Bayesian Analysis of Latent Threshold Dynamic Models

We discuss a general approach to dynamic sparsity modeling in multivariate time series analysis. Time-varying parameters are linked to latent processes that are thresholded to induce zero values adaptively, providing natural mechanisms for dynamic variable inclusion/selection. We discuss Bayesian model specification, analysis and prediction in dynamic regressions, time-varying vector autoregressions, and multivariate volatility models using latent thresholding. Application to a topical macroeconomic time series problem illustrates some of the benefits of the approach in terms of statistical and economic interpretations as well as improved predictions. Supplementary materials for this article are available online. © 2013 Copyright Taylor and Francis Group, LLC.

Bayesian Learning with Dependency Structures via Latent Factors, Mixtures, and Copulas

Bayesian methods offer a flexible and convenient probabilistic learning framework to extract interpretable knowledge from complex and structured data. Such methods can characterize dependencies among multiple levels of hidden variables and share statistical strength across heterogeneous sources. In the first part of this dissertation, we develop two dependent variational inference methods for full posterior approximation in non-conjugate Bayesian models through hierarchical mixture- and copula-based variational proposals, respectively. The proposed methods move beyond the widely used factorized approximation to the posterior and provide generic applicability to a broad class of probabilistic models with minimal model-specific derivations. In the second part of this dissertation, we design probabilistic graphical models to accommodate multimodal data, describe dynamical behaviors and account for task heterogeneity. In particular, the sparse latent factor model is able to reveal common low-dimensional structures from high-dimensional data. We demonstrate the effectiveness of the proposed statistical learning methods on both synthetic and real-world data.

Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

We 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.

An evaluation of remifentanil-sevoflurane response surface models in patients emerging from anesthesia: model improvement using effect-site sevoflurane concentrations.

INTRODUCTION: We previously reported models that characterized the synergistic interaction between remifentanil and sevoflurane in blunting responses to verbal and painful stimuli. This preliminary study evaluated the ability of these models to predict a return of responsiveness during emergence from anesthesia and a response to tibial pressure when patients required analgesics in the recovery room. We hypothesized that model predictions would be consistent with observed responses. We also hypothesized that under non-steady-state conditions, accounting for the lag time between sevoflurane effect-site concentration (Ce) and end-tidal (ET) concentration would improve predictions. METHODS: Twenty patients received a sevoflurane, remifentanil, and fentanyl anesthetic. Two model predictions of responsiveness were recorded at emergence: an ET-based and a Ce-based prediction. Similarly, 2 predictions of a response to noxious stimuli were recorded when patients first required analgesics in the recovery room. Model predictions were compared with observations with graphical and temporal analyses. RESULTS: While patients were anesthetized, model predictions indicated a high likelihood that patients would be unresponsive (> or = 99%). However, after termination of the anesthetic, models exhibited a wide range of predictions at emergence (1%-97%). Although wide, the Ce-based predictions of responsiveness were better distributed over a percentage ranking of observations than the ET-based predictions. For the ET-based model, 45% of the patients awoke within 2 min of the 50% model predicted probability of unresponsiveness and 65% awoke within 4 min. For the Ce-based model, 45% of the patients awoke within 1 min of the 50% model predicted probability of unresponsiveness and 85% awoke within 3.2 min. Predictions of a response to a painful stimulus in the recovery room were similar for the Ce- and ET-based models. DISCUSSION: Results confirmed, in part, our study hypothesis; accounting for the lag time between Ce and ET sevoflurane concentrations improved model predictions of responsiveness but had no effect on predicting a response to a noxious stimulus in the recovery room. These models may be useful in predicting events of clinical interest but large-scale evaluations with numerous patients are needed to better characterize model performance.