Robust approximate Bayesian inference

We discuss an approach for deriving robust posterior distributions from $M$-estimating functions using Approximate Bayesian Computation (ABC) methods. In particular, we use $M$-estimating functions to construct suitable summary statistics in ABC algorithms. The theoretical properties of the robust posterior distributions are discussed. Special attention is given to the application of the method to linear mixed models. Simulation results and an application to a clinical study demonstrate the usefulness of the method. An R implementation is also provided in the robustBLME package.Comment: This is a revised and personal manuscript version of the article that has been accepted for publication by Journal of Statistical Planning and Inferenc

Design of Experiments for Screening

The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared

Use of orthogonal arrays, quasi-Monte Carlo sampling and kriging response models for reservoir simulation with many varying factors

Asset development teams may adjust simulation model parameters using experimental design to reveal which factors have the greatest impact on the reservoir performance. Response surfaces and experimental design make sensitivity analysis less expensive and more accurate, helping to optimize recovery under geological and economical uncertainties. In this thesis, experimental designs including orthogonal arrays, factorial designs, Latin hypercubes and Hammersley sequences are compared and analyzed. These methods are demonstrated for a gas well with water coning problem to illustrate the efficiency of orthogonal arrays. Eleven geologic factors are varied while optimizing three engineering factors (total of fourteen factors). The objective is to optimize completion length, tubing head pressure, and tubing diameter for a partially penetrating well with uncertain reservoir properties. A nearly orthogonal array was specified with three levels for eight factors and four levels for the remaining six geologic and engineering factors. This design requires only 36 simulations compared to (26,873,856) runs for a full factorial design. Hyperkriging surfaces are an alternative model form for large numbers. Hyperkriging uses the maximum likelihood variogram model parameters to minimize prediction errors. Kriging is compared to conventional polynomial response models. The robustness of the response surfaces generated by kriging and polynomial regression are compared using jackknifing and bootstrapping. Sensitivity analysis and uncertainty analysis can be performed inexpensively and efficiently using response surfaces. The proposed design approach requires fewer simulations and provides accurate response models, efficient optimization, and flexible sensitivity and uncertainty assessment

Recent Developments in the Econometrics of Program Evaluation

Many empirical questions in economics and other social sciences depend on causal effects of programs or policies. In the last two decades much research has been done on the econometric and statistical analysis of the effects of such programs or treatments. This recent theoretical literature has built on, and combined features of, earlier work in both the statistics and econometrics literatures. It has by now reached a level of maturity that makes it an important tool in many areas of empirical research in economics, including labor economics, public finance, development economics, industrial organization and other areas of empirical micro-economics. In this review we discuss some of the recent developments. We focus primarily on practical issues for empirical researchers, as well as provide a historical overview of the area and give references to more technical research.program evaluation, causality, unconfoundedness, Rubin Causal Model, potential outcomes, instrumental variables

Systematically missing confounders in individual participant data meta-analysis of observational cohort studies.

One difficulty in performing meta-analyses of observational cohort studies is that the availability of confounders may vary between cohorts, so that some cohorts provide fully adjusted analyses while others only provide partially adjusted analyses. Commonly, analyses of the association between an exposure and disease either are restricted to cohorts with full confounder information, or use all cohorts but do not fully adjust for confounding. We propose using a bivariate random-effects meta-analysis model to use information from all available cohorts while still adjusting for all the potential confounders. Our method uses both the fully adjusted and the partially adjusted estimated effects in the cohorts with full confounder information, together with an estimate of their within-cohort correlation. The method is applied to estimate the association between fibrinogen level and coronary heart disease incidence using data from 154,012 participants in 31 cohort

Recent developments in the econometrics of program evaluation

Many empirical questions in economics and other social sciences depend on causal effects of programs or policies. In the last two decades much research has been done on the econometric and statistical analysis of the effects of such programs or treatments. This recent theoretical literature has built on, and combined features of, earlier work in both the statistics and econometrics literatures. It has by now reached a level of maturity that makes it an important tool in many areas of empirical research in economics, including labor economics, public finance, development economics, industrial organization and other areas of empirical micro-economics. In this review we discuss some of the recent developments. We focus primarily on practical issues for empirical researchers, as well as provide a historical overview of the area and give references to more technical research.

Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment