arXiv subjects

Abel Rodriguez

Publications and source records attributed to Abel Rodriguez.

28 records · Page 2Linked to original sources

arXiv2016

Stochastic blockmodels for exchangeable collections of networks

We construct a novel class of stochastic blockmodels using Bayesian nonparametric mixtures. These model allows us to jointly estimate the structure of multiple networks and explicitly compare the community structures underlying them, while allowing us to capture realistic properties of the underlying networks. Inference is carried out using MCMC algorithms that incorporates sequentially allocated split-merge steps to improve mixing. The models are illustrated using a simulation study and a variety of real-life examples.

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arXiv2016

Bayesian stochastic volatility models for high-frequency data

We formulate a discrete-time Bayesian stochastic volatility model for high-frequency stock-market data that directly accounts for microstructure noise, and outline a Markov chain Monte Carlo algorithm for parameter estimation. The methods described in this paper are designed to be coherent across all sampling timescales, with the goal of estimating the latent log-volatility signal from data collected at arbitrarily short sampling periods. In keeping with this goal, we carefully develop a method for eliciting priors. The empirical results derived from both simulated and real data show that directly accounting for microstructure in a state-space formulation allows for well-calibrated estimates of the log-volatility process driving prices.

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arXiv2016

Assessing differences in legislators' revealed preferences: A case study on the 107th U.S. Senate

Roll call data are widely used to assess legislators' preferences and ideology, as well as test theories of legislative behavior. In particular, roll call data is often used to determine whether the revealed preferences of legislators are affected by outside forces such as party pressure, minority status or procedural rules. This paper describes a Bayesian hierarchical model that extends existing spatial voting models to test sharp hypotheses about differences in preferences the using posterior probabilities associated with such hypotheses. We use our model to investigate the effect of the change of party majority status during the 107th U.S. Senate on the revealed preferences of senators. This analysis provides evidence that change in party affiliation might affect the revealed preferences of legislators, but provides no evidence about the effect of majority status on the revealed preferences of legislators.

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arXiv2015

Bayesian protein structure alignment

The analysis of the three-dimensional structure of proteins is an important topic in molecular biochemistry. Structure plays a critical role in defining the function of proteins and is more strongly conserved than amino acid sequence over evolutionary timescales. A key challenge is the identification and evaluation of structural similarity between proteins; such analysis can aid in understanding the role of newly discovered proteins and help elucidate evolutionary relationships between organisms. Computational biologists have developed many clever algorithmic techniques for comparing protein structures, however, all are based on heuristic optimization criteria, making statistical interpretation somewhat difficult. Here we present a fully probabilistic framework for pairwise structural alignment of proteins. Our approach has several advantages, including the ability to capture alignment uncertainty and to estimate key "gap" parameters which critically affect the quality of the alignment. We show that several existing alignment methods arise as maximum a posteriori estimates under specific choices of prior distributions and error models. Our probabilistic framework is also easily extended to incorporate additional information, which we demonstrate by including primary sequence information to generate simultaneous sequence-structure alignments that can resolve ambiguities obtained using structure alone. This combined model also provides a natural approach for the difficult task of estimating evolutionary distance based on structural alignments. The model is illustrated by comparison with well-established methods on several challenging protein alignment examples.

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arXiv2014

Functional clustering in nested designs: Modeling variability in reproductive epidemiology studies

We discuss functional clustering procedures for nested designs, where multiple curves are collected for each subject in the study. We start by considering the application of standard functional clustering tools to this problem, which leads to groupings based on the average profile for each subject. After discussing some of the shortcomings of this approach, we present a mixture model based on a generalization of the nested Dirichlet process that clusters subjects based on the distribution of their curves. By using mixtures of generalized Dirichlet processes, the model induces a much more flexible prior on the partition structure than other popular model-based clustering methods, allowing for different rates of introduction of new clusters as the number of observations increases. The methods are illustrated using hormone profiles from multiple menstrual cycles collected for women in the Early Pregnancy Study.

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arXiv2012

Default Bayesian Analysis for the Multivariate Ewens Distribution

We derive the Jeffreys prior for the parameter of the Multivariate Ewens Distribution and study some of its properties. In particular, we show that this prior is proper and has no finite moments. We also investigate the impact of this default prior on the a priori distribution of the number of species and the a priori probability of discovery of a new species, which are usually employed in subjective prior elicitation. The effect of the Jeffreys prior for posterior inference is illustrated using examples arising in the context of inference for species sampling models and Dirichlet process mixture models.

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arXiv2010

Bayesian inference for general Gaussian graphical models with application to multivariate lattice data

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on the analysis of spatial data. These models embed a great deal of flexibility in estimating both the correlation structure across outcomes and the spatial correlation structure, thereby allowing for adaptive smoothing and spatial autocorrelation parameters. Our methods are illustrated using simulated and real-world examples, including an application to cancer mortality surveillance.

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arXiv2010

Sparse covariance estimation in heterogeneous samples

Standard Gaussian graphical models (GGMs) implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected form heterogeneous populations where such assumption is not satisfied, leading in turn to nonlinear relationships among variables. To tackle these problems we explore mixtures of GGMs; in particular, we consider both infinite mixture models of GGMs and infinite hidden Markov models with GGM emission distributions. Such models allow us to divide a heterogeneous population into homogenous groups, with each cluster having its own conditional independence structure. The main advantage of considering infinite mixtures is that they allow us easily to estimate the number of number of subpopulations in the sample. As an illustration, we study the trends in exchange rate fluctuations in the pre-Euro era. This example demonstrates that the models are very flexible while providing extremely interesting interesting insights into real-life applications.

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arXiv2009

Stochastic Volatility Models Including Open, Close, High and Low Prices

Mounting empirical evidence suggests that the observed extreme prices within a trading period can provide valuable information about the volatility of the process within that period. In this paper we define a class of stochastic volatility models that uses opening and closing prices along with the minimum and maximum prices within a trading period to infer the dynamics underlying the volatility process of asset prices and compares it with similar models that have been previously presented in the literature. The paper also discusses sequential Monte Carlo algorithms to fit this class of models and illustrates its features using both a simulation study and data form the SP500 index.

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arXiv2008

Measuring expectations in options markets: An application to the SP500 index

Extracting market expectations has always been an important issue when making national policies and investment decisions in financial markets. In option markets, the most popular way has been to extract implied volatilities to assess the future variability of the underlying with the use of the Black and Scholes formula. In this manuscript, we propose a novel way to extract the whole time varying distribution of the market implied asset price from option prices. We use a Bayesian nonparametric method that makes use of the Sethuraman representation for Dirichlet processes to take into account the evolution of distributions in time. As an illustration, we present the analysis of options on the SP500 index.

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