# Browsing by Author "West, Mike"

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Item Open Access Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.(J Comput Graph Stat, 2010-06-01) Niemi, Jarad; West, MikeWe describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.Item Open Access Advances in Bayesian Modelling and Computation: Spatio-Temporal Processes, Model Assessment and Adaptive MCMC(2009) Ji, ChunlinThe modelling and analysis of complex stochastic systems with increasingly large data sets, state-spaces and parameters provides major stimulus to research in Bayesian nonparametric methods and Bayesian computation. This dissertation presents advances in both nonparametric modelling and statistical computation stimulated by challenging problems of analysis in complex spatio-temporal systems and core computational issues in model fitting and model assessment. The first part of the thesis, represented by chapters 2 to 4, concerns novel, nonparametric Bayesian mixture models for spatial point processes, with advances in modelling, computation and applications in biological contexts. Chapter 2 describes and develops models for spatial point processes in which the point outcomes are latent, where indirect observations related to the point outcomes are available, and in which the underlying spatial intensity functions are typically highly heterogenous. Spatial intensities of inhomogeneous Poisson processes are represented via flexible nonparametric Bayesian mixture models. Computational approaches are presented for this new class of spatial point process mixtures and extended to the context of unobserved point process outcomes. Two examples drawn from a central, motivating context, that of immunofluorescence histology analysis in biological studies generating high-resolution imaging data, demonstrate the modelling approach and computational methodology. Chapters 3 and 4 extend this framework to define a class of flexible Bayesian nonparametric models for inhomogeneous spatio-temporal point processes, adding dynamic models for underlying intensity patterns. Dependent Dirichlet process mixture models are introduced as core components of this new time-varying spatial model. Utilizing such nonparametric mixture models for the spatial process intensity functions allows the introduction of time variation via dynamic, state-space models for parameters characterizing the intensities. Bayesian inference and model-fitting is addressed via novel particle filtering ideas and methods. Illustrative simulation examples include studies in problems of extended target tracking and substantive data analysis in cell fluorescent microscopic imaging tracking problems.

The second part of the thesis, consisting of chapters 5 and chapter 6, concerns advances in computational methods for some core and generic Bayesian inferential problems. Chapter 5 develops a novel approach to estimation of upper and lower bounds for marginal likelihoods in Bayesian modelling using refinements of existing variational methods. Traditional variational approaches only provide lower bound estimation; this new lower/upper bound analysis is able to provide accurate and tight bounds in many problems, so facilitates more reliable computation for Bayesian model comparison while also providing a way to assess adequacy of variational densities as approximations to exact, intractable posteriors. The advances also include demonstration of the significant improvements that may be achieved in marginal likelihood estimation by marginalizing some parameters in the model. A distinct contribution to Bayesian computation is covered in Chapter 6. This concerns a generic framework for designing adaptive MCMC algorithms, emphasizing the adaptive Metropolized independence sampler and an effective adaptation strategy using a family of mixture distribution proposals. This work is coupled with development of a novel adaptive approach to computation in nonparametric modelling with large data sets; here a sequential learning approach is defined that iteratively utilizes smaller data subsets. Under the general framework of importance sampling based marginal likelihood computation, the proposed adaptive Monte Carlo method and sequential learning approach can facilitate improved accuracy in marginal likelihood computation. The approaches are exemplified in studies of both synthetic data examples, and in a real data analysis arising in astro-statistics.

Finally, chapter 7 summarizes the dissertation and discusses possible extensions of the specific modelling and computational innovations, as well as potential future work.

Item Open Access Applied Dynamic Factor Analysis for Macroeconomic Forecasting(2018) Eastman, WilliamThe use of dynamic factor analysis in statistical modeling has broad utility across an array of applications. This paper presents a novel hierachical structure suited to a particular class of predictive problems - those which necessitate the aggregation of numerous forecasts in the presence of substantial data missingness and a need for systematic dimensionality reduction. The model hierarchy is presented in the context of the prediction of U.S. Nonfarm Payrolls, a well-known economic statistic, though can be generally applied for any context exhibiting an analagous data structure.

Item Open Access Approximate Bayesian Computation for Complex Dynamic Systems(2013) Bonassi, Fernando VieiraThis thesis focuses on the development of ABC methods for statistical modeling in complex dynamic systems. Motivated by real applications in biology, I propose computational strategies for Bayesian inference in contexts where standard Monte Carlo methods cannot be directly applied due to the high complexity of the dynamic model and/or data limitations.

Chapter 2 focuses on stochastic bionetwork models applied to data generated from the marginal distribution of a few network nodes at snapshots in time. I present a Bayesian computational strategy, coupled with an approach to summarizing and numerically characterizing biological phenotypes that are represented in terms of the resulting sample distributions of cellular markers. ABC and mixture modeling are used to define the approach to linking mechanistic mathematical models of network dynamics to snapshot data, using a toggle switch example integrating simulated and real data as context.

Chapter 3 focuses on the application of the methodology presented in Chapter 2 to the Myc/Rb/E2F network. This network involves a relatively high number of parameters and stochastic equations in the model specification and, thus, is substantially more complex than the toggle switch example. The analysis of the Myc/Rb/E2F network is performed with simulated and real data. I demonstrate that the proposed method can indicate which parameters can be learned about using the marginal data.

In Chapter 4, I present an ABC SMC method that uses data-based adaptive weights. This easily implemented and computationally trivial extension of ABC SMC can substantially improve acceptance rates. This is demonstrated through a series of examples with simulated and real data, including the toggle switch example. Theoretical justification is also provided to explain why this method is expected to improve the effectiveness of ABC SMC.

In Chapter 5, I present an integrated Bayesian computational strategy for fitting complex dynamic models to sparse time-series data. This is applied to experimental data from an immunization response study with Indian Rhesus macaques. The computational strategy consists of two stages: first, MCMC is implemented based on simplified sampling steps, and then, the resulting approximate output is used to generate a proposal distribution for the parameters that results in an efficient ABC procedure. The incorporation of ABC as a correction tool improves the model fit, as is demonstrated through predictive posterior analysis on the data sets of the study.

Chapter 6 presents additional discussion and comments on potential future research directions.

Item Open Access Bayesian Analysis and Computational Methods for Dynamic Modeling(2009) Niemi, JaradDynamic models, also termed state space models, comprise an extremely rich model class for time series analysis. This dissertation focuses on building state space models for a variety of contexts and computationally efficient methods for Bayesian inference for simultaneous estimation of latent states and unknown fixed parameters.

Chapter 1 introduces state space models and methods of inference in these models. Chapter 2 describes a novel method for jointly sampling the entire latent state vector in a nonlinear Gaussian state space model using a computationally efficient adaptive mixture modeling procedure. This method is embedded in an overall Markov chain Monte Carlo algorithm for estimating fixed parameters as well as states. In Chapter 3 the method of the previous chapter is implemented in a few illustrative

nonlinear models and compared to standard existing methods. This chapter also looks at the effect of the number of mixture components as well as length of the time series on the efficiency of the method. I then turn to an biological application in Chapter 4. I discuss modeling choices as well as derivation of the state space model to be used in this application. Parameter and state estimation are analyzed in these models for both simulated and real data. Chapter 5 extends the methodology introduced in Chapter 2 from nonlinear Gaussian models to general state space models. The method is then applied to a financial

stochastic volatility model on US $ - British £ exchange rates. Bayesian inference in the previous chapter is accomplished through Markov chain Monte Carlo which is suitable for batch analyses, but computationally limiting in sequential analysis. Chapter 6 introduces sequential Monte Carlo. It discusses two methods currently available for simultaneous sequential estimation of latent states and fixed parameters and then introduces a novel algorithm that reduces the key, limiting degeneracy issue while being usable in a wide model class. Chapter 7 implements the novel algorithm in a disease surveillance context modeling influenza epidemics. Finally, Chapter 8 suggests areas for future work in both modeling and Bayesian inference. Several appendices provide detailed technical support material as well as relevant related work.

