138 research outputs found
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
Simultaneous transformation and rounding (STAR) models for integer-valued data
We propose a simple yet powerful framework for modeling integer-valued data,
such as counts, scores, and rounded data. The data-generating process is
defined by Simultaneously Transforming and Rounding (STAR) a continuous-valued
process, which produces a flexible family of integer-valued distributions
capable of modeling zero-inflation, bounded or censored data, and over- or
underdispersion. The transformation is modeled as unknown for greater
distributional flexibility, while the rounding operation ensures a coherent
integer-valued data-generating process. An efficient MCMC algorithm is
developed for posterior inference and provides a mechanism for adaptation of
successful Bayesian models and algorithms for continuous data to the
integer-valued data setting. Using the STAR framework, we design a new Bayesian
Additive Regression Tree (BART) model for integer-valued data, which
demonstrates impressive predictive distribution accuracy for both synthetic
data and a large healthcare utilization dataset. For interpretable
regression-based inference, we develop a STAR additive model, which offers
greater flexibility and scalability than existing integer-valued models. The
STAR additive model is applied to study the recent decline in Amazon river
dolphins
Monte Carlo inference for semiparametric Bayesian regression
Data transformations are essential for broad applicability of parametric
regression models. However, for Bayesian analysis, joint inference of the
transformation and model parameters typically involves restrictive parametric
transformations or nonparametric representations that are computationally
inefficient and cumbersome for implementation and theoretical analysis, which
limits their usability in practice. This paper introduces a simple, general,
and efficient strategy for joint posterior inference of an unknown
transformation and all regression model parameters. The proposed approach
directly targets the posterior distribution of the transformation by linking it
with the marginal distributions of the independent and dependent variables, and
then deploys a Bayesian nonparametric model via the Bayesian bootstrap.
Crucially, this approach delivers (1) joint posterior consistency under general
conditions, including multiple model misspecifications, and (2) efficient Monte
Carlo (not Markov chain Monte Carlo) inference for the transformation and all
parameters for important special cases. These tools apply across a variety of
data domains, including real-valued, integer-valued, compactly-supported, and
positive data. Simulation studies and an empirical application demonstrate the
effectiveness and efficiency of this strategy for semiparametric Bayesian
analysis with linear models, quantile regression, and Gaussian processes
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