# Browsing by Author "Berger, James O"

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Item Open Access Bayesian Adjustment for Multiplicity(2009) Scott, James GordonThis thesis is about Bayesian approaches for handling multiplicity. It considers three main kinds of multiple-testing scenarios: tests of exchangeable experimental units, tests for variable inclusion in linear regresson models, and tests for conditional independence in jointly normal vectors. Multiplicity adjustment in these three areas will be seen to have many common structural features. Though the modeling approach throughout is Bayesian, frequentist reasoning regarding error rates will often be employed.

Chapter 1 frames the issues in the context of historical debates about Bayesian multiplicity adjustment. Chapter 2 confronts the problem of large-scale screening of functional data, where control over Type-I error rates is a crucial issue. Chapter 3 develops new theory for comparing Bayes and empirical-Bayes approaches for multiplicity correction in regression variable selection. Chapters 4 and 5 describe new theoretical and computational tools for Gaussian graphical-model selection, where multiplicity arises in performing many simultaneous tests of pairwise conditional independence. Chapter 6 introduces a new approach to sparse-signal modeling based upon local shrinkage rules. Here the focus is not on multiplicity per se, but rather on using ideas from Bayesian multiple-testing models to motivate a new class of multivariate scale-mixture priors. Finally, Chapter 7 describes some directions for future study, many of which are the subjects of my current research agenda.

Item Open Access Development and Implementation of Bayesian Computer Model Emulators(2011) Lopes, Danilo LourencoOur interest is the risk assessment of rare natural hazards, such as

large volcanic pyroclastic flows. Since catastrophic consequences of

volcanic flows are rare events, our analysis benefits from the use of

a computer model to provide information about these events under

natural conditions that may not have been observed in reality.

A common problem in the analysis of computer experiments, however, is the high computational cost associated with each simulation of a complex physical process. We tackle this problem by using a statistical approximation (emulator) to predict the output of this computer model at untried values of inputs. Gaussian process response surface is a technique commonly used in these applications, because it is fast and easy to use in the analysis.

We explore several aspects of the implementation of Gaussian process emulators in a Bayesian context. First, we propose an improvement for the implementation of the plug-in approach to Gaussian processes. Next, we also evaluate the performance of a spatial model for large data sets in the context of computer experiments.

Computer model data can also be combined to field observations in order to calibrate the emulator and obtain statistical approximations to the computer model that are closer to reality. We present an application where we learn the joint distribution of inputs from field data and then bind this auxiliary information to the emulator in a calibration process.

One of the outputs of our computer model is a surface of maximum volcanic flow height over some geographical area. We show how the topography of the volcano area plays an important role in determining the shape of this surface, and we propose methods

to incorporate geophysical information in the multivariate analysis of computer model output.

Item Open Access On Uncertainty Quantification for Systems of Computer Models(2017) Kyzyurova, KseniaScientific inquiry about natural phenomena and processes are increasingly relying on the use of computer models as simulators of such processes. The challenge of using computer models for scientific investigation is that they are expensive in terms of computational cost and resources. However, the core methodology of fast statistical emulation (approximation) of a computer model overcomes this computational problem.

Complex phenomena and processes are often described not by a single computer model, but by a system of computer models or simulators. Direct emulation of a system of simulators may be infeasible for computational and logistical reasons.

This thesis proposes a statistical framework for fast emulation of systems of computer models and demonstrates its potential for inferential and predictive scientific goals.

The first chapter of the thesis introduces the Gaussian stochastic process (GaSP) emulator of a single simulator and summarizes ideas and findings in the rest of the thesis. The second chapter investigates the possibility of using independent GaSP emulators of computer models for fast construction of emulators of systems of computer models. The resulting approximation to a system of computer models is called the linked emulator. The third chapter discusses the irrelevance of attempting to model multivariate output of a computer model, for the purpose of emulation of that model. The linear model of coregionalization (LMC) is used to demonstrate this irrelevance, from both a theoretical perspective and from simulation studies. The fourth chapter introduces a framework for calibration of a system of computer models, using its linked emulator. The linked emulator allows for development of independent emulators of submodels on their own separately constructed design spaces, thus leading to effective dimension reduction in explored parameter space. The fifth chapter addresses the use of some non-Gaussian emulators, in particular censored and truncated GaSP emulators. The censored emulator is constructed to appropriately account for zero-inflated output of a computer model, arising when there are large regions of the input space for which the computer model output is zero. The truncated GaSP accommodates computer model output that is constrained to appear in a certain region. The linked emulator, for systems of computer models whose individual subemulators are either censored or truncated, is also presented. The last chapter concludes with an exposition of further research directions based on the ideas explored in the thesis.

The methodology developed in this thesis is illustrated by an application to quantification of the hazard from pyroclastic flow from the Soufri\`{e}re Hills Volcano on the island of Montserrat; a case study on prediction of volcanic ash transport and dispersal from the Eyjafjallaj{\"o}kull volcano, Iceland in April 14-16, 2010; and calibration of a vapour-liquid equilibrium model, a submodel of the Aspen Plus \textcopyright~chemical process software for design and deployment of amine-based $\mathrm{CO_2}$ capture systems.

Item Open Access Redefine statistical significance(Nature Human Behaviour, 2017-09-03) Benjamin, Daniel J; Berger, James O; Johannesson, Magnus; Nosek, Brian A; Wagenmakers, E-J; Berk, Richard; Bollen, Kenneth A; Brembs, Björn; Brown, Lawrence; Camerer, Colin; Cesarini, David; Chambers, Christopher D; Clyde, Merlise; Cook, Thomas D; De Boeck, Paul; Dienes, Zoltan; Dreber, Anna; Easwaran, Kenny; Efferson, Charles; Fehr, Ernst; Fidler, Fiona; Field, Andy P; Forster, Malcolm; George, Edward I; Gonzalez, Richard; Goodman, Steven; Green, Edwin; Green, Donald P; Greenwald, Anthony G; Hadfield, Jarrod D; Hedges, Larry V; Held, Leonhard; Hua Ho, Teck; Hoijtink, Herbert; Hruschka, Daniel J; Imai, Kosuke; Imbens, Guido; Ioannidis, John PA; Jeon, Minjeong; Jones, James Holland; Kirchler, Michael; Laibson, David; List, John; Little, Roderick; Lupia, Arthur; Machery, Edouard; Maxwell, Scott E; McCarthy, Michael; Moore, Don A; Morgan, Stephen L; Munafó, Marcus; Nakagawa, Shinichi; Nyhan, Brendan; Parker, Timothy H; Pericchi, Luis; Perugini, Marco; Rouder, Jeff; Rousseau, Judith; Savalei, Victoria; Schönbrodt, Felix D; Sellke, Thomas; Sinclair, Betsy; Tingley, Dustin; Van Zandt, Trisha; Vazire, Simine; Watts, Duncan J; Winship, Christopher; Wolpert, Robert L; Xie, Yu; Young, Cristobal; Zinman, Jonathan; Johnson, Valen E