Models with intractable normalizing functions have numerous applications. Because the normalizing constants are functions of the parameters of interest, standard Markov chain Monte Carlo cannot be used for Bayesian inference for these models. A number of algorithms have been developed for such models. Some have the posterior distribution as their asymptotic distribution. Other "asymptotically inexact" algorithms do not possess this property. There is limited guidance for evaluating approximations based on these algorithms. Hence it is very hard to tune them. We propose two new diagnostics that address these problems for intractable normalizing function models. Our first diagnostic, inspired by the second Bartlett identity, is in principle broadly applicable to Monte Carlo approximations beyond the normalizing function problem. We develop an approximate version of this diagnostic that is applicable to intractable normalizing function problems. Our second diagnostic is a Monte Carlo approximation to a kernel Stein discrepancy-based diagnostic introduced by Gorham and Mackey (2017). We provide theoretical justification for our methods and apply them to several algorithms in challenging simulated and real data examples including an Ising model, an exponential random graph model, and a Conway-Maxwell-Poisson regression model, obtaining interesting insights about the algorithms in these contexts.

There is an increasing interest in techniques that support analysis and measurement of fielded software systems. These techniques typically deploy numerous instrumented instances of a software system, collect execution data when the instances run in the field, and analyze the remotely collected data to better understand the system's in-the-field behavior. One common need for these techniques is the ability to distinguish execution outcomes (e.g., to collect only data corresponding to some behavior or to determine how often and under which condition a specific behavior occurs). Most current approaches, however, do not perform any kind of classification of remote executions and either focus on easily observable behaviors (e.g., crashes) or assume that outcomes' classifications are externally provided (e.g., by the users). To address the limitations of existing approaches, we have developed three techniques for automatically classifying execution data as belonging to one of several classes. In this paper, we introduce our techniques and apply them to the binary classification of passing and failing behaviors. Our three techniques impose different overheads on program instances and, thus, each is appropriate for different application scenarios. We performed several empirical studies to evaluate and refine our techniques and to investigate the trade-offs among them. Our results show that 1) the first technique can build very accurate models, but requires a complete set of execution data; 2) the second technique produces slightly less accurate models, but needs only a small fraction of the total execution data; and 3) the third technique allows for even further cost reductions by building the models incrementally, but requires some sequential ordering of the software instances' instrumentation.

There is an increasing interest in techniques that support measurement and analysis of fielded software systems. One of the main goals of these techniques is to better understand how software actually behaves in the field. In particular, many of these techniques require a way to distinguish, in the field, failing from passing executions. So far, researchers and practitioners have only partially addressed this problem: they have simply assumed that program failure status is either obvious (i.e., the program crashes) or provided by an external source (e.g., the users). In this paper, we propose a technique for automatically classifying execution data, collected in the field, as coming from either passing or failing program runs. (Failing program runs are executions that terminate with a failure, such as a wrong outcome.) We use statistical learning algorithms to build the classification models. Our approach builds the models by analyzing executions performed in a controlled environment (e.g., test cases run in-house) and then uses the models to predict whether execution data produced by a fielded instance were generated by a passing or failing program execution. We also present results from an initial feasibility study, based on multiple versions of a software subject, in which we investigate several issues vital to the applicability of the technique. Finally, we present some lessons learned regarding the interplay between the reliability of classification models and the amount and type of data collected.