Item Open Access Bayesian Analysis of Latent Threshold Dynamic Models(2012) Nakajima, JochiTime series modeling faces increasingly high-dimensional problems in many scientific areas. Lack of relevant, data-based constraints typically leads to increased uncer-tainty in estimation and degradation of predictive performance. This dissertation addresses these general questions with a new and broadly applicable idea based on latent threshold models. The latent threshold approach is a model-based framework for inducing data-driven shrinkage of elements of parameter processes, collapsing them fully to zero when redundant or irrelevant while allowing for time-varying non-zero values when supported by the data. This dynamic sparsity modeling technique is implemented in broad classes of multivariate time series models with application tovarious time series data. The analyses demonstrate the utility of the latent threshold idea in reducing estimation uncertainty and improving predictions as well as model interpretation. Chapter 1 overviews the idea of the latent threshold approach and outlines the dissertation. Chapter 2 introduces the new approach to dynamic sparsity using latent threshold modeling and also discusses Bayesian analysis and computation for model fitting. Chapter 3 describes latent threshold multivariate models for a wide range of applications in the real data analysis that follows. Chapter 4 provides US and Japanese macroeconomic data analysis using latent threshold VAR models. Chapter 5 analyzes time series of foreign currency exchange rates (FX) using latent thresh-old dynamic factor models. Chapter 6 provides a study of electroencephalographic (EEG) time series using latent threshold factor process models. Chapter 7 develops a new framework of dynamic network modeling for multivariate time series using the latent threshold approach. Finally, Chapter 8 concludes the dissertation with open questions and future works.Item Open Access Bayesian Computation for Variable Selection and Multivariate Forecasting in Dynamic Models(2020) Lavine, IsaacChallenges arise in time series analysis due to the need for sequential forecasting and updating of model parameters as data is observed. This dissertation presents techniques for efficient Bayesian computation in multivariate time series analysis. Computational scalability is a core focus of this work, and often rests on the decouple-recouple concept in which multivariate models are decoupled into univariate models for efficient inference, and then recoupled to produce joint forecasts. The first section of this dissertation develops novel methods for variable selection in which models are scored and weighted based on specific forecasting and decision goals. In the time series setting, standard marginal likelihoods correspond to 1−step forecast densities, and considering alternate objectives is shown to improve long-term forecast accuracy. Scoring models based on forecast objectives can be computationally intensive, so the model space is reduced by evaluating univariate models separately along each dimension. This enables an efficient search over large, higher dimensional model spaces. A second area of focus in this dissertation is product demand forecasting, driven by applied considerations in grocery store sales. A novel copula model is developed for multivariate forecasting with Dynamic Generalized Linear Models (DGLMs), with a variational Bayes strategy for inference in latent factor DGLMs. Three applied case studies demonstrate that these techniques increase computational efficiency by several orders of magnitude over comparable multivariate models, without any loss of forecast accuracy. An additional area of interest in product demand forecasting is the effect of holidays and special events. An error correction model is introduced for this context, demonstrating strong predictive performance across a variety of holidays and retail item categories. Finally, a new Python package for Bayesian DGLM analysis, PyBATS, provides a set of tools for user-friendly analysis of univariate and multivariate time series.

