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External Bayesian Analysis for Computer Simulators *

Michael Goldstein

in Bayesian Statistics 9

Computer simulators offer a powerful approach for studying complex physical systems. We consider their use in current practice and the role of external uncertainty in bridging the gap between the ... More

Computer simulators offer a powerful approach for studying complex physical systems. We consider their use in current practice and the role of external uncertainty in bridging the gap between the properties of the model and of the system. The interpretation of this uncertainty analysis raises questions about the role and meaning of the Bayesian approach. We summarize some theory which is helpful to clarify and amplify the role of external specifications of uncertainty, and illustrate some of the types of calculation suggested by this approach.Less

Principles of Probability

N. Thompson Hobbs and Mevin B. Hooten

in Bayesian Models: A Statistical Primer for Ecologists

This chapter describes the rules of probability as well as probability distributions. Because models are inherently, deliberately approximate, there comes a need to understand the approximation ... More

This chapter describes the rules of probability as well as probability distributions. Because models are inherently, deliberately approximate, there comes a need to understand the approximation inherent in models in terms of uncertainty. Thus, equipped with a proper understanding of the principles of probability, ecologists can analyze the particular research problem at hand regardless of its idiosyncrasies. These analyses extend logically from first principles rather than from a particular statistical recipe. The chapter starts with the definition of probability and develops a logical progression of concepts extending from it to a fully specified and implemented Bayesian analysis appropriate for a broad range of research problems in ecology.Less

Momentum density studies by the Maximum Entropy Method

L. Dobrzyński

in X-Ray Compton Scattering

This chapter discusses the Maximum Entropy Method (MEM). It begins with a general introduction to MEM, then develops the application to the reconstruction of the three-dimensional electron density ... More

This chapter discusses the Maximum Entropy Method (MEM). It begins with a general introduction to MEM, then develops the application to the reconstruction of the three-dimensional electron density distribution from the measured one dimensional projections (the directional Compton profiles) using both the MEED code and the exact solution method. Statistical errors in the reconstruction maps are considered and results for a number of real data sets presented. The chapter, which has 30 references, forms an introduction to MEM generally for x-ray practitioners.Less

Bayesian Meta-analysis

Christopher H. Schmid and Kerrie Mengersen

in Handbook of Meta-analysis in Ecology and Evolution

This chapter introduces a Bayesian approach to meta-analysis. It discusses the ways in which a Bayesian approach differs from the method of moments and maximum likelihood methods described in ... More

This chapter introduces a Bayesian approach to meta-analysis. It discusses the ways in which a Bayesian approach differs from the method of moments and maximum likelihood methods described in chapters 9 and 10, and summarizes the steps required for a Bayesian analysis. It shows that Bayesian methods provide the basis for a rich variety of very flexible models, explicit statements about uncertainty of model parameters, inclusion of other information relevant to an analysis, and direct probabilistic statements about parameters of interest. In a meta-analysis context, this allows for more straightforward accommodation of study-specific differences and similarities, nonnormality and other distributional features of the data, missing data, small studies, and so forth.Less

Bayesian dynamic modelling

West Mike

in Bayesian Theory and Applications

This chapter focuses on some key models and ideas in Bayesian time series and forecasting, along with extracts from a few time series analysis and forecasting examples. It discusses specific ... More

This chapter focuses on some key models and ideas in Bayesian time series and forecasting, along with extracts from a few time series analysis and forecasting examples. It discusses specific modelling innovations that relate directly to the goals of addressing analysis of increasingly high-dimensional time series and nonlinear models. These include dynamic graphical and matrix models, dynamic matrix models for stochastic volatility, time-varying sparsity modelling, and nonlinear dynamical systems.Less

Extensions

Francis X. Diebold and Glenn D. Rudebusch

in Yield Curve Modeling and Forecasting: The Dynamic Nelson-Siegel Approach

This chapter highlights aspects of the vibrant ongoing research program associated with the ideas developed in earlier chapters. It begins with a collage-style sketch of work involving Bayesian ... More

This chapter highlights aspects of the vibrant ongoing research program associated with the ideas developed in earlier chapters. It begins with a collage-style sketch of work involving Bayesian analysis, functional form for factor loadings, term structures of credit spreads, and nonlinearities. It then discusses in greater detail the incorporation of more than three yield factors. Next, it treats stochastic volatility in both dynamic Nelson–Siegel model (DNS) and arbitrage-free DNS (AFNS) environments, with some attention to the issue of unspanned stochastic volatility. Finally, it discusses the incorporation of macroeconomic fundamentals in their relation to bond yields. It also introduces aspects of modeling real versus nominal yields in DNS/AFNS environments, a theme treated in detail in Chapter 5.Less

