ABCel: An Empirical Likelihood-based Method for Approximate Bayesian Computation

This project will develop a new, efficient, easy-to-use, and well-justified methodology called ABCel for a purely data-driven statistical inference for many complex models routinely used in natural, engineering, social, and environmental sciences. Examples of such models include phylogenetic trees, dynamical systems, exponential random graph models, etc. Due to the complexity and size of the underlying model classes traditional parameter-based statistical procedures cannot be employed here. The ABCel procedure would draw inferences by comparing the observed data set and multiple new data sets simulated from the model for various values of its parameters. It will require almost no tuning—it could be used off the rack, making it easier to benefit collaborative projects on the spread of diseases (e.g., AIDS, STDs, certain kinds of addictions), monitoring terrorists and similar networks, modeling networks in social media, DEI research, poverty mapping, precision agriculture, and many other fields of study. The project will mentor graduate students, develop course modules, short courses, and several user-friendly software based on the obtained results. The ABCel procedure is a new empirical likelihood-based methodology for Approximate Bayesian Computation (ABC) used for analyzing processes with intractable likelihoods. Such processes allow easy simulation of multiple data sets for any input value of their parameters. However, they behave like a "black box", i.e. because of the complexity and size of the underlying model classes, it is impossible to compute the likelihood of any parameter value. Traditional ABC methods are typically computationally intensive, and not very well-justified. Furthermore, they often require specification of tolerances, smoothing parameters, and distances which crucially affect their performances. For the ABCel procedure, the only inputs required will be a choice of summary statistics, their observed values, and the ability to simulate the chosen summaries for any parameter input. Unlike the traditional ABC methods, no tuning parameters as described above will be required. The parameter posterior will be approximated using an empirical likelihood computed using estimating equations only based on the observed and newly generated summary values. The project will find rigorous justification for the approximation using information theory. Appropriate statistical performance guarantees for the method will be furnished. The team will explore the consistency of the approximate posterior, and its performance under a growing number of samples, replication, and summaries. The procedure will be applied to a detailed analysis of exponential random graph models (ERGM). Such models of social networks are routinely used in epidemiology, sociometry, criminology, national defense, agronomy, small-area estimation, etc. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.