Esther Salazar

Generalized spatial dynamic factor models

This paper introduces a new class of spatio-temporal models for measurements belonging to the exponential family of distributions. In this new class, the spatial and temporal components are conditionally independently modeled via a latent factor analysis structure for the (canonical) transformation of the measurements mean function. The factor loadings matrix is responsible for modeling spatial variation, while the common factors are responsible for modeling the temporal variation. One of the main advantages of our model with spatially structured loadings is the possibility of detecting similar regions associated to distinct dynamic factors. We also show that the new class outperforms a large class of spatial-temporal models that are commonly used in the literature. Posterior inference for fixed parameters and dynamic latent factors is performed via a custom tailored Markov chain Monte Carlo scheme for multivariate dynamic systems that combines extended Kalman filter-based Metropolis-Hastings proposal densities with block-sampling schemes. Factor model uncertainty is also fully addressed by a reversible jump Markov chain Monte Carlo algorithm designed to learn about the number of common factors. Three applications, two based on synthetic Gamma and Bernoulli data and one based on real Bernoulli data, are presented in order to illustrate the flexibility and generality of the new class of models, as well as to discuss features of the proposed MCMC algorithm.

Spatio-Temporal Modeling of Legislation and Votes

A model is presented for analysis of multivariate binary data with spatio-temporal dependencies, and applied to congressional roll call data from the United States House of Representatives and Senate. The model considers each legislators constituency (location), the congressional session (time) of each vote, and the details (text) of each piece of legislation. The model can predict votes of new legislation from only text, while imposing smooth temporal evolution of legislator latent features, and correlation of legislators with adjacent constituencies. Additionally, the model estimates the number of latent dimensions required to represent the data. A Gibbs sampler is developed for posterior inference. The model is demonstrated as an exploratory tool of legislation and it performs well in quantitative comparisons to a traditional ideal-point model.

Bayesian reference analysis for exponential power regression models

We develop Bayesian reference analyses for linear regression models when the errors follow an exponential power distribution. Specifically, we obtain explicit expressions for reference priors for all the six possible orderings of the model parameters and show that, associated with these six parameters orderings, there are only two reference priors. Further, we show that both of these reference priors lead to proper posterior distributions. Furthermore, we show that the proposed reference Bayesian analyses compare favorably to an analysis based on a competing noninformative prior. Finally, we illustrate these Bayesian reference analyses for exponential power regression models with applications to two datasets. The first application analyzes per capita spending in public schools in the United States. The second application studies the relationship between sold home videos versus profits at the box office.MSC62F15; 62F35; 62J05

Analysis of space-time relational data with application to legislative voting

We consider modeling spatio-temporally indexed relational data, motivated by analysis of voting data for the United States House of Representatives over two decades. The data are characterized by incomplete binary matrices, representing votes of legislators on legislation over time. The spatial covariates correspond to the location of a legislators district, and time corresponds to the year of a vote. We seek to infer latent features associated with legislators and legislation, incorporating spatio-temporal structure. A model of such data must impose a flexible representation of the space-time structure, since the apportionment of House seats and the total number of legislators change over time. There are 435 congressional districts, with one legislator at a time for each district; however, the total number of legislators typically changes from year to year, for example due to deaths. A matrix kernel stick-breaking process (MKSBP) is proposed, with the model employed within a probit-regression construction. Theoretical properties of the model are discussed and posterior inference is developed using Markov chain Monte Carlo methods. Advantages over benchmark models are shown in terms of vote prediction and treatment of missing data. Marked improvements in results are observed based on leveraging spatial (geographical) information.

Temporal Aggregation of Lognormal AR Processes

We consider temporal aggregation of lognormal autoregressive (AR) processes. More specifically, we develop a novel moment‐matching approximation for temporally aggregated lognormal AR processes. In addition, we show that our approximation provides the closest lognormal AR process in terms of Kullback–Leibler divergence. Moreover, we perform a simulation study to compare our proposed approximation with two competing approximations. This study shows that in terms of L1‐ and L2‐norm distances our approximation provides superior results. Our results have an important practical application and one main practical implication. In terms of practical application, our approximation can provide possible candidate solutions for simulation‐based algorithms such as the Metropolis–Hastings algorithm. The practical implication gives support to common practice: when the original fine‐level process follows a lognormal AR process but only aggregated data are available, then instead of assuming a Gaussian process it is better to assume a lognormal AR process at the aggregated level. Finally, we illustrate the utility of our results with two applications. The first example considers a simulated dataset whereas the second example examines the number of yearly sunspots in the period 1700–1984.

Observation-based blended projections from ensembles of regional climate models

We consider the problem of projecting future climate from ensembles of regional climate model (RCM) simulations using results from the North American Regional Climate Change Assessment Program (NARCCAP). To this end, we develop a hierarchical Bayesian space-time model that quantifies the discrepancies between different members of an ensemble of RCMs corresponding to present day conditions, and observational records. Discrepancies are then propagated into the future to obtain high resolution blended projections of 21st century climate. In addition to blended projections, the proposed method provides location-dependent comparisons between the different simulations by estimating the different modes of spatial variability, and using the climate model-specific coefficients of the spatial factors for comparisons. The approach has the flexibility to provide projections at customizable scales of potential interest to stakeholders while accounting for the uncertainties associated with projections at these scales based on a comprehensive statistical framework. We demonstrate the methodology with simulations from the Weather Research & Forecasting regional model (WRF) using three different boundary conditions. We use simulations for two time periods: current climate conditions, covering 1971 to 2000, and future climate conditions under the Special Report on Emissions Scenarios (SRES) A2 emissions scenario, covering 2041 to 2070. We investigate and project yearly mean summer and winter temperatures for a domain in the South West of the United States.