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LF1: Likelihood-free Statistical Design and Inference
10:30am - 12:10pm
Session Chair: Werner G. MÜLLER
Location:HS 403 (Green Lecture Hall)
10:30am - 10:55am
Optimal Bayesian Design For Models With Intractable Likelihoods Via Supervised Learning Methods
Markus HAINY1, David James PRICE2, Olivier RESTIF3, Christopher DROVANDI4
1Johannes Kepler University, Austria; 2University of Melbourne, Australia; 3University of Cambridge, United Kingdom; 4Queensland University of Technology, Australia
Optimal Bayesian experimental design is often computationally intensive due to the need to approximate many posterior distributions for datasets simulated from the prior predictive distribution. The issues are compounded further when the statistical models of interest do not possess tractable likelihood functions and only simulation is feasible. We employ supervised learning methods to facilitate the computation of utility values in optimal Bayesian design. This approach requires considerably fewer simulations from the candidate models than previous approaches using approximate Bayesian computation. The approach is particularly useful in the presence of models with intractable likelihoods but can also provide computational advantages when the likelihoods are manageable. We consider the two experimental goals of model discrimination and parameter estimation. The methods are applied to find optimal designs for models in epidemiology and cell biology.
10:55am - 11:20am
Bayesian Design For Intractable Likelihood Models
University of Southampton, United Kingdom
Bayesian designs are found by maximising the expectation of a utility function where the utility function is chosen to represent the aim of the experiment. There are several hurdles to overcome when considering Bayesian design for intractable models. Firstly, common to nearly all Bayesian design problems, the expected utility function is not analytically tractable and requires approximation. Secondly, this approximate expected utility needs to be maximised over a potentially high-dimensional design space. To compound these problems, thirdly, the likelihood is intractable, i.e. has no closed form. New approaches to maximise an approximation to the expected utility for intractable models are developed and applied to illustrative exemplar design problems with experimental aims of parameter estimation and model selection.
11:20am - 11:45am
Efficient Bayesian Experimental Design for Implicit Models
Steven KLEINEGESSE, Michael GUTMANN
University of Edinburgh, United Kingdom
Bayesian experimental design involves the optimal allocation of resources in an experiment, with the aim of optimising cost and performance. For implicit models, where the likelihood is intractable but sampling from the model is possible, this task is particularly difficult and therefore largely unexplored. This is mainly due to technical difficulties associated with approximating posterior distributions and utility functions. We devise a novel experimental design framework for implicit models that improves upon previous work in two ways. First, we use the mutual information between parameters and data as the utility function, which has previously not been feasible. We achieve this by utilising Likelihood-Free Inference by Ratio Estimation (LFIRE) to approximate posterior distributions, instead of the traditional approximate Bayesian computation or synthetic likelihood methods. Secondly, we use Bayesian optimisation in order to solve the optimal design problem, as opposed to the typically used grid search or sampling-based methods. We find that this increases efficiency and allows us to consider higher design dimensions.
11:45am - 12:10pm
Invited Discussion of the Talks
Christian P ROBERT1, Jürgen PILZ2
1University Paris Dauphine, France; 2Alpen Adria Universität Klagenfurt, Austria
Christian Robert and Jürgen Pilz will discuss the talks that have been presented in this session.