Understanding the heterogeneity over spatial locations is an important problem that has been widely studied in many applications such as economics and environmental science. In this paper, we focus on regression models for spatial panel data analysis, where repeated measurements are collected over time at various spatial locations. We propose a novel class of nonparametric priors that combines Markov random field (MRF) with the product partition model (PPM), and show that the resulting prior, called by MRF-PPM, is capable of identifying the latent group structure among the spatial locations while efficiently utilizing the spatial dependence information. We derive a closed-form conditional distribution for the proposed prior and introduce a new way to compute the marginal likelihood that renders efficient Bayesian inference. We further study the theoretical properties of the proposed MRF-PPM prior and show a clustering consistency result for the posterior distribution. We demonstrate the excellent empirical performance of our method via extensive simulation studies and applications to a US precipitation data and a California median household income data study.
Panel data, also known as longitudinal data, consist of a collection of time series. Each time series, which could itself be multivariate, comprises a sequence of measurements taken on a distinct unit. Mechanistic modeling involves writing down scientifically motivated equations describing the collection of dynamic systems giving rise to the observations on each unit. A defining characteristic of panel systems is that the dynamic interaction between units should be negligible. Panel models therefore consist of a collection of independent stochastic processes, generally linked through shared pa…
In this paper, We propose a new style panel data factor stochastic volatility model with observable factors and unobservable factors based on the multivariate stochastic volatility model, which is mainly composed of three parts, such as the mean equation, volatility equation and factor volatility evolution. The stochastic volatility equation is a 1-step forward prediction process with high dimensional parameters to be estimated. Using the Markov Chain Monte Carlo Simulation (MCMC) method, the Forward Filtering Backward Sampling (FFBS) algorithm of the stochastic volatility equation is mainly u…
A novel copula-based multivariate panel ordinal model is developed to estimate structural relations among components of well-being. Each ordinal time-series is modelled using a copula-based Markov model to relate the marginal distributions of the response at each time of observation and then, at each observation time, the conditional distributions of each ordinal time-series are joined using a multivariate t copula. Maximum simulated likelihood based on evaluating the multidimensional integrals of the likelihood with randomized quasi Monte Carlo methods is used for the estimation. Asymptotic c…
This paper introduces a new model for panel data with Markov-switching GARCH effects. The model incorporates a series-specific hidden Markov chain process that drives the GARCH parameters. To cope with the high-dimensionality of the parameter space, the paper exploits the cross-sectional clustering of the series by first assuming a soft parameter pooling through a hierarchical prior distribution with two-step procedure, and then introducing clustering effects in the parameter space through a nonparametric prior distribution. The model and the proposed inference are evaluated through a simulati…
We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed method allows the fixed effects components to vary between dependent random partitions of the covariate space at different time points. The mechanism not only allows different sets of covariates to be included in the model at different time points but also allows the selected predictors' influences to vary flexibly over time. Smooth time-varying additive ran…
This study proposes a new Bayesian approach to infer binary treatment effects. The approach treats counterfactual untreated outcomes as missing observations and infers them by completing a matrix composed of realized and potential untreated outcomes using a data augmentation technique. We also develop a tailored prior that helps in the identification of parameters and induces the matrix of untreated outcomes to be approximately low rank. Posterior draws are simulated using a Markov Chain Monte Carlo sampler. While the proposed approach is similar to synthetic control methods and other related …
In this paper, the panel count data analysis for recurrent events is considered. Such analysis is useful for studying tumor or infection recurrences in both clinical trial and observational studies. A bivariate Gaussian Cox process model is proposed to jointly model the observation process and the recurrent event process. Bayesian nonparametric inference is proposed for simultaneously estimating regression parameters, bivariate frailty effects and baseline intensity functions. Inference is done through Markov chain Monte Carlo, with fully developed computational techniques. Predictive inferenc…
This paper proposes a non-Gaussian Markov field with a special feature: an explicit partition function. To the best of our knowledge, this is an original contribution. Moreover, the explicit expression of the partition function enables the development of an unsupervised edge-preserving convex deconvolution method. The method is fully Bayesian, and produces an estimate in the sense of the posterior mean, numerically calculated by means of a Monte-Carlo Markov Chain technique. The approach is particularly effective and the computational practicability of the method is shown on a simple simulated…