Item Open Access Bayesian Dynamic Modeling and Forecasting of Count Time Series(2019) Berry, Lindsay RebeccaProblems of forecasting related time series of counts arise in a diverse array of applications such as consumer sales, epidemiology, ecology, law enforcement, and tourism. Characteristics of high-frequency count data including many zeros, high variation, extreme values, and varying means make the application of traditional time series methods inappropriate. In many settings, an additional challenge is producing on-line, multi-step forecasts for thousands of individual series in an efficient and flexible manner. This dissertation introduces novel classes of models to address efficiency, efficacy and scalability of dynamic models based on the concept of decouple/recouple applied to multiple series that are individually represented via novel univariate state-space models. The novel dynamic count mixture model involves dynamic generalized linear models for binary and conditionally Poisson time series, with dynamic random effects for overdispersion, and the use of dynamic covariates in both binary and non-zero components. New multivariate models then enable information sharing in contexts where data at a more highly aggregated level provide more incisive inference on shared patterns such as trends and seasonality. This novel decouple/recouple strategy incorporates cross-series linkages while insulating parallel estimation of univariate models. We extend these models to a general framework appropriate for settings in which count data arises through a compound process. The motivating application is in consumer sales contexts where variability in high-frequency sales data arises from the compounding effects of the number of transactions and the number of sales-per-transactions. This framework involves adapting the dynamic count mixture model to forecast transactions, coupled with a binary cascade concept using a sequence of Bayesian models to predict the number of units per transaction. The motivation behind the binary cascade is that the appropriate way to model rare events is through a sequence of conditional probabilities of increasingly rare outcomes. Several case studies in many-item, multi-step ahead supermarket sales forecasting demonstrate improved forecasting performance using the proposed models, with discussion of forecast accuracy metrics and the benefits of probabilistic forecast accuracy assessment.

Item Open Access Bayesian Dynamic Modeling for Streaming Network Data(2017) Chen, XiStreaming network data of various forms arises in many applications, raising interest in research to model and quantify the nature of stochasticity and structure in dynamics underlying such data. One example context is that of traffic flow count data in networks, such as in automobile or aviation transportation, certain directed social network contexts, and Internet studies. Using an example of Internet browser traffic flows through site-segments of an international news website, I present Bayesian analyses of two new, linked classes of models which, in tandem, allow fast, scalable and interpretable Bayesian inference on dynamic patterns over time underlying flows. I develop two kinds of flexible state-space models for streaming count data, able to adaptively characterize and quantify network dynamics efficiently in real-time. These models are then used as emulators of more structured, time-varying gravity models that allow formal dissection of network dynamics. This yields interpretable inferences on traffic flow characteristics, and on dynamics in interactions among network nodes. Bayesian monitoring theory defines a strategy for sequential model assessment and adaptation in cases when network flow data deviates from model-based predictions. Exploratory and sequential monitoring analyses of evolving traffic on a network of web site-segments in e-commerce demonstrate the utility of this coupled Bayesian emulation approach to analysis of streaming network count data.

A second, different dynamic network context is that involving relational data. Examples include contexts of binary network data indicating communications or relationships between pairs of network nodes over time. Some popular examples include friendships over social networks and communications between different functional zones in brain. Using an example of co-movements of company stock indices, I develop and compare two different approaches. One involves latent threshold models mapping latent processes to binary entries via a probabilistic link function, a second involves dynamic generalized linear models for binary outcomes. Analyses implement using Markov chain Monte Carlo methods are available for these models, but naturally computationally demanding and not scalable to relevant network dimensions for many contexts. In contrast, dynamic generalized linear models can implemented using fast, effective approximate Bayesian computations for both sequential and retrospective analyses to enable linear-time computations. I also demonstrate the use of a model decoupling/recoupling strategy to enable scaling in network size.

Item Open Access Bayesian Dynamic Network Modeling for Social Media Political Talk(2019) Chen, HaohanStreaming social media network data have been used in recent studies on political behavior and institutions. Modeling time dynamics in such data helps political scientists produce robust results and efficiently manage their data collection process. However, existing political science methods are yet to provide researchers with the tools to analyze and monitor streaming social media network data. In this thesis, I introduce Bayesian dynamic network modeling for political science research. An extension of the recent development of dynamic modeling techniques, the method enables political scientists to track trends and detect anomalies in streaming social media network data. I illustrate the method with an application to an original dataset of political discourse from a Chinese social networking site. The model detects citizens' behavioral responses to political and non-political events. It also suggests the Chinese government censors and fabricates online discourse during politically sensitive periods.

