Bayesian nonparametric models for spatially indexed data of mixed type

We develop Bayesian nonparametric models for spatially indexed data of mixed type. Our work is motivated by challenges that occur in environmental epidemiology, where the usual presence of several confounding variables that exhibit complex interactions and high correlations makes it difficult to estimate and understand the effects of risk factors on health outcomes of interest. The modeling approach we adopt assumes that responses and confounding variables are manifestations of continuous latent variables, and uses multivariate Gaussians to jointly model these. Responses and confounding variables are not treated equally as relevant parameters of the distributions of the responses only are modeled in terms of explanatory variables or risk factors. Spatial dependence is introduced by allowing the weights of the nonparametric process priors to be location specific, obtained as probit transformations of Gaussian Markov random fields. Confounding variables and spatial configuration have a similar role in the model, in that they only influence, along with the responses, the allocation probabilities of the areas into the mixture components, thereby allowing for flexible adjustment of the effects of observed confounders, while allowing for the possibility of residual spatial structure, possibly occurring due to unmeasured or undiscovered spatially varying factors. Aspects of the model are illustrated in simulation studies and an application to a real data set

State space mixed models for longitudinal obsservations with binary and binomial responses

We propose a new class of state space models for longitudinal discrete response data where the observation equation is specified in an additive form involving both deterministic and random linear predictors. These models allow us to explicitly address the effects of trend, seaonal or other time-varying covariates while preserving the power of state space models in modeling serial dependence in the data. We develop a Markov Chain Monte Carlo algorithm to carry out statistical inferene for models with binary and binomial responses, in which we invoke de Jong and Shephard's (1995) simulaton smoother to establish an efficent sampling procedure for the state variables. To quantify and control the sensitivity of posteriors on the priors of variance parameters, we add a signal-to-noise ratio type parmeter in the specification of these priors. Finally, we ilustrate the applicability of the proposed state space mixed models for longitudinal binomial response data in both simulation studies and data examples

Hebbian-inspired rewiring of a random network replicates pattern of selectivity seen in PFC

Responses of neurons in pre-frontal cortex (PFC) are very diverse and often depend on complex non-linear combinations of task-relevant variables (a property known as mixed selectivity). We recently showed that this type of selectivity is a signature of high dimensional neural representations and can be important for performing complex cognitive tasks. Previous modeling work has shown that mixed selectivity can arise when cells receive fixed random synaptic inputs from populations that represent the task-relevant variables. Here we show by analyzing the data that these simple models only partially explain the mixed selectivity observed in the data

Advocating better habitat use and selection models in bird ecology

Studies on habitat use and habitat selection represent a basic aspect of bird ecology, due to its importance in natural history, distribution, response to environmental changes, management and conservation. Basically, a statistical model that identifies environmental variables linked to a species presence is searched for. In this sense, there is a wide array of analytical methods that identify important explanatory variables within a model, with higher explanatory and predictive power than classical regression approaches. However, some of these powerful models are not widespread in ornithological studies, partly because of their complex theory, and in some cases, difficulties on their implementation and interpretation. Here, I describe generalized linear models and other five statistical models for the analysis of bird habitat use and selection outperforming classical approaches: generalized additive models, mixed effects models, occupancy models, binomial N-mixture models and decision trees (classification and regression trees, bagging, random forests and boosting). Each of these models has its benefits and drawbacks, but major advantages include dealing with non-normal distributions (presence-absence and abundance data typically found in habitat use and selection studies), heterogeneous variances, non-linear and complex relationships among variables, lack of statistical independence and imperfect detection. To aid ornithologists in making use of the methods described, a readable description of each method is provided, as well as a flowchart along with some recommendations to help them decide the most appropriate analysis. The use of these models in ornithological studies is encouraged, given their huge potential as statistical tools in bird ecology.Fil: Palacio, Facundo Xavier. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo. División Zoología de Vertebrados. Sección Ornitología; Argentin