$. I can efficiently sample from $W|U,V$, $U|V$, and $V|U$. My initial intuition was to do a variable-at-a-time ...
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In A General Metric for Riemannian Manifold Hamiltonian Monte Carlo (Betancourt, 2013), the author writes: The first  and still most common choice of the conditional density, $\pi(p|q)$, is a ...