In the present paper we study switching state space models from a Bayesian point of view. For estimation, the model is reformulated as a hierarchical model. We discuss various MCMC methods for Bayesian estimation, among them unconstrained Gibbs sampling, constrained sampling and permutation sampling. We address in detail the problem of unidentifiability, and discuss potential information available from an unidentified model. Furthermore the paper discusses issues in model selection such as selecting the number of states or testing for the presence of Markov switching heterogeneity. The model likelihoods of all possible hypotheses are estimated by using the method of bridge sampling. We conclude the paper with applications to simulated data as well as to modelling the U.S./U.K. real exchange rate. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

Hidden Markov models have become a popular tool for modeling long-term investment guarantees. Many different variations of hidden Markov models have been proposed over the past decades for modeling indexes such as the S&P 500, and they capture the tail risk inherent in the market to varying degrees. However, goodness-of-fit testing, such as residual-based testing, for hidden Markov models is a relatively undeveloped area of research. This work focuses on hidden Markov model assessment, and develops a stochastic approach to deriving a residual set that is ideal for standard residual tests. This result allows hidden-state models to be tested for goodness-of-fit with the well developed testing strategies for single-state models. This work also focuses on parameter uncertainty for the popular long-term equity hidden Markov models. There is a special focus on underlying states that represent lower returns and higher volatility in the market, as these states can have the largest impact on investment guarantee valuation. A Bayesian approach for the hidden Markov models is applied to address the issue of parameter uncertainty and the impact it can have on investment guarantee models. Also in this thesis, the areas of portfolio optimization and portfolio replication under a hidden Markov model setting are further developed. Different strategies for optimization and portfolio hedging under hidden Markov models are presented and compared using real world data. The impact of parameter uncertainty, particularly with model parameters that are connected with higher market volatility, is once again a focus, and the effects of not taking parameter uncertainty into account when optimizing or hedging in a hidden Markov are demonstrated.

<p>Many biological processes are effectively modeled as networks, but a frequent assumption is that these networks do not change during data collection. However, that assumption does not hold for many phenomena, such as neural growth during learning or changes in genetic regulation during cell differentiation. Approaches are needed that explicitly model networks as they change in time and that characterize the nature of those changes.</p><p>In this work, we develop a new class of graphical models in which the conditional dependence structure of the underlying data-generation process is permitted to change over time. We first present the model, explain how to derive it from Bayesian networks, and develop an efficient MCMC sampling algorithm that easily generalizes under varying levels of uncertainty about the data generation process. We then characterize the nature of evolving networks in several biological datasets.</p><p>We initially focus on learning how neural information flow networks change in songbirds with implanted electrodes. We characterize how they change in response to different sound stimuli and during the process of habituation. We continue to explore the neurobiology of songbirds by identifying changes in neural information flow in another habituation experiment using fMRI data. Finally, we briefly examine evolving genetic regulatory networks involved in Drosophila muscle differentiation during development.</p><p>We conclude by suggesting new experimental directions and statistical extensions to the model for predicting novel neural flow results.</p> / Dissertation

A wager is a one time bet, staking money on one among a collection of alternatives having uncertain reward. Wagers represent a common class of engineering decision, where “bets” are placed on the design, deployment, and/or operation of technology. Often such wagers are characterized by alternatives having value that evolves according to some future cash flow. Here, the values of specific alternatives are derived from a cash flow modeled as a stochastic marked point process. A principal difficulty with these engineering wagers is that the probability laws governing the dynamics of random cash flow typically are not (completely) available; hence, separating the gambler’s preference among wager alternatives is quite difficult. In this dissertation, we investigate a computational approach for separating preferences among alternatives of a wager where the alternatives have values that evolve according to a marked point processes. We are particularly concerned with separating a gambler’s preferences when the probability laws on the available alternatives are not completely specified.

