Abstract
We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several socalled likelihoodfree methods have been developed to perform inference in the absence of a likelihood function. The popular synthetic likelihood approach infers the parameters by modelling summary statistics of the data by a Gaussian probability distribution. In another popular approach called approximate Bayesian computation, the inference is performed by identifying parameter values for which the summary statistics of the simulated data are close to those of the observed data. Synthetic likelihood is easier to use as no measure of “closeness” is required but the Gaussianity assumption is often limiting. Moreover, both approaches require judiciously chosen summary statistics. We here present an alternative inference approach that is as easy to use as synthetic likelihood but not as restricted in its assumptions, and that, in a natural way, enables automatic selection of relevant summary statistic from a large set of candidates. The basic idea is to frame the problem of estimating the posterior as a problem of estimating the ratio between the data generating distribution and the marginal distribution. This problem can be solved by logistic regression, and including regularising penalty terms enables automatic selection of the summary statistics relevant to the inference task. We illustrate the general theory on canonical examples and employ it to perform inference for challenging stochastic nonlinear dynamical systems and highdimensional summary statistics.
Original language  English 

Pages (fromto)  131 
Number of pages  31 
Journal  Bayesian analysis 
Volume  17 
Issue number  1 
Early online date  12 Sep 2020 
DOIs  
Publication status  Published  1 Mar 2022 
Keywords
 approximate Bayesian computation
 densityratio estimation
 likelihoodfree inference
 logistic regression
 probabilistic classification
 stochastic dynamical systems
 summary statistics selection
 synthetic likelihood
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Michael Gutmann
 School of Informatics  Senior Lecturer in Machine Learning
 Institute for Adaptive and Neural Computation
 Data Science and Artificial Intelligence
Person: Academic: Research Active