Conditional density estimation (density regression) estimates the distribution of a response variable y conditional on covariates x. Utilizing a partition model framework, a conditional density estimation method is proposed using logistic Gaussian processes. The partition is created using a Voronoi tessellation and is learned from the data using a reversible jump Markov chain Monte Carlo algorithm. The Markov chain Monte Carlo algorithm is made possible through a Laplace approximation on the latent variables of the logistic Gaussian process model. This approximation marginalizes the parameters…
We examine a general multi-factor model for commodity spot prices and futures valuation. We extend the multi-factor long-short model in Schwartz and Smith (2000) and Yan (2002) in two important aspects: firstly we allow for both the long and short term dynamic factors to be mean reverting incorporating stochastic volatility factors and secondly we develop an additive structural seasonality model. Then a Milstein discretized non-linear stochastic volatility state space representation for the model is developed which allows for futures and options contracts in the observation equation. We then d…
We introduce a probabilistic framework for two-sample comparison based on a nonparametric process taking the form of a Markov model that transitions between a "divide" and a "merge" state on a multi-resolution partition tree of the sample space. Multi-scale two-sample comparison is achieved through inferring the underlying state of the process along the partition tree. The Markov design allows the process to incorporate spatial clustering of differential structures, which is commonly observed in two-sample problems but ignored by existing methods. Inference is carried out under the Bayesian pa…
This article develops a Bayesian approach for estimating panel quantile regression with binary outcomes in the presence of correlated random effects. We construct a working likelihood using an asymmetric Laplace (AL) error distribution and combine it with suitable prior distributions to obtain the complete joint posterior distribution. For posterior inference, we propose two Markov chain Monte Carlo (MCMC) algorithms but prefer the algorithm that exploits the blocking procedure to produce lower autocorrelation in the MCMC draws. We also explain how to use the MCMC draws to calculate the margin…
Understanding the dynamics of functional brain connectivity patterns using noninvasive neuroimaging techniques is an important focus in human neuroscience. Vector autoregressive (VAR) processes and Granger causality analysis (GCA) have been extensively used for this purpose. While high-resolution multi-subject neuroimaging data are routinely collected now-a-days, the statistics literature on VAR models has remained heavily focused on small-to-moderate dimensional problems and single-subject data. Motivated by these issues, we develop a novel Bayesian random effects panel VAR model for multi-su…
The Pólya tree (PT) process is a general-purpose Bayesian nonparametric model that has found wide application in a range of inference problems. It has a simple analytic form and the posterior computation boils down to beta-binomial conjugate updates along a partition tree over the sample space. Recent development in PT models shows that performance of these models can be substantially improved by (i) allowing the partition tree to adapt to the structure of the underlying distributions and (ii) incorporating latent state variables that characterize local features of the underlying distributions…
Markov chain Monte Carlo (MCMC) methods are often used in clustering since they guarantee asymptotically exact expectations in the infinite-time limit. In finite time, though, slow mixing often leads to poor performance. Modern computing environments offer massive parallelism, but naive implementations of parallel MCMC can exhibit substantial bias. In MCMC samplers of continuous random variables, Markov chain couplings can overcome bias. But these approaches depend crucially on paired chains meetings after a small number of transitions. We show that straightforward applications of existing cou…
Traditional Bayesian random partition models assume that the size of each cluster grows linearly with the number of data points. While this is appealing for some applications, this assumption is not appropriate for other tasks such as entity resolution, modeling of sparse networks, and DNA sequencing tasks. Such applications require models that yield clusters whose sizes grow sublinearly with the total number of data points -- the microclustering property. Motivated by these issues, we propose a general class of random partition models that satisfy the microclustering property with well-charac…
Divide-and-conquer strategies for Monte Carlo algorithms are an increasingly popular approach to making Bayesian inference scalable to large data sets. In its simplest form, the data are partitioned across multiple computing cores and a separate Markov chain Monte Carlo algorithm on each core targets the associated partial posterior distribution, which we refer to as a sub-posterior, that is the posterior given only the data from the segment of the partition associated with that core. Divide-and-conquer techniques reduce computational, memory and disk bottle-necks, but make it difficult to rec…