The main goal of this research is to estimate the model parameters and to detect multiple change points in the long memory parameter of Gaussian ARFIMA(p, d, q) processes. Our approach is Bayesian and inference is done on wavelet domain. Long memory processes have been widely used in many scienti&#64257;c &#64257;elds such as economics, &#64257;nance and computer science. Wavelets have a strong connection with these processes. The ability of wavelets to simultaneously localize a process in time and scale domain results in representing many dense variance-covariance matrices of the process in a sparse form. A wavelet-based Bayesian estimation procedure for the parameters of Gaussian ARFIMA(p, d, q) process is proposed. This entails calculating the exact variance-covariance matrix of given ARFIMA(p, d, q) process and transforming them into wavelet domains using two dimensional discrete wavelet transform (DWT2). Metropolis algorithm is used for sampling the model parameters from the posterior distributions. Simulations with di&#64256;erent values of the parameters and of the sample size are performed. A real data application to the U.S. GNP data is also reported. Detection and estimation of multiple change points in the long memory parameter is also investigated. The reversible jump MCMC is used for posterior inference. Performances are evaluated on simulated data and on the Nile River dataset.

Le praticien, lors de l'étape de prédétermination des débits de crue, est souvent confronté à un jeu de données restreint. Dans notre travail de recherche, nous avons proposé trois nouveaux modèles probabilistes spécialement conçus pour l'estimation des caractéristiques du régime des crues en contexte partiellement jaugé. Parmi ces modèles, deux d'entre eux sont des modèles dits régionaux, i.e. intégrant de l'information en provenance de stations ayant un comportement réputé similaire à celui du site étudié. Ces modèles, basés sur la théorie Bayésienne, ont montré une grande robustesse au degré d'hétérogénéité des sites appartenant à la région. De même, il est apparu que pour l'estimation des forts quantiles (T > 50 ans), l'idée d'un paramètre régional contrôlant l'extrapolation est pertinente mais doit d'être intégrée de manière souple et non imposée au sein de la vraisemblance. L'information la plus précieuse dont le praticien dispose étant celle en provenance du site d'étude, le troisième modèle proposé revient sur l'estimation à partir des seules données contemporaines au site d'étude. Ce nouveau modèle utilise une information plus riche que celle issue d'un échantillonnage classique de v.a.i.id. maximales puisque toute la chronique est exploitée. Dès lors, même avec seulement cinq années d'enregistrement et grâce à une modélisation de la dépendance entres les observations successives, la taille des échantillons exploités est alors bien plus importante. Nous avons montré que pour l'estimation des quantiles de crues, ce modèle surpasse très nettement les approches locales classiquement utilisées en hydrologie. Ce résultat est d'autant plus vrai lorsque les périodes de retour deviennent importantes. Enfin, part construction, cette approche permet également d'obtenir une estimation probabiliste de la dynamique des crues.

This dissertation explores the estimation of endogenous treatment effects in the presence of heterogeneous responses. A Bayesian Nonparametric approach is taken to model the heterogeneity in treatment effects. Specifically, I adopt the Dirichlet Process Mixture (DPM) model to capture the heterogeneity and show that DPM often outperforms Finite Mixture Model (FMM) in providing more flexible function forms and thus better model fit. Rather than fixing the number of components in a mixture model, DPM allows the data and prior knowledge to determine the number of components in the data, thus providing an automatic mechanism for model selection. Two DPM models are presented in this dissertation. The first DPM model is based on a two-equation selection model. A Dirichlet Process (DP) prior is specified on some or all the parameters of the structural equation, and marginal likelihoods are calculated to select the best DPM model. This model is used to study the incentive and selection effects of having prescription drug coverage on total drug expenditures among Medicare beneficiaries. The second DPM model utilizes a three-equation Roy-type framework to model the observed heterogeneity that arises due to the treatment status, while the unobserved heterogeneity is handled by separate DPM models for the treated and untreated outcomes. This Roy-type DPM model is applied to a data set consisting of 33,081 independent individuals from the Medical Expenditure Panel Survey (MEPS), and the treatment effects of having private medical insurance on the outpatient expenditures are estimated. Key Words: Treatment Effects, Endogeneity, Heterogeneity, Finite Mixture Model, Dirichlet Process Prior, Dirichlet Process Mixture, Roy-type Modeling, Importance Sampling, Bridge Sampling

