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Results tagged with markov-chain-montecarlo
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user 119414
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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MCMC Acceptance ratio [duplicate]
I have a model I want to fit parameters to. I know the likelihood $P(D|\theta)$. Let's say I have two parameters with prior belief, $\theta^1 \sim \mathcal{N}(\mu_2,\sigma_2^2)$, $\theta^2 \sim \mathc …
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MCMC - reject value or keep the same
In MCMC you calculate a value $\alpha$, which tells you the probability of you accepting or rejecting the current sample.
If you end up rejecting the current sample, you then set $x_{n+1} = x_n$. So …
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Adaptive MCMC with low acceptance rate
I'm running an MCMC scheme defined in A tutorial on adaptive MCMC. Christophe Andrieu·Johannes Thoms. Stat Comput (2008) 18: 343–373DOI 10.1007/s11222-008-9110-y.
They say the optimal scaling factor f …
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Metropolis Hastings Stuck in Local maxima
I've been running the metropolis hastings algorithm to infer some parameters.
After running multiple chains, there are typically two places the chains get stuck in, one of which has a higher likelihoo …
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MCMC - one chain behaving differently
I'm using an adaptive MCMC (metropolis-hastings) scheme to infer some parameters. I've run 7 chains, each starting from a random point.
6 of the chains vaguely converge to the same area, but one of t …
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MCMC with missing data
I want to perform some parameter inference on a dataset. In particular, I have some data $y$, with which I want do find posterior distributions for the parameters $\theta$. I have a Metropolis Hasting …
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Discrete Proposal distribution MCMC
If you want to perform MCMC (Metropolis-Hastings) to infer discrete values, what are some proposal distributions you can use for this. I can't think of a way to extend the notion of a gaussian proposa …
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Bayesian Analysis: Point Estimates for a Beta Posterior
The mode probably isn't a great statistic to take in that case. How about the median or the mean (particularly since you aren't affected by extremely large values, as you are bounded between 0 and 1)? …
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