Item Open Access Bayesian Dynamic Network Modeling with Censored Flow Data(2020) Cozzi, Brian ThomasThere is an abundance of applied and theoretical statistical research focused on the analysis of network data. However, few applications have the flexibility to account for the inherently limited flow that results from constrained capacity at destination nodes and, thus, may provide an incomplete picture of the underlying data generating process. This thesis works to address this shortcoming by applying Bayesian Dynamic Flow Modeling in a context where the capacity at the destination node is limited. To that end, it develops a methodology for updating beliefs about flow rates when the flow is censored. These methods are applied to a publicly available bike sharing dataset that exhibits censoring during high-volume times of the day. The results show a comparison of network characterization from a model built under the assumption of censored flows and a model without that assumption. This analysis highlights specific circumstances in which the estimates of underlying demand from both models are most at odds with one another and provides a framework for guiding the analysis of datasets that can be similarly represented.

Item Open Access Bayesian Emulation for Sequential Modeling, Inference and Decision Analysis(2016) Irie, KaoruThe advances in three related areas of state-space modeling, sequential Bayesian learning, and decision analysis are addressed, with the statistical challenges of scalability and associated dynamic sparsity. The key theme that ties the three areas is Bayesian model emulation: solving challenging analysis/computational problems using creative model emulators. This idea defines theoretical and applied advances in non-linear, non-Gaussian state-space modeling, dynamic sparsity, decision analysis and statistical computation, across linked contexts of multivariate time series and dynamic networks studies. Examples and applications in financial time series and portfolio analysis, macroeconomics and internet studies from computational advertising demonstrate the utility of the core methodological innovations.

Chapter 1 summarizes the three areas/problems and the key idea of emulating in those areas. Chapter 2 discusses the sequential analysis of latent threshold models with use of emulating models that allows for analytical filtering to enhance the efficiency of posterior sampling. Chapter 3 examines the emulator model in decision analysis, or the synthetic model, that is equivalent to the loss function in the original minimization problem, and shows its performance in the context of sequential portfolio optimization. Chapter 4 describes the method for modeling the steaming data of counts observed on a large network that relies on emulating the whole, dependent network model by independent, conjugate sub-models customized to each set of flow. Chapter 5 reviews those advances and makes the concluding remarks.

Item Open Access Bayesian Learning in Sparse Graphical Factor Models via Variational Mean-Field Annealing.(J Mach Learn Res, 2010-05-01) Yoshida, Ryo; West, MikeWe describe a class of sparse latent factor models, called graphical factor models (GFMs), and relevant sparse learning algorithms for posterior mode estimation. Linear, Gaussian GFMs have sparse, orthogonal factor loadings matrices, that, in addition to sparsity of the implied covariance matrices, also induce conditional independence structures via zeros in the implied precision matrices. We describe the models and their use for robust estimation of sparse latent factor structure and data/signal reconstruction. We develop computational algorithms for model exploration and posterior mode search, addressing the hard combinatorial optimization involved in the search over a huge space of potential sparse configurations. A mean-field variational technique coupled with annealing is developed to successively generate "artificial" posterior distributions that, at the limiting temperature in the annealing schedule, define required posterior modes in the GFM parameter space. Several detailed empirical studies and comparisons to related approaches are discussed, including analyses of handwritten digit image and cancer gene expression data.Item Open Access Bayesian Modelling and Computation in Dynamic and Spatial Systems(2011) Mukherjee, ChiranjitApplied studies in multiple areas involving spatial and dynamic systems increasingly challenge our modelling and computational abilities as data volumes increase, and as spatial and temporal scales move to increasingly high-resolutions with parallel increase in complexity of dependency patterns. Motivated by two challenging problems of this sort, study of cellular dynamics in bacterial communication and global Carbon monoxide emissions prediction based on high-resolution global satellite imagery, this dissertation focuses on building sparse models and computational methods for data-dense dynamic, spatial and spatio-dynamic systems.

