# Tagged Questions

Markov Chain Monte Carlo (MCMC) refers to a class of methods for generating samples from a 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 ...

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### setting log-uniform priors in Stan

I have been using Stan for a couple months now and I want to adopt a log-uniform prior on some parameter array real theta[N]. I want to do something like a ...
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### sampling from a distribution: other ways than Markov Chain Monte Carlo

I have this density $f(y|z) = \kappa*\exp(-\kappa y) / (1 - \exp(-\kappa z))$, where $\kappa$ is some known value and $0 < y < \kappa$. I get the distribution by integrating with respect to $y$. ...
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### When 2% of the Bayesian Model have not converged?

I have model with 20000 latent parameters, set up in a Gibb's sampler. 98% of the parameters and sometimes 99.5% of the parameters satisfy the Geweke convergence statistic, have low autocorrelation ...
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### Discrete state space sampeled from a symmetric proposal distribution (monte carlo sampling) in R

I am new to MCMC, but proficient in R. I want to draw Markov chain Monte Carlo samples for the following scenario: The state space consists of all combinations of ...
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### Strange likelihood trace from MCMC chain

I've got a model that goes: Single parameter -> Complex likelihood function -> Log-likelihood. I executed an MCMC chain (using pymc) and plotted the trace of ...
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### Gibbs sampling, what to use?

My question concerns Gibbs sampling. Suppose that I have three unknown quantities, $\mu, \sigma^2$ and $c$. I have given prior information and I have given the likelihood which allows me to compute ...
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### Gibbs sampling and Conjugate Priors

Are conjugate priors required when performing Gibbs sampling?
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### RJMCMC acceptance probability of split/combine move

I have a question about the acceptance probability of Richardson & Green's RJMCMC split/combine move from their paper "On Bayesian Analysis of Mixtures with an Unknown Number of Components". In ...
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### Noisy (and biased) MCMC?

When estimating intractable expectations using MCMC, we usually assume we can evaluate the (unnormalized) target density exactly at any point. I.e. we're interested in evaluating expectations w.r.t. ...
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### Does MCMC perform better than a random walk?

I have read about and implemented a MCMC sampling based optimization for one of the optimization problems that I'm facing. It seems the "magic" of MCMC, and the "inefficient" behavior comes in when, ...
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### How should I compare posterior samples of the same parameter from two Bayesian models?

I have run 2 Bayesian regression models and would like to compare the posterior samples of a parameter that is common to both models. For example, if model A is $y=\alpha + \beta_1x_1$ and model ...
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### MCMC diagnostics for EMC or SMC

Are diagnostics developed for MCMC (e.g. Gelman-Rubin, Geweke) suitable for output from Evolutionary Monte Carlo (EMC) or Sequential Monte Carlo (SMC)?
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### fitting a dynamic bayesian model to irregular time data

I have a dynamic epidemiological model which I solve with scipy's ODEint and fit to my data using pymc. My data is irregular in ...
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### Hamiltonion monte carlo

Can someone explain the main idea behind Hamiltonion Monte Carlo methods and in which cases they will yield better results than Markov Chain Monte Carlo methods ?
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### Why would I use any MC technique other than basic sampling

I'm trying to learn sampling techniques. Lots of tutorials say that they are useful when "you can't sample directly from the pdf...." q1) If I have the algebraic form of the pdf can't I always sample ...
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