Linked Questions

9
votes
2answers
2k views

Robust MCMC estimator of marginal likelihood?

I'm trying to compute the marginal likelihood for a statistical model by Monte Carlo methods: $$f(x) = \int f(x\mid\theta) \pi(\theta)\, d\theta$$ The likelihood is well behaved - smooth, log-...
12
votes
1answer
1k views

Marginal Likelihood from the Gibbs Output

I'm reproducing from scratch the results in Section 4.2.1 of Marginal Likelihood from the Gibbs Output Siddhartha Chib Journal of the American Statistical Association, Vol. 90, No. 432. (Dec., 1995)...
3
votes
2answers
1k views

Approximating 1D integral with Metropolis - Hastings Markov Chain Monte Carlo

I've been asked to approximate the integral of a one dimensional unnormalised posterior with a flat prior, using a Metropolis Hastings Markov Chain Monte Carlo, I realise that this isn't a practical ...
4
votes
1answer
1k views

Importance sampling: unbiased estimator of the normalizing constant

$\newcommand{\E}{\mathbb{E}}$I'm reading a book on machine learning and sampling methods and I want to know why the estimator of the normalizing constant is unbiased, but the estimator of $\E\left[f(x)...
0
votes
0answers
524 views

Calculating the evidence from an MCMC sample

I have a an MCMC sample file containing a list of points in parameter space. I have the value of the parameters in my model at each point, and the likelihood at each point. Of course I also have the ...
3
votes
0answers
386 views

Approximating the marginal likelihood in Bayesian Model Comparison

Given some data $y$, my interest centers around a collection of models $\{\mathcal{M}_1,\mathcal{M}_2,\cdots,\mathcal{M}_L\}$ representing competing hypotheses about $y$. Each model $\mathcal{M}_l$ ...
5
votes
1answer
102 views

Can MCMC algorithm estimate partition function (normalizing constant)?

Importance Sampling can estimated the normalizing constant by averaging the weights (the ratio of unnoramlized distribution and importance distribution). Is there anyway that MCMC algorithm can ...
1
vote
1answer
134 views

Bayes factors from MCMC samples

I'm working to implement Bayesian model selection among models whose posteriors have already been sampled via MCMC. After reviewing some discussions of Bayes factors, I understand that they are ...
3
votes
0answers
67 views

Nested sampling integral on a previously obtained MCMC sample

This question concerns the calculation of the evidence, or marginal likelihood, from an existing MCMC sample without having to resample. There is an exhaustive and very helpful answer here: [...
1
vote
0answers
38 views

How to perform MCMC integration when no prior over the integrated function is available? [closed]

As far as I can tell, MCMC integration (e.g. VEGAS) is performed by sampling from a distribution proportional to $f(x)$ using MCMC, then building a density estimator $g(x)$ using these samples (for ...