Multivariate ordinal response data, such as severity of pain, degree of disability, and satisfaction with a healthcare provider, are prevalent in many areas of research including public health, biomedical, and social science research. Ignoring the multivariate features of the response variables, that is, by not taking the correlation between the errors across models into account, may lead to substantially biased estimates and inference. In addition, such multivariate ordinal outcomes frequently exhibit a high percentage of zeros (zero inflation) at the lower end of the ordinal scales, as compared to what is expected under a multivariate ordinal distribution. Thus, zero inflation coupled with the multivariate structure make it difficult to analyze such data and properly interpret the results. Methods that have been developed to address the zero-inflated data are limited to univariate-logit or univariate-probit model, and extension to bivariate (or multivariate) probit models has been very limited to date. In this research, a latent variable approach was used to develop a Mixture Bivariate Zero-Inflated Ordered Probit (MBZIOP) model. A Bayesian MCMC technique was used for parameter estimation. A simulation study was then conducted to compare the performances of the estimators of the proposed model with two existing models. The simulation study suggested that for data with at least a moderate proportion of zeros in bivariate responses, the proposed model performed better than the comparison models both in terms of lower bias and greater accuracy (RMSE). Finally, the proposed method was illustrated with a publicly-available drug-abuse dataset to identify highly probable predictors of: (i) being a user/nonuser of marijuana, cocaine, or both; and (ii), conditional on user status, the level of consumption of these drugs. The results from the analysis suggested that older individuals, smokers, and people with a prior criminal background have a higher risk of being a marijuana only user, or being the user of both drugs. However, cocaine only users were predicted on the basis of being younger and having been engaged in the criminal-justice system. Given that an individual is a user of marijuana only, or user of both drugs, age appears to have an inverse effect on the latent level of consumption of marijuana as well as cocaine. Similarly, given that a respondent is a user of cocaine only, all covariates--age, involvement in criminal activities, and being of black race--are strong predictors of the level of cocaine consumption. The finding of older age being associated with higher drug consumption may represent a survival bias whereby previous younger users with high consumption may have been at elevated risk of premature mortality. Finally, the analysis indicated that blacks are likely to use less marijuana, but have a higher latent level of cocaine given that they are user of both drugs.

This paper presents a spatial utility model of support for multiple political parties. The model includes a "valence" term, which I reparameterize to include both party competence and the voters' key sociodemographic concerns. The paper shows how this spatial utility model can be interpreted as a hierarchical model using data from the 2009 European Elections Study. I estimate this model via Bayesian Markov Chain Monte Carlo (MCMC) using a block Gibbs sampler and show that the model can capture broad European-wide trends while allowing for significant amounts of heterogeneity. This approach, however, which assumes a normal dependent variable, is only able to partially reproduce the data generating process. I show that the data generating process can be reproduced more accurately with an ordered probit model. Finally, I discuss trade-offs between parsimony and descriptive richness and other practical challenges that may be encountered when v building models of party support and make recommendations for capturing the best of both approaches. / text

We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. This dissertation demonstrates that MCMC inference can be accelerated in a model of parallel computation that uses speculation to predict and complete computational work ahead of when it is known to be useful. By exploiting fast, iterative approximations to the target density, we can speculatively evaluate many potential future steps of the chain in parallel. In Bayesian inference problems, this approach can accelerate sampling from the target distribution, without compromising exactness, by exploiting subsets of data. It takes advantage of whatever parallel resources are available, but produces results exactly equivalent to standard serial execution. In the initial burn-in phase of chain evaluation, it achieves speedup over serial evaluation that is close to linear in the number of available cores. / Engineering and Applied Sciences