- Title: Inference via Likelihood-free approximate Bayesian computation
- Description: Since early '90s the application of Markov Chain Monte Carlo (MCMC) methods have revolutionised the way statistics is applied to large and complex problems that were previously impossible to treat. In particular, Bayesian statistics has enjoyed a new "epiphany". With increasing computational power and exponentially increasing size of data, (not unexpectedly) increasingly complex models started to emerge. In some cases MCMC for Bayesian inference shows its limitations when it comes to sampling from high dimensional (posterior) distributions and when the likelihood function is not readily available. In recent years a new, approximate, Bayesian aproach has shown incredible potential in a variety of scenarios. This has been named ABC (Approximate Bayesian Computation). ABC turns especially useful in situations where evaluation of the likelihood is computationally prohibitive, or whenever suitable likelihoods are not available. The project will consider some of these "likelihood-free" ABC approaches and apply them to some data. The specific application can be decided together with the student. The project will have a strong computational flavour and a non-negligible fraction of time will be spent on software coding. In particular, algorithmic procedures will have to be coded from scratch and therefore it is necessary to be passionate about computer implementation of probabilistic methods. Some background on MCMC and Bayesian statistics is desirable but not necessary. Resources: http://en.wikipedia.org/wiki/Approximate_Bayesian_computation
- Contact: Umberto Picchini
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Last update: 2013-04-11
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