Marco A. R. Ferreira

Markov Random Field Models for High-Dimensional Parameters in Simulations of Fluid Flow in Porous Media

We give an approach for using flow information from a system of wells to characterize hydrologic properties of an aquifer. In particular, we consider experiments where an impulse of tracer fluid is injected along with the water at the input wells and its concentration is recorded over time at the uptake wells. We focus on characterizing the spatially varying permeability field, which is a key attribute of the aquifer for determining flow paths and rates for a given flow experiment. As is standard for estimation from such flow data, we use complicated subsurface flow code that simulates the fluid flow through the aquifer for a particular well configuration and aquifer specification, in particular the permeability field over a grid. The solution to this ill-posed problem requires that some regularity conditions be imposed on the permeability field. Typically, this regularity is accomplished by specifying a stationary Gaussian process model for the permeability field. Here we use an intrinsically stationary Markov random field, which compares favorably to Gaussian process models and offers some additional flexibility and computational advantages. Our interest in quantifying uncertainty leads us to take a Bayesian approach, using Markov chain Monte Carlo for exploring the high-dimensional posterior distribution. We demonstrate our approach with several examples. We also note that the methodology is general and is not specific to hydrology applications.

miR-124,-128, and-137 Orchestrate Neural Differentiation by Acting on Overlapping Gene Sets Containing a Highly Connected Transcription Factor Network

The ventricular‐subventricular zone harbors neural stem cells (NSCs) that can differentiate into neurons, astrocytes, and oligodendrocytes. This process requires loss of stem cell properties and gain of characteristics associated with differentiated cells. miRNAs function as important drivers of this transition; miR‐124, ‐128, and ‐137 are among the most relevant ones and have been shown to share commonalities and act as proneurogenic regulators. We conducted biological and genomic analyses to dissect their target repertoire during neurogenesis and tested the hypothesis that they act cooperatively to promote differentiation. To map their target genes, we transfected NSCs with antagomiRs and analyzed differences in their mRNA profile throughout differentiation with respect to controls. This strategy led to the identification of 910 targets for miR‐124, 216 for miR‐128, and 652 for miR‐137. The target sets show extensive overlap. Inspection by gene ontology and network analysis indicated that transcription factors are a major component of these miRNAs target sets. Moreover, several of these transcription factors form a highly interconnected network. Sp1 was determined to be the main node of this network and was further investigated. Our data suggest that miR‐124, ‐128, and ‐137 act synergistically to regulate Sp1 expression. Sp1 levels are dramatically reduced as cells differentiate and silencing of its expression reduced neuronal production and affected NSC viability and proliferation. In summary, our results show that miRNAs can act cooperatively and synergistically to regulate complex biological processes like neurogenesis and that transcription factors are heavily targeted to branch out their regulatory effect. Stem Cells 2016;34:220–232

Spatiotemporal Models for Gaussian Areal Data

We introduce a class of spatiotemporal models for Gaussian areal data. These models assume a latent random field process that evolves through time with random field convolutions; the convolving fields follow proper Gaussian Markov random field (PGMRF) processes. At each time, the latent random field process is linearly related to observations through an observational equation with errors that also follow a PGMRF. The use of PGMRF errors brings modeling and computational advantages. With respect to modeling, it allows more flexible model structures such as different but interacting temporal trends for each region, as well as distinct temporal gradients for each region. Computationally, building upon the fact that PGMRF errors have proper density functions, we have developed an efficient Bayesian estimation procedure based on Markov chain Monte Carlo with an embedded forward information filter backward sampler (FIFBS) algorithm. We show that, when compared with the traditional one-at-a-time Gibbs sampler, our novel FIFBS-based algorithm explores the posterior distribution much more efficiently. Finally, we have developed a simulation-based conditional Bayes factor suitable for the comparison of nonnested spatiotemporal models. An analysis of the number of homicides in Rio de Janeiro State illustrates the power of the proposed spatiotemporal framework. Supplemental materials for this article are available online in the journal’s webpage.

Bayesian Multiscale Multiple Imputation With Implications for Data Confidentiality

Many scientific, sociological, and economic applications present data that are collected on multiple scales of resolution. One particular form of multiscale data arises when data are aggregated across different scales both longitudinally and by economic sector. Frequently, such datasets experience missing observations in a manner that they can be accurately imputed, while respecting the constraints imposed by the multiscale nature of the data, using the method we propose known as Bayesian multiscale multiple imputation. Our approach couples dynamic linear models with a novel imputation step based on singular normal distribution theory. Although our method is of independent interest, one important implication of such methodology is its potential effect on confidential databases protected by means of cell suppression. In order to demonstrate the proposed methodology and to assess the effectiveness of disclosure practices in longitudinal databases, we conduct a large-scale empirical study using the U.S. Bureau of Labor Statistics Quarterly Census of Employment and Wages (QCEW). During the course of our empirical investigation it is determined that several of the predicted cells are within 1% accuracy, thus causing potential concerns for data confidentiality.

Bayesian hierarchical multi-subject multiscale analysis of functional MRI data

We develop a methodology for Bayesian hierarchical multi-subject multiscale analysis of functional Magnetic Resonance Imaging (fMRI) data. We begin by modeling the brain images temporally with a standard general linear model. After that, we transform the resulting estimated standardized regression coefficient maps through a discrete wavelet transformation to obtain a sparse representation in the wavelet space. Subsequently, we assign to the wavelet coefficients a prior that is a mixture of a point mass at zero and a Gaussian white noise. In this mixture prior for the wavelet coefficients, the mixture probabilities are related to the pattern of brain activity across different resolutions. To incorporate this information, we assume that the mixture probabilities for wavelet coefficients at the same location and level are common across subjects. Furthermore, we assign for the mixture probabilities a prior that depends on a few hyperparameters. We develop an empirical Bayes methodology to estimate the hyperparameters and, as these hyperparameters are shared by all subjects, we obtain precise estimated values. Then we carry out inference in the wavelet space and obtain smoothed images of the regression coefficients by applying the inverse wavelet transform to the posterior means of the wavelet coefficients. An application to computer simulated synthetic data has shown that, when compared to single-subject analysis, our multi-subject methodology performs better in terms of mean squared error. Finally, we illustrate the utility and flexibility of our multi-subject methodology with an application to an event-related fMRI dataset generated by Postle (2005) through a multi-subject fMRI study of working memory related brain activation.

