Bruno Sansó

Objective Bayesian Analysis of Spatially Correlated Data

Spatially varying phenomena are often modeled using Gaussian random fields, specified by their mean function and covariance function. The spatial correlation structure of these models is commonly specified to be of a certain form (e.g., spherical, power exponential, rational quadratic, or Matérn) with a small number of unknown parameters. We consider objective Bayesian analysis of such spatial models, when the mean function of the Gaussian random field is specified as in a linear model. It is thus necessary to determine an objective (or default) prior distribution for the unknown mean and covariance parameters of the random field. We first show that common choices of default prior distributions, such as the constant prior and the independent Jeffreys prior, typically result in improper posterior distributions for this model. Next, the reference prior for the model is developed and is shown to yield a proper posterior distribution. A further attractive property of the reference prior is that it can be used directly for computation of Bayes factors or posterior probabilities of hypotheses to compare different correlation functions, even though the reference prior is improper. An illustration is given using a spatial dataset of topographic elevations.

Dynamic models for spatiotemporal data

We propose a model for non-stationary spatiotemporal data. To account for spatial variability, we model the mean function at each time period as a locally weighted mixture of linear regressions. To incorporate temporal variation, we allow the regression coefficients to change through time. The model is cast in a Gaussian state space framework, which allows us to include temporal components such as trends, seasonal effects and autoregressions, and permits a fast implementation and full probabilistic inference for the parameters, interpolations and forecasts. To illustrate the model, we apply it to two large environmental data sets: tropical rainfall levels and Atlantic Ocean temperatures.

Optimal Bayesian Design by Inhomogeneous Markov Chain Simulation

We consider decision problems defined by a utility function and an underlying probability model for all unknowns. The utility function quantifies the decision makers preferences over consequences. The optimal decision maximizes the expected utility function where the expectation is taken with respect to all unknowns, that is, future data and parameters. In many problems, the solution is not analytically tractable. For example, the utility function might involve moments that can be computed only by numerical integration or simulation. Also, the nature of the decision space (i.e., the set of all possible actions) might have a shape or dimension that complicates the maximization. The motivating application for this discussion is the choice of a monitoring network when the optimization is performed over the high-dimensional set of all possible locations of monitoring stations, possibly including choice of the number of locations. We propose an approach to optimal Bayesian design based on inhomogeneous Markov chain simulation. We define a chain such that the limiting distribution identifies the optimal solution. The approach is closely related to simulated annealing. Standard simulated annealing algorithms assume that the target function can be evaluated for any given choice of the variable with respect to which we wish to optimize. For optimal design problems the target function (i. e., expected utility) is in general not available for efficient evaluation and might require numerical integration. We overcome the problem by defining an inhomogeneous Markov chain on an appropriately augmented space. The proposed inhomogeneous Markov chain Monte Carlo method addresses within one simulation both problems, evaluation of the expected utility and maximization.

Biological communities in San Francisco Bay track large-scale climate forcing over the North Pacific.

Long-term observations show that fish and plankton populations in the ocean fluctuate in synchrony with large-scale climate patterns, but similar evidence is lacking for estuaries because of shorter observational records. Marine fish and invertebrates have been sampled in San Francisco Bay since 1980 and exhibit large, unexplained population changes including record-high abundances of common species after 1999. Our analysis shows that populations of demersal fish, crabs and shrimp covary with the Pacific Decadal Oscillation (PDO) and North Pacific Gyre Oscillation (NPGO), both of which reversed signs in 1999. A time series model forced by the atmospheric driver of NPGO accounts for two-thirds of the variability in the first principal component of species abundances, and generalized linear models forced by PDO and NPGO account for most of the annual variability of individual species. We infer that synchronous shifts in climate patterns and community variability in San Francisco Bay are related to changes in oceanic wind forcing that modify coastal currents, upwelling intensity, surface temperature, and their influence on recruitment of marine species that utilize estuaries as nursery habitat. Ecological forecasts of estuarine responses to climate change must therefore consider how altered patterns of atmospheric forcing across ocean basins influence coastal oceanography as well as watershed hydrology.

Nonparametric Dark Energy Reconstruction from Supernova Data

Understanding the origin of the accelerated expansion of the Universe poses one of the greatest challenges in physics today. Lacking a compelling fundamental theory to test, observational efforts are targeted at a better characterization of the underlying cause. If a new form of mass-energy, dark energy, is driving the acceleration, the redshift evolution of the equation of state parameter w(z) will hold essential clues as to its origin. To best exploit data from observations it is necessary to develop a robust and accurate reconstruction approach, with controlled errors, for w(z). We introduce a new, nonparametric method for solving the associated statistical inverse problem based on Gaussian process modeling and Markov chain Monte Carlo sampling. Applying this method to recent supernova measurements, we reconstruct the continuous history of w out to redshift z=1.5.

