Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.
Concept
Nested sampling algorithm
Summary
The nested sampling algorithm is a computational approach to the Bayesian statistics problems of comparing models and generating samples from posterior distributions. It was developed in 2004 by physicist John Skilling.
Bayes' theorem can be applied to a pair of competing models and for data , one of which may be true (though which one is unknown) but which both cannot be true simultaneously. The posterior probability for may be calculated as:
The prior probabilities and are already known, as they are chosen by the researcher ahead of time. However, the remaining Bayes factor is not so easy to evaluate, since in general it requires marginalizing nuisance parameters. Generally, has a set of parameters that can be grouped together and called , and has its own vector of parameters that may be of different dimensionality, but is still termed . The marginalization for is
and likewise for . This integral is often analytically intractable, and in these cases it is necessary to employ a numerical algorithm to find an approximation. The nested sampling algorithm was developed by John Skilling specifically to approximate these marginalization integrals, and it has the added benefit of generating samples from the posterior distribution . It is an alternative to methods from the Bayesian literature such as bridge sampling and defensive importance sampling.
Here is a simple version of the nested sampling algorithm, followed by a description of how it computes the marginal probability density where is or :
Start with points sampled from prior.
for to do % The number of iterations j is chosen by guesswork.
current likelihood values of the points;
Save the point with least likelihood as a sample point with weight .
Update the point with least likelihood with some Markov chain Monte Carlo steps according to the prior, accepting only steps that
keep the likelihood above .
end
return ;
At each iteration, is an estimate of the amount of prior mass covered by the hypervolume in parameter space of all points with likelihood greater than .
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.