Abstract
Increasingly complex generative models are being used across disciplines as they allow for realistic characterization of data, but a common difficulty with them is the prohibitively large computational cost to evaluate the likelihood function and thus to perform likelihood-based statistical inference. A likelihood-free inference framework has emerged where the parameters are identified by finding values that yield simulated data resembling the observed data. While widely applicable, a major difficulty in this framework is how to measure the discrepancy between the simulated and observed data. Transforming the original problem into a problem of classifying the data into simulated versus observed, we find that classification accuracy can be used to assess the discrepancy. The complete arsenal of classification methods becomes thereby available for inference of intractable generative models. We validate our approach using theory and simulations for both point estimation and Bayesian inference, and demonstrate its use on real data by inferring an individual-based epidemiological model for bacterial infections in child care centers.
Highlights
The likelihood function plays a central role in statistical inference by quantifying to which extent some values of the model parameters are consistent with the observed data
This paper is about statistical inference for generative models whose likelihood function cannot be computed in a reasonable time
The goal of this paper is to show that the complete arsenal of classification methods can be brought to our disposal to measure the discrepancy, and to perform inference for intractable generative models
Summary
The likelihood function plays a central role in statistical inference by quantifying to which extent some values of the model parameters are consistent with the observed data. A generative model is here defined as a parametrized probabilistic mechanism which specifies how the data are generated. It is usually implemented as a computer program that takes a state of the random number generator and some values of the model parameters θ as input and that returns simulated data Yθ as output. The mapping from the parameters θ to simulated data Yθ is stochastic, and running the computer program for different states of the random number generator corresponds to sampling from the model. Generative models are known as simulator- or simulation-based
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