The first part of the thesis develops a novel particle filtering algorithm for very long state-space models with sparse observations arising in studies of dynamic cellular networks. The need for increasing sample size with increasing dimension is met with parallel developments in informed resample-move strategies and distributed implementation. Fundamental innovations in the particle filtering literature are identified and used for designing an efficient particle filter.

The second part of the thesis focuses on sparse spatial modelling of high-resolution lattice data. Gaussian Markov random field models, defined through spatial autoregressions, are adopted for their computational properties. Their potential is evidenced in an applied example in atmospheric chemistry where the focus is on inversion of satellite data combined with computer model predictions to infer ground-level CO emissions from multiple candidate sources on a global scale. Further, extending the framework of simultaneous autoregressive models, a novel hierarchical autoregressive model is developed for non-homogeneous spatial random-fields.

The final part of the thesis develops a novel space-time model for data on a rectangular lattice. The dynamic spatial factor model framework is extended with matrix normal spatial factor loadings. A new class of Gaussian Markov random field models for random matrices, defined with low-dimensional row and column conditional independence graphs, is used to model sparse spatial factor loadings. Further dimensionality reduction is achieved through the dynamic factor model framework, which makes this class of models extremely attractive for systematically evolving non-homogeneous, high-resolution space-time data on rectangular lattices. Flexible choices for prior distributions and posterior computations are presented and illustrated with a synthetic data example.

Item Open Access Bayesian multi- and matrix-variate modelling: Graphical models and time series(2010) Wang, HaoModelling and inference with higher-dimensional variables, including studies in multivariate time series analysis, raise challenges to our ability to ``scale-up'' statistical approaches that involve both modelling and computational issues. Modelling issues relate to the interest in parsimony of parametrisation and control over proliferation of parameters; computational issues relate to the basic challenges to the efficiency of statistical computation (simulation and optimisation) with increasingly high-dimensional and structured models. This thesis addresses these questions and explores Bayesian approaches inducing relevant sparsity and structure into parameter spaces, with a particular focus on time series and dynamic modelling.

Chapter 1 introduces the challenge of estimating covariance matrices in multivariate time series problems, and reviews Bayesian treatments of Gaussian graphical models that are useful for estimating covariance matrices. Chapter 2 and 3 introduce the development and application of matrix-variate graphical models and time series models. Chapter 4 develops dynamic graphical models for multivariate financial time series. Chapter 5 and 6 propose an integrated approach for dynamic multivariate regression modelling with simultaneous selection of variables and graphical-model structured covariance matrices. Finally, Chapter 7 summarises the dissertation and discusses a number of new and open research directions.

Item Open Access Bayesian Multiregression Dynamic Models with Applications in Finance and Business(2015) Zhao, YiThis thesis discusses novel developments in Bayesian analytics for high-dimensional multivariate time series. The focus is on the class of multiregression dynamic models (MDMs), which can be decomposed into sets of univariate models processed in parallel yet coupled for forecasting and decision making. Parallel processing greatly speeds up the computations and vastly expands the range of time series to which the analysis can be applied.

I begin by defining a new sparse representation of the dependence between the components of a multivariate time series. Using this representation, innovations involve sparse dynamic dependence networks, idiosyncrasies in time-varying auto-regressive lag structures, and flexibility of discounting methods for stochastic volatilities.

For exploration of the model space, I define a variant of the Shotgun Stochastic Search (SSS) algorithm. Under the parallelizable framework, this new SSS algorithm allows the stochastic search to move in each dimension simultaneously at each iteration, and thus it moves much faster to high probability regions of model space than does traditional SSS.

