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A large auditing literature concludes that Big N auditors provide higher audit quality than non-Big N auditors. Recently, however, a high-profile study suggests that propensity score matching (PSM) on client characteristics eliminates the Big N effect [Lawrence A, Minutti-Meza M, Zhang P (2011) Can Big 4 versus non-Big 4 differences in audit-quality proxies be attributed to client characteristics? Accounting Rev. 86(1):259–286]. We conjecture that this finding may be affected by PSM’s sensitivity to its design choices and/or by the validity of the audit quality measures used in the analysis. To investigate, we examine random combinations of PSM design choices that achieve covariate balance, and four commonly used audit quality measures. We find that the majority of these design choices support a Big N effect for most of the audit quality measures. Overall, our findings show that it is premature to suggest that PSM eliminates the Big N effect. This paper was accepted by Suraj Srinivasan, accounting .

Agent-based modeling (ABM) is a bottom-up modeling approach, where each entity of the system being modeled is uniquely represented as an independent decision-making agent. ABMs are very sensitive to implementation details. Thus, it is very easy to inadvertently introduce changes which modify model dynamics. Such problems usually arise due to the lack of transparency in model descriptions, which constrains how models are assessed, implemented and replicated. In this paper, we present PPHPC, a model which aims to serve as a standard in agent based modeling research, namely, but not limited to, conceptual model specification, statistical analysis of simulation output, model comparison and parallelization studies. This paper focuses on the first two aspects (conceptual model specification and statistical analysis of simulation output), also providing a canonical implementation of PPHPC. The paper serves as a complete reference to the presented model, and can be used as a tutorial for simulation practitioners who wish to improve the way they communicate their ABMs.

Learning about experts in a portfolio choice problem: The Black–Litterman model provides a framework for combining the forecasts of an equilibrium model and the forward-looking opinions of several experts in a portfolio allocation decision. In “A Generalized Black–Litterman Model,” Chen and Lim propose a generalization of the classical model that accounts for model misspecification and bias in the equilibrium and expert models and show how it can be calibrated using historical view and return data. More generally, this paper shows how the views of multiple experts can be modeled as a Bayesian graphical model and estimated using historical data, which may be of interest in applications that involve the aggregation of expert opinions for the purpose of decision making. The Black–Litterman model provides a framework for combining the forecasts of a backward-looking equilibrium model with the views of (several) forward-looking experts in a portfolio allocation decision. The classical version uses the capital asset pricing model to specify expected returns, and assumes that expert views are unbiased noisy observations of future returns. It combines the two using Bayes’ rule and the portfolio allocation decision is made on the basis of the updated forecast. The classical Black–Litterman model assumes that the equilibrium and expert models are accurately specified. This is generally not the case, however, and there may be substantial efficiency loss if misspecification is ignored. In this paper, we formulate a generalized Black–Litterman model that accounts for both misspecification and bias in the equilibrium and expert models. We show how to calibrate this model using historical view and return data, and study the value of our generalized model for portfolio construction. More generally, this paper shows how the views of multiple experts can be modeled as a Bayesian graphical model and estimated using historical data, which may be of interest in applications that involve the aggregation of expert opinions for the purpose of decision making.

“Bayesian learning works even with censored information” We often learn about a problem from information that is incomplete or censored: for example, a medical treatment may cause side effects with no indication of what the right dose should have been. Bayesian belief models are useful in such settings, but cannot be constructed using traditional methods; as a result, practitioners have developed ways of constructing them approximately. These approximations have been very successful in many application domains, yet until now have lacked theoretical support. The paper “Consistency analysis of sequential learning under approximate Bayesian inference,” by Chen and Ryzhov, links approximate Bayesian learning to stochastic approximation theory. Using this link, the authors prove – for the first time – the consistency of a suite of approximate Bayesian methods culled from the literature. One highlight is an entirely new consistency proof for Bayesian logistic regression, a well-established approximation technique that essentially treats logistic regression as if it were ordinary least squares. Approximate Bayesian inference is a powerful methodology for constructing computationally efficient statistical mechanisms for sequential learning from incomplete or censored information. Approximate Bayesian learning models have proven successful in a variety of operations research and business problems; however, prior work in this area has been primarily computational, and the consistency of approximate Bayesian estimators has been a largely open problem. We develop a new consistency theory by interpreting approximate Bayesian inference as a form of stochastic approximation (SA) with an additional “bias” term. We prove the convergence of a general SA algorithm of this form and leverage this analysis to derive the first consistency proofs for a suite of approximate Bayesian models from the recent literature.

