Bayesian Emulation for Sequential Modeling, Inference and Decision Analysis

The 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.

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.