A Bayesian Multivariate Functional Dynamic Linear Model

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework. The proposed methods identify a time-invariant functional basis for the functional observations, which is smooth and interpretable, and can be made common across multivariate observations for additional information sharing. The Bayesian framework permits joint estimation of the model parameters, provides exact inference (up to MCMC error) on specific parameters, and allows generalized dependence structures. Sampling from the posterior distribution is accomplished with an efficient Gibbs sampling algorithm. We illustrate the proposed framework with two applications: (1) multi-economy yield curve data from the recent global recession, and (2) local field potential brain signals in rats, for which we develop a multivariate functional time series approach for multivariate time-frequency analysis. Supplementary materials, including R code and the multi-economy yield curve data, are available online

The mbsts package: Multivariate Bayesian Structural Time Series Models in R

The multivariate Bayesian structural time series (MBSTS) model \citep{qiu2018multivariate,Jammalamadaka2019Predicting} as a generalized version of many structural time series models, deals with inference and prediction for multiple correlated time series, where one also has the choice of using a different candidate pool of contemporaneous predictors for each target series. The MBSTS model has wide applications and is ideal for feature selection, time series forecasting, nowcasting, inferring causal impact, and others. This paper demonstrates how to use the R package \pkg{mbsts} for MBSTS modeling, establishing a bridge between user-friendly and developer-friendly functions in package and the corresponding methodology. A simulated dataset and object-oriented functions in the \pkg{mbsts} package are explained in the way that enables users to flexibly add or deduct some components, as well as to simplify or complicate some settings

Endogenous Jurisprudential Regimes

Jurisprudential regime theory is a legal explanation of decision-making on the U.S. Supreme Court that asserts that a key precedent in an area of law fundamentally restructures the relationship between case characteristics and the outcomes of future cases. In this article, we offer a multivariate multiple change-point probit model that can be used to endogenously test for the existence of jurisprudential regimes. Unlike the previously employed methods, our model does so by estimating the locations of many possible changepoints along with structural parameters. We estimate the model using Markov chain Monte Carlo methods, and use Bayesian model comparison to determine the number of change-points. Our findings are consistent with jurisprudential regimes in the Establishment Clause and administrative law contexts. We find little support for hypothesized regimes in the areas of free speech and search-and-seizure. The Bayesian multivariate change-point model we propose has broad potential applications to studying structural breaks in either regular or irregular time-series data about political institutions or processes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/116095/1/pa12.pd

Region-Referenced Spectral Power Dynamics of EEG Signals: A Hierarchical Modeling Approach

Functional brain imaging through electroencephalography (EEG) relies upon the analysis and interpretation of high-dimensional, spatially organized time series. We propose to represent time-localized frequency domain characterizations of EEG data as region-referenced functional data. This representation is coupled with a hierarchical modeling approach to multivariate functional observations. Within this familiar setting, we discuss how several prior models relate to structural assumptions about multivariate covariance operators. An overarching modeling framework, based on infinite factorial decompositions, is finally proposed to balance flexibility and efficiency in estimation. The motivating application stems from a study of implicit auditory learning, in which typically developing (TD) children, and children with autism spectrum disorder (ASD) were exposed to a continuous speech stream. Using the proposed model, we examine differential band power dynamics as brain function is interrogated throughout the duration of a computer-controlled experiment. Our work offers a novel look at previous findings in psychiatry, and provides further insights into the understanding of ASD. Our approach to inference is fully Bayesian and implemented in a highly optimized Rcpp package

BVAR: Bayesian Vector Autoregressions with Hierarchical Prior Selection in R

Vector autoregression (VAR) models are widely used for multivariate time series analysis in macroeconomics, finance, and related fields. Bayesian methods are often employed to deal with their dense parameterization, imposing structure on model coefficients via prior information. The optimal choice of the degree of informativeness implied by these priors is subject of much debate and can be approached via hierarchical modeling. This paper introduces BVAR, an R package dedicated to the estimation of Bayesian VAR models with hierarchical prior selection. It implements functionalities and options that permit addressing a wide range of research problems, while retaining an easy-to-use and transparent interface. Features include structural analysis of impulse responses, forecasts, the most commonly used conjugate priors, as well as a framework for defining custom dummy-observation priors. BVAR makes Bayesian VAR models user-friendly and provides an accessible reference implementation

Multivariate Bayesian Predictive Synthesis in Macroeconomic Forecasting

We develop the methodology and a detailed case study in use of a class of Bayesian predictive synthesis (BPS) models for multivariate time series forecasting. This extends the recently introduced foundational framework of BPS to the multivariate setting, with detailed application in the topical and challenging context of multi-step macroeconomic forecasting in a monetary policy setting. BPS evaluates-- sequentially and adaptively over time-- varying forecast biases and facets of miscalibration of individual forecast densities, and-- critically-- of time-varying inter-dependencies among them over multiple series. We develop new BPS methodology for a specific subclass of the dynamic multivariate latent factor models implied by BPS theory. Structured dynamic latent factor BPS is here motivated by the application context-- sequential forecasting of multiple US macroeconomic time series with forecasts generated from several traditional econometric time series models. The case study highlights the potential of BPS to improve of forecasts of multiple series at multiple forecast horizons, and its use in learning dynamic relationships among forecasting models or agents