Uncertainty in Foreign Policy Making: Changing Relations among South Korea, North Korea, and the United States of America in the Twenty-First Century

HeeMin Kim

in Korean Democracy in Transition: A Rational Blueprint for Developing Societies

This chapter discusses the changing political situation on the Korean peninsula. It establishes that the situation is amenable to Bayesian game analysis and presents an analysis of Bayesian games ... More

This chapter discusses the changing political situation on the Korean peninsula. It establishes that the situation is amenable to Bayesian game analysis and presents an analysis of Bayesian games played between North and South Korea, and North Korea and the United States. It also discusses the insights and substantive implications that these models provide, after presenting a solution to the equilibria of these games.Less

Empirical Models

Kevin A. Clarke and David M. Primo

in A Model Discipline: Political Science and the Logic of Representations

Empirical models are the subject of this chapter. We begin by defining what an empirical model is and its relationship to the data. We discuss how to understand an empirical model under the ... More

Empirical models are the subject of this chapter. We begin by defining what an empirical model is and its relationship to the data. We discuss how to understand an empirical model under the model-based account. We argue that empirical models can be useful in one or more of three ways: prediction, measurement, and characterization. We pay particular attention to theory testing as the most common use of empirical models and the use to which empirical models are least suited. We demonstrate that the combination of a hypothetico-deductive relationship between the theoretical model and the hypothesis to be tested and a hypothetico-deductive relationship between the hypothesis to be tested and the data prevents empirical model testing. This logic holds regardless of the statistical approach—falsificationist, verificationist, or Bayesian—taken. We then address the other uses of empirical modeling by presenting examples of empirical models drawn from the literature that eschew theory testing while remaining useful, and by most accounts, scientific.Less

Bayes, Hume, Price, and Miracles

John Earman

in Bayes's Theorem

This chapter discusses the Bayesian analysis of miracles. It is set in the context of the eighteenth-century debate on miracles. The discussion is focused on the probable response of Thomas Bayes to ... More

This chapter discusses the Bayesian analysis of miracles. It is set in the context of the eighteenth-century debate on miracles. The discussion is focused on the probable response of Thomas Bayes to David Hume's celebrated argument against miracles. The chapter presents the claim that the criticisms Richard Price made against Hume's argument against miracles were largely solid.Less

Bayesian estimation of parameters

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

This chapter discusses the use of importance sampling for the estimation of parameters in Bayesian analysis for models of Part I and Part II. It first develops the analysis of the linear Gaussian ... More

This chapter discusses the use of importance sampling for the estimation of parameters in Bayesian analysis for models of Part I and Part II. It first develops the analysis of the linear Gaussian state space model by constructing importance samples of additional parameters. It then shows how to combine these with Kalman filter and smoother outputs to obtain the estimates of state parameters required. A brief description is also given of the alternative simulation technique, Markov chain Monte Carlo methods.Less

Inverse problems

Fox Colin, Haario Heikki, and Christen J Andrés

in Bayesian Theory and Applications

This chapter discusses the features that are characteristic for the problems most typically treated under the umbrella of inverse problems. It begins by listing representative examples of inverse ... More

This chapter discusses the features that are characteristic for the problems most typically treated under the umbrella of inverse problems. It begins by listing representative examples of inverse problems followed by a discussion of the key mathematical property of ill-posedness. It then discusses deterministic and regularization methods, and presents some history of Bayesian analysis, as viewed from physics. Next, it provides the framework for current methodology and describes some of the recent advances in Markov chain Monte Carlo (MCMC) algorithms. The chapter concludes with a glimpse of future directions.Less

The Use of Proximal Information Scent to Forage for Distal Content on the World Wide Web

Peter Pirolli

in Adaptive Perspectives on Human–Technology Interaction: Methods and Models for Cognitive Engineering and Human-Computer Interaction

This chapter summarizes information foraging research on use of the World Wide Web (the Web). The particular focus is placed on a psychological theory of information scent that is embedded in a ... More

This chapter summarizes information foraging research on use of the World Wide Web (the Web). The particular focus is placed on a psychological theory of information scent that is embedded in a broader model of information foraging on the Web. It specifically presents a theoretical account of information scent that supports the development of models of navigation choice. Next, it reports some aspects of the Web environment that will be relevant to developing a model of how people assess information scent cues to navigate. The Brunswik's lens model view is then used to frame the development of a stochastic model of individual utility judgment and choice that derives from a Bayesian analysis of the environment. Finally, it evaluates a model of Web foraging that addresses data collected from Web users working on tasks in a study that attempted to follow Brunswik's tenets of representative design.Less