For the assessment of model uncertainty in MDMs, I propose an innovative method that converts model uncertainties from the multivariate context to the univariate context using Bayesian Model Averaging and power discounting techniques. I show that this approach can succeed in effectively capturing time-varying model uncertainties on various model parameters, while also identifying practically superior predictive and lucrative models in financial studies.

Finally I introduce common state coupled DLMs/MDMs (CSCDLMs/CSCMDMs), a new class of models for multivariate time series. These models are related to the established class of dynamic linear models, but include both common and series-specific state vectors and incorporate multivariate stochastic volatility. Bayesian analytics are developed including sequential updating, using a novel forward-filtering-backward-sampling scheme. Online and analytic learning of observation variances is achieved by an approximation method using variance discounting. This method results in faster computation for sequential step-ahead forecasting than MCMC, satisfying the requirement of speed for real-world applications.

A motivating example is the problem of short-term prediction of electricity demand in a "Smart Grid" scenario. Previous models do not enable either time-varying, correlated structure or online learning of the covariance structure of the state and observational evolution noise vectors. I address these issues by using a CSCMDM and applying a variance discounting method for learning correlation structure. Experimental results on a real data set, including comparisons with previous models, validate the effectiveness of the new framework.

Item Open Access Bayesian Predictive Decision Synthesis: Methodology and Applications(2024) Tallman, EmilyDecision-guided perspectives on model uncertainty expand traditional statistical thinking about managing, comparing, and combining inferences from sets of models. In this dissertation, we present a novel framework entitled Bayesian predictive decision synthesis (BPDS) which advances conceptual and theoretical foundations in the intersection of model uncertainty and decision theory. We define new methodology that explicitly integrates decision-analytic outcomes into the evaluation, comparison and potential combination of candidate models. BPDS extends recent theoretical and practical advances based on both Bayesian predictive synthesis (BPS) and empirical goal-focused model uncertainty analysis. Specifically, we focus on the utilization of a specific outcome-dependent weight function in combination with more traditional model averaging methods that incorporate model performance. This outcome-dependent weight function is enabled by the development of a novel subjective Bayesian perspective on model weighting in predictive decision settings, with theoretical connections to Entropic Tilting and generalized Bayesian updating. We include multiple in-depth case studies from applied contexts to illustrate the use cases of BPDS and raise and investigate relevant questions. These case studies include applications in both the case where predictions depend on the decision at hand and the case where the decision has no impact on predictions. In the decision-dependent case, we present an optimal design for regression prediction and a collaboration involving macroeconomic forecasting. In the decision-independent case, we focus on a setting of sequential time series forecasting for financial portfolio decisions. Overall, these case studies are able to demonstrate the potential for BPDS to improve decisions and thus realized outcomes.

Item Open Access Bayesian Predictive Synthesis: Forecast Calibration and Combination(2017) Johnson, Matthew ChaseThe combination of forecast densities, whether they result from a set of models,

a group of consulted experts, or other sources, is becoming increasingly important

in the fields of economics, policy, and finance, among others. Requiring methodology

that goes beyond standard Bayesian model uncertainty and model mixing -

with its well-known limitations based on a clearly proscribed theoretical basis - multiple

`density combination' methods have been proposed. While some proposals have

demonstrated empirical success, most apparently lack a core philosophical and theoretical

foundation. Interesting recent examples generalize the common `linear opinion

pool' with

flexible mixing weights that depend on the forecast variable itself -

i.e., outcome-dependent mixing. This dissertation takes a foundational subjective

Bayesian perspective in order to show that such a density combination scheme is

in fact justified as one example of Bayesian agent opinion analysis, or `predictive

synthesis'. This logically coherent framework clearly delineates the underlying assumptions

as well as the theoretical constraints and limitations of many combination

`rules', defining a broad class of Bayesian models for the general problem. A number

of examples, including applications to sets of predictive densities for foreign exchange

and United States inflation time series data, provide illustrations.