A mean square error analysis of finite-difference sensitivity estimators for stochastic systems is presented and an expression for the optimal size of the increment is derived. The asymptotic behavior of the optimal increments, and the behavior of the corresponding optimal finite-difference (FD) estimators are investigated for finite-horizon experiments. Steady-state estimation is also considered for regenerative systems and in this context a convergence analysis of ratio estimators is presented. The use of variance reduction techniques for these FD estimates, such as common random numbers in simulation experiments, is not considered here. In the case here, direct gradient estimation techniques (such as perturbation analysis and likelihood ratio methods) whenever applicable, are shown to converge asymptotically faster than the optimal FD estimators.

In this paper, we address the problem of finding the simulated system with the best (maximum or minimum) expected performance when the number of alternatives is finite, but large enough that ranking-and-selection (R&S) procedures may require too much computation to be practical. Our approach is to use the data provided by the first stage of sampling in an R&S procedure to screen out alternatives that are not competitive, and thereby avoid the (typically much larger) second-stage sample for these systems. Our procedures represent a compromise between standard R&S procedures-which are easy to implement, but can be computationally inefficient-and fully sequential procedures-which can be statistically efficient, but are more difficult to implement and depend on more restrictive assumptions. We present a general theory for constructing combined screening and indifference-zone selection procedures, several specific procedures and a portion of an extensive empirical evaluation.

In this paper we address the problem of finding the simulated system with the best (maximum or minimum) expected performance when the number of systems is large and initial samples from each system have already been taken. This problem may be encountered when a heuristic search procedure-perhaps one originally designed for use in a deterministic environment-has been applied in a simulation-optimization context. Because of stochastic variation, the system with the best sample mean at the end of the search procedure may not coincide with the true best system encountered during the search. This paper develops statistical procedures that return the best system encountered by the search (or one near the best) with a prespecified probability. We approach this problem using combinations of statistical subset selection and indifference-zone ranking procedures. The subset-selection procedures, which use only the data already collected, screen out the obviously inferior systems, while the indifference-zone procedures, which require additional simulation effort, distinguish the best from the less obviously inferior systems.

Standard \"indifference-zone\" procedures that allocate computer resources to infer the best of a finite set of simulated systems are designed with a statistically conservative, least favorable configuration assumption consider the probability of correct selection (but not the opportunity cost) and assume that the cost of simulating each system is the same. Recent Bayesian work considers opportunity cost and shows that an average case analysis may be less conservative but assumes a known output variance, an assumption that typically is violated in simulation. This paper presents new two-stage and sequential selection procedures that integrate attractive features of both lines of research. They are derived assuming that the simulation output is normally distributed with unknown mean and variance that may differ for each system. We permit the reduction of either opportunity cost loss or the probability of incorrect selection and allow for different replication costs for each system. The generality of our formulation comes at the expense of difficulty in obtaining exact closed-form solutions. We therefore derive a bound for the expected loss associated potentially incorrect selections, then asymptotically minimize that bound. Theoretical and empirical results indicate that our approach compares favorably with indifference-zone procedures.

We consider the problem of constructing a confidence interval for the steady-state mean of a stochastic process by means of simulation, and study the five main methods which have been proposed (replication, batch means, autoregressive representation, spectrum analysis, and regeneration cycles) for the case when the length of the simulation is fixed in advance. Comparing the performances of these methods on stochastic models with known steady-state means, we find that the simulator should exercise caution in interpreting the results from a simulation of fixed length, and that the length of a simulation adequate for acceptable performance is highly model-dependent. We also investigate possible sources of error for the methods, and conclude that variance estimator bias is more important than point estimator bias in confidence interval coverage degradation.

A number of authors have identified problematic issues with techniques used in current simulation practice for selecting probability distributions and their parameters for input to stochastic simulations. A major goal of this paper is to address some of those issues by presenting a self-consistent evaluation of the uncertainty about the mean value of the simulation output, when there is uncertainty in both the parameters and functional form of input distributions (structural uncertainty), and uncertainty due to the stochastic nature of simulation output (stochastic uncertainty), as is common in simulation practice. The analysis leads to an algorithm for randomly sampling input distributions and parameters before each simulation replication, using a Bayesian posterior distribution for input distributions and parameters, given historical data. Mechanisms for addressing issues of importance to the discrete-event simulation community are illustrated by example, such as the specification of prior distributions, and analysis for shifted distributions.