Time-varying models for extreme values

We propose a new approach for modeling extreme values that are measured in time and space. First we assume that the observations follow a Generalized Extreme Value (GEV) distribution for which the location, scale or shape parameters define the space–time structure. The temporal component is defined through a Dynamic Linear Model (DLM) or state space representation that allows to estimate the trend or seasonality of the data in time. The spatial element is imposed through the evolution matrix of the DLM where we adopt a process convolution form. We show how to produce temporal and spatial estimates of our model via customized Markov Chain Monte Carlo (MCMC) simulation. We illustrate our methodology with extreme values of ozone levels produced daily in the metropolitan area of Mexico City and with rainfall extremes measured at the Caribbean coast of Venezuela.

Spatio-temporal variability of ocean temperature in the Portugal Current System

A dynamic process convolution model (DPCM) is used to investigate the evolution and spatial distribution of monthly ocean temperature anomalies in the Portugal Current System. The analysis is performed with 20th century standard depth measurements from the National Oceanographic Data Center, ranging from the surface to 500 m depth. The proposed DPCM decomposes the temporal variability into short-term non-linear components and long-term linear trends, with both components varying smoothly across latitude, longitude and depth. An important feature of the DPCM is that it allows the assessment of trend significance without ad hoc corrections, since the residuals are spatially and temporally uncorrelated. In the analyzed period, an overall warming of coastal surface waters off the west Iberian Peninsula is found, together with fading cross-shelf temperature gradients and increased coastal stratification. Since previous studies also found that upwelling-favorable winds have weakened from the 1940s onward, these results most likely reflect a long-term weakening of the coastal upwelling regime. Transient periods of temperature change are also described and associated with known variability in the North Atlantic, and a final discussion on the link between the observed trends and anthropogenic forcing on climate is presented.

A Nonstationary Multisite Model for Rainfall

Abstract Estimation and prediction of the amount of rainfall in time and space is a problem of fundamental importance in many applications in agriculture, hydrology, and ecology. Stochastic simulation of rainfall data is also an important step in the development of stochastic downscaling methods where large-scale climate information is considered as an additional explanatory variable of rainfall behavior at the local scale. Simulated rainfall has also been used as input data for many agricultural, hydrological, and ecological models, especially when rainfall measurements are not available for locations of interest or when historical records are not of sufficient length to evaluate important rainfall characteristics as extreme values. Rainfall estimation and prediction were carried out for an agricultural region of Venezuela in the central plains state of Guárico, where rainfall for 10-day periods is available for 80 different locations. The measurement network is relatively sparse for some areas, and aggregated rainfall at time resolutions of days or less is of very poor quality or nonexistent. We consider a model for rainfall based on a truncated normal distribution that has been proposed in the literature. We assume that the data y it, where i indexes location and t indexes time, correspond to normal random variates w it that have been truncated and transformed. According to this model, the dry periods correspond to the (unobserved) negative values and the wet periods correspond to a transformation of the positive ones. The serial structure present in series of rainfall data can be modeled by considering a stochastic process for w it. We use a dynamic linear model on w t = (w1t, …, wNt) that includes a Fourier representation to allow for the seasonality of the data that is assumed to be the same for all sites, plus a linear combination of functions of the location of each site. This approach captures year-to-year variability and provides a tool for short-term forecasting. The model is fitted using a Markov chain Monte Carlo method that uses latent variables to handle dry periods and missing values.

Venezuelan rainfall data analysed by using a Bayesian space-time model

We consider a set of data from 80 stations in the Venezuelan state of Guarico consisting of accumulated monthly rainfall in a time span of 16 years. The problem of modelling rainfall accumulated over fixed periods of time and recorded at meteorological stations at different sites is studied by using a model based on the assumption that the data follow a truncated and transformed multivariate normal distribution. The spatial correlation is modelled by using an exponentially decreasing correlation function and an interpolating surface for the means. Missing data and dry periods are handled within a Markov chain Monte Carlo framework using latent variables. We estimate the amount of rainfall as well as the probability of a dry period by using the predictive density of the data. We considered a model based on a full second-degree polynomial over the spatial co-ordinates as well as the first two Fourier harmonics to describe the variability during the year. Predictive inferences on the data show very realistic results, capturing the typical rainfall variability in time and space for that region. Important extensions of the model are also discussed.

ENZYME-LINKED IMMUNOSORBENT ASSAY (ELISA) FOR DETECTION OF ANTI-TRYPANOSOMA EVANSI EQUINE ANTIBODIES

The standardization of ELISA for the detection of anti-Trypanosoma evansi antibodies in naturally and experimentally infected horses is described. Bayesian analysis was used to establish the cutoff between positive and negative sera. In order to determine the assessment of the ELISA test, the results obtained were compared with those from an IFA. A relative sensibility of 98.39%, a specificity of 95.12% and a predictive value of 96.83% were determined. The standardized technique was used to evaluate the antibody production against trypanosome in an experimentally infected equine, in which the sera converted 15 days after infection. The test was also used for a study of sera prevalence in a non-random sample from two different populations. A prevalence of 81.7% in workhorse and 57.14% in stable horses was found.