Chapters 1-2 introduce and describe the ideas involved in Bayesian predictive

synthesis (BPS) as a method of subjective analysis. Chapters 3-4 describe different

possible formulations of outcome-dependent mixing. Chapter 5 places the analysis into a time series context and covers relevant inference techniques. Chapters 6 and 7

apply the time series analysis to euro currency forecasts and United States inflation

data. Chapter 8 concludes.

Item Open Access Bayesian Variable Selection in Clustering and Hierarchical Mixture Modeling(2012) Lin, LinClustering methods are designed to separate heterogeneous data into groups of similar objects such that objects within a group are similar, and objects in different groups are dissimilar. From the machine learning perspective, clustering can also be viewed as one of the most important topics within the unsupervised learning problem, which involves finding structures in a collection of unlabeled data. Various clustering methods have been developed under different problem contexts. Specifically, high dimensional data has stimulated a high level of interest in combining clustering algorithms and variable selection procedures; large data sets with expanding dimension have provoked an increasing need for relevant, customized clustering algorithms that offer the ability to detect low probability clusters.

This dissertation focuses on the model-based Bayesian approach to clustering. I first develop a new Bayesian Expectation-Maximization algorithm in fitting Dirichlet process mixture models and an algorithm to identify clusters under mixture models by aggregating mixture components. These two algorithms are used extensively throughout the dissertation. I then develop the concept and theory of a new variable selection method that is based on an evaluation of subsets of variables for the discriminatory evidence they provide in multivariate mixture modeling. This new approach to discriminative information analysis uses a natural measure of concordance between mixture component densities. The approach is both effective and computationally attractive for routine use in assessing and prioritizing subsets of variables according to their roles in the discrimination of one or more clusters. I demonstrate that the approach is useful for providing an objective basis for including or excluding specific variables in flow cytometry data analysis. These studies demonstrate how ranked sets of such variables can be used to optimize clustering strategies and selectively visualize identified clusters of the data of interest.

Next, I create a new approach to Bayesian mixture modeling with large data sets for a specific, important class of problems in biological subtype identification. The context, that of combinatorial encoding in flow cytometry, naturally introduces the hierarchical structure that these new models are designed to incorporate. I describe these novel classes of Bayesian mixture models with hierarchical structures that reflect the underlying problem context. The Bayesian analysis involves structured priors and computations using customized Markov chain Monte Carlo methods for model fitting that exploit a distributed GPU (graphics processing unit) implementation. The hierarchical mixture model is applied in the novel use of automated flow cytometry technology to measure levels of protein markers on thousands to millions of cells.

Finally, I develop a new approach to cluster high dimensional data based on Kingman's coalescent tree modeling ideas. Under traditional clustering models, the number of parameters required to construct the model increases exponentially with the number of dimensions. This phenomenon can lead to model overfitting and an enormous computational search challenge. The approach addresses these issues by proposing to learn the data structure in each individual dimension and combining these dimensions in a flexible tree-based model class. The new tree-based mixture model is studied extensively under various simulation studies, under which the model's superiority is reflected compared with traditional mixture models.

Item Open Access Clustering Multiple Related Datasets with a Hierarchical Dirichlet Process(2011) de Oliveira Sales, Ana PaulaI consider the problem of clustering multiple related groups of data. My approach entails mixture models in the context of hierarchical Dirichlet processes, focusing on their ability to perform inference on the unknown number of components in the mixture, as well as to facilitate the sharing of information and borrowing of strength across the various data groups. Here, I build upon the hierarchical Dirichlet process model proposed by Muller et al. (2004), revising some relevant aspects of the model, as well as improving the MCMC sampler's convergence by combining local Gibbs sampler moves with global Metropolis-Hastings split-merge moves. I demonstrate the strengths of my model by employing it to cluster both synthetic and real datasets.