Morphological analogy: Only a beginning

John Goldsmith

in Analogy in Grammar: Form and Acquisition

A range of approaches to word structure assume segmentation of words into morphs. This chapter proposes explicit algorithm that takes natural language text as its input, and produces the ... More

A range of approaches to word structure assume segmentation of words into morphs. This chapter proposes explicit algorithm that takes natural language text as its input, and produces the morphological structure of text as its output. Within this model, formal notions that correspond naturally to the traditional notion of analogy are useful and important as part of a boot-strapping heuristic for the discovery of morphological structure. At the same time, it is necessary to develop a refined quantitative model in order to find the kind of articulated linguistic structures that are to be found in natural languages.Less

Bayesians, Frequentists, and the Dna Database Search Controversy

in Truth Machine: The Contentious History of DNA Fingerprinting

This chapter, which discusses the controversy among statisticians in the United States over the analysis of DNA database “cold hits,” considers the defense use of Bayesian analysis to unpack and ... More

This chapter, which discusses the controversy among statisticians in the United States over the analysis of DNA database “cold hits,” considers the defense use of Bayesian analysis to unpack and neutralize the impressive random match probabilities presented by the prosecution's experts. It suggests that Bayesian treatments can potentially open up a creative repackaging of evidence that disrupts settled legal and vernacular distinctions between expert and commonsense knowledge.Less

Oil Shocks in a DSGE Model for the Korean Economy

Sungbae An and Kang Heedon

in Commodity Prices and Markets

This chapter describes the oil shocks using a dynamic stochastic general equilibrium (DSGE) model for the Korean economy. The Korean economy depends entirely on imports for its acquisition of crude ... More

This chapter describes the oil shocks using a dynamic stochastic general equilibrium (DSGE) model for the Korean economy. The Korean economy depends entirely on imports for its acquisition of crude oil, and households, entrepreneurs, and policymakers are interested in knowing to what extent the rise in oil prices affects the economy. Within an Bayesian estimation framework including DSGE-vector autoregressions (VARs), the empirical analysis used is based on Korean aggregate data. Using Bayesian analysis, the model is used to check the importance of each channel that transmits an oil price shock to the economy. It is found that the model economy produces reasonable posterior estimates of the structural parameters and works relatively well compared to impulse responses from the VAR with optimal prior weight from the DSGE model. A more elaborated model on government behavior is anticipated to investigate the pass-through of oil price shocks.Less

The Portrait Problem: Bayesian Inference with Joint Likelihood

Therese M. Donovan and Ruth M. Mickey

in Bayesian Statistics for Beginners: a step-by-step approach

Chapter 7 discusses the “Portrait Problem,” which concerns the dispute about whether a portrait frequently associated with Thomas Bayes (and used, in fact, as the cover of this book!) is actually a ... More

Chapter 7 discusses the “Portrait Problem,” which concerns the dispute about whether a portrait frequently associated with Thomas Bayes (and used, in fact, as the cover of this book!) is actually a picture of him. In doing so, the chapter highlights the fact that multiple pieces of information can be used in a Bayesian analysis. A key concept in this chapter is that multiple sources of data can be combined in a Bayesian inference framework. The main take-home point is that Bayesian analysis can be very, very flexible. A Bayesian analysis is possible as long as the likelihood of observing the data under each hypothesis can be computed. The chapter also discusses the concepts of joint likelihood and independence.Less

Rational analysis as a link between human memory and information retrieval

Mark Steyvers and Thomas L. Griffiths

in The Probabilistic Mind:: Prospects for Bayesian cognitive science

This chapter provides a complementary Bayesian analysis of the problem of memory retrieval. A Bayesian model that is able both to classify words into semantically coherent groups, merely from ... More

This chapter provides a complementary Bayesian analysis of the problem of memory retrieval. A Bayesian model that is able both to classify words into semantically coherent groups, merely from observing their co-occurrence patterns in texts, is used as the basis for understanding aspects not only of how some linguistic categories might be created, but also how relevant information can be retrieved, using probabilistic principles. This work can be viewed as a natural follow-on from Anderson and colleagues' pioneering rational analyses of memory (Anderson & Milson, 1989; Anderson & Schooler, 1991). This chapter uses innovations in information retrieval as a way to explore the connections between research on human memory and information retrieval systems. It also provides an example of how cognitive research can help information retrieval research by formalizing theories of knowledge and memory organization that have been proposed by cognitive psychologists.Less