Multi-Scale and Hidden Resolution Time Series Models

We introduce a class of multi-scale models for time series. The novel framework couples standard linear models at different levels of resolution via stochastic links across scales. Jeffrey’s rule of conditioning is used to revise the implied distributions and ensure that the probability distributions at the different levels are strictly compatible. This results in a new class of models for time series with three key characteristics: this class exhibits a variety of autocorrelation structures based on a parsimonious parameterization, it has the ability to combine information across levels of resolution, and it also has the capacity to emulate long memory processes. The potential applications of such multi-scale models include problems in which it is of interest to develop consistent stochastic models across time-scales and levels of resolution, in order to coherently combine and integrate information arising at different levels of resolution. Bayesian estimation based on MCMC analysis and forecasting based on simulation are developed. One application to the analysis of the flow of a river illustrates the new class of models and its utility.

Transfer functions in dynamic generalized linear models

In a time series analysis it is sometimes necessary to assume that the effect of a regressor does not have only immediate impact on the mean response, but that its effects somehow propagate to future times. We adopt, in this work, transfer functions to model such impacts, represented by structural blocks present in dynamic generalized linear models. All the inference is carried under the Bayesian paradigm. Two sources of difficulties emerge for the analytical derivation of posterior distributions: non-Gaussian nature of the response, associated to non-conjugate priors and also non-linearity of the predictor on auto regressive parameters present in transfer functions. The purpose of this work is to produce full Bayesian inference on dynamic generalized linear models with transfer functions, using Markov chain Monte Carlo methods to build samples of the posterior joint distribution of the parameters involved in such models. Several transfer structures are specified, associated to Poisson, Binomial, Gamma and inverse Gaussian responses. Simulated data are analyzed under the resulting models in order to assess their performance. Finally, two applications to real data concerning environmental sciences are made under different model formulations.

A multispecies occupancy model for two or more interacting species

Summary Species occurrence is influenced by environmental conditions and the presence of other species. Current approaches for multispecies occupancy modelling are practically limited to two interacting species and often require the assumption of asymmetric interactions. We propose a multispecies occupancy model that can accommodate two or more interacting species. We generalize the single-species occupancy model to two or more interacting species by assuming the latent occupancy state is a multivariate Bernoulli random variable. We propose modelling the probability of each potential latent occupancy state with both a multinomial logit and a multinomial probit model and present details of a Gibbs sampler for the latter. As an example, we model co-occurrence probabilities of bobcat (Lynx rufus), coyote (Canis latrans), grey fox (Urocyon cinereoargenteus) and red fox (Vulpes vulpes) as a function of human disturbance variables throughout 6 Mid-Atlantic states in the eastern United States. We found evidence for pairwise interactions among most species, and the probability of some pairs of species occupying the same site varied along environmental gradients; for example, occupancy probabilities of coyote and grey fox were independent at sites with little human disturbance, but these two species were more likely to occur together at sites with high human disturbance. Ecological communities are composed of multiple interacting species. Our proposed method improves our ability to draw inference from such communities by permitting modelling of detection/non-detection data from an arbitrary number of species, without assuming asymmetric interactions. Additionally, our proposed method permits modelling the probability two or more species occur together as a function of environmental variables. These advancements represent an important improvement in our ability to draw community-level inference from multiple interacting species that are subject to imperfect detection.

Dynamic Multiscale Spatiotemporal Models for Poisson Data

ABSTRACT We propose a new class of dynamic multiscale models for Poisson spatiotemporal processes. Specifically, we use a multiscale spatial Poisson factorization to decompose the Poisson process at each time point into spatiotemporal multiscale coefficients. We then connect these spatiotemporal multiscale coefficients through time with a novel Dirichlet evolution. Further, we propose a simulation-based full Bayesian posterior analysis. In particular, we develop filtering equations for updating of information forward in time and smoothing equations for integration of information backward in time, and use these equations to develop a forward filter backward sampler for the spatiotemporal multiscale coefficients. Because the multiscale coefficients are conditionally independent a posteriori, our full Bayesian posterior analysis is scalable, computationally efficient, and highly parallelizable. Moreover, the Dirichlet evolution of each spatiotemporal multiscale coefficient is parametrized by a discount factor that encodes the relevance of the temporal evolution of the spatiotemporal multiscale coefficient. Therefore, the analysis of discount factors provides a powerful way to identify regions with distinctive spatiotemporal dynamics. Finally, we illustrate the usefulness of our multiscale spatiotemporal Poisson methodology with two applications. The first application examines mortality ratios in the state of Missouri, and the second application considers tornado reports in the American Midwest.

Consistency of hyper-

We study the consistency of a Bayesian variable selection procedure for generalized linear models. Specifically, we consider the consistency of a Bayes factor based on g-priors proposed by Sabanes Bove and Held (2011). The integrals necessary for the computation of this Bayes factor are performed with Laplace approximation and Gaussian quadrature. We show that, under certain regularity conditions, the resulting Bayes factor is consistent. Furthermore, a simulation study confirms our theoretical results. Finally, we illustrate this model selection procedure with an application to a real ecological dataset.