arXiv subjects

Alan E. Gelfand

Publications and source records attributed to Alan E. Gelfand.

At least 37 records · Page 2Linked to original sources

arXiv2021

Spatial Functional Data Modeling of Plant Reflectances

Plant reflectance spectra - the profile of light reflected by leaves across different wavelengths - supply the spectral signature for a species at a spatial location to enable estimation of functional and taxonomic diversity for plants. We consider leaf spectra as "responses" to be explained spatially. These spectra/reflectances are functions over a wavelength band that respond to the environment. Our motivating data are gathered for several families from the Cape Floristic Region (CFR) in South Africa and lead us to develop rich novel spatial models that can explain spectra for genera within families. Wavelength responses for an individual leaf are viewed as a function of wavelength, leading to functional data modeling. Local environmental features become covariates. We introduce wavelength - covariate interaction since the response to environmental regressors may vary with wavelength, so may variance. Formal spatial modeling enables prediction of reflectances for genera at unobserved locations with known environmental features. We incorporate spatial dependence, wavelength dependence, and space-wavelength interaction (in the spirit of space-time interaction). We implement out-of-sample validation to select a best model, discovering that the model features listed above are all informative for the functional data analysis. We then supply interpretation of the results under the selected model.

stat.AP↗

arXiv2020

Approximate Bayesian inference for a spatial point process model exhibiting regularity and random aggregation

In this paper, we propose a doubly stochastic spatial point process model with both aggregation and repulsion. This model combines the ideas behind Strauss processes and log Gaussian Cox processes. The likelihood for this model is not expressible in closed form but it is easy to simulate realisations under the model. We therefore explain how to use approximate Bayesian computation (ABC) to carry out statistical inference for this model. We suggest a method for model validation based on posterior predictions and global envelopes. We illustrate the ABC procedure and model validation approach using both simulated point patterns and a real data example.

stat.ME↗

arXiv2020

Long-term Spatial Modeling for Characteristics of Extreme Heat Events

There is increasing evidence that global warming manifests itself in more frequent warm days and that heat waves will become more frequent. Presently, a formal definition of a heat wave is not agreed upon in the literature. To avoid this debate, we consider extreme heat events, which, at a given location, are well-defined as a run of consecutive days above an associated local threshold. Characteristics of EHEs are of primary interest, such as incidence and duration, as well as the magnitude of the average exceedance and maximum exceedance above the threshold during the EHE. Using approximately 60-year time series of daily maximum temperature data collected at 18 locations in a given region, we propose a spatio-temporal model to study the characteristics of EHEs over time. The model enables prediction of the behavior of EHE characteristics at unobserved locations within the region. Specifically, our approach employs a two-state space-time model for EHEs with local thresholds where one state defines above threshold daily maximum temperatures and the other below threshold temperatures. We show that our model is able to recover the EHE characteristics of interest and outperforms a corresponding autoregressive model that ignores thresholds based on out-of-sample prediction.

stat.AP↗

arXiv2019

Generalized Evolutionary Point Processes: Model Specifications and Model Comparison

Generalized evolutionary point processes offer a class of point process models that allows for either excitation or inhibition based upon the history of the process. In this regard, we propose modeling which comprises generalization of the nonlinear Hawkes process. Working within a Bayesian framework, model fitting is implemented through Markov chain Monte Carlo. This entails discussion of computation of the likelihood for such point patterns. Furthermore, for this class of models, we discuss strategies for model comparison. Using simulation, we illustrate how well we can distinguish these models from point pattern specifications with conditionally independent event times, e.g., Poisson processes. Specifically, we demonstrate that these models can correctly identify true relationships (i.e., excitation or inhibition/control). Then, we consider a novel extension of the log Gaussian Cox process that incorporates evolutionary behavior and illustrate that our model comparison approach prefers the evolutionary log Gaussian Cox process compared to simpler models. We also examine a real dataset consisting of violent crime events from the 11th police district in Chicago from the year 2018. This data exhibits strong daily seasonality and changes across the year. After we account for these data attributes, we find significant but mild self-excitation, implying that event occurrence increases the intensity of future events.

stat.ME↗

arXiv2019

Clarifying species dependence under joint species distribution modeling

Joint species distribution modeling is attracting increasing attention these days, acknowledging the fact that individual level modeling fails to take into account expected dependence/interaction between species. These models attempt to capture species dependence through an associated correlation matrix arising from a set of latent multivariate normal variables. However, these associations offer little insight into dependence behavior between species at sites. We focus on presence/absence data using joint species modeling which incorporates spatial dependence between sites. For pairs of species, we emphasize the induced odds ratios (along with the joint probabilities of occurrence); they provide much clearer understanding of joint presence/absence behavior. In fact, we propose a spatial odds ratio surface over the region of interest to capture how dependence varies over the region. We illustrate with a dataset from the Cape Floristic Region of South Africa consisting of more than 600 species at more than 600 sites. We present the spatial distribution of odds ratios for pairs of species that are positively correlated and pairs that are negatively correlated under the joint species distribution model. The multivariate normal covariance matrix associated with a collection of species is only a device for creating dependence among species but it lacks interpretation. By considering odds ratios, the quantitative ecologist will be able to better appreciate the practical dependence between species that is implicit in these joint species distribution modeling specifications.

stat.ME↗

arXiv2019

Multivariate Functional Data Modeling with Time-varying Clustering

We consider the situation where multivariate functional data has been collected over time at each of a set of sites. Our illustrative setting is bivariate, monitoring ozone and PM$_{10}$ levels as a function of time over the course of a year at a set of monitoring sites. The data we work with is from 24 monitoring sites in Mexico City which record hourly ozone and PM$_{10}$ levels. We use the data for the year 2017. Hence, we have 48 functions to work with. Our objective is to implement model-based clustering of the functions across the sites. Using our example, such clustering can be considered for ozone and PM$_{10}$ individually or jointly. It may occur differentially for the two pollutants. More importantly for us, we allow that such clustering can vary with time. We model the multivariate functions across sites using a multivariate Gaussian process. With many sites and several functions at each site, we use dimension reduction to provide a stochastic process specification for the distribution of the collection of multivariate functions over the say $n$ sites. Furthermore, to cluster the functions, either individually by component or jointly with all components, we use the Dirichlet process which enables shared labeling of the functions across the sites. Specifically, we cluster functions based on their response to exogenous variables. Though the functions arise in continuous time, clustering in continuous time is extremely computationally demanding and not of practical interest. Therefore, we employ a partitioning of the time scale to capture time-varying clustering.

stat.ME↗

arXiv2018

Spatial Joint Species Distribution Modeling using Dirichlet Processes

Species distribution models usually attempt to explain presence-absence or abundance of a species at a site in terms of the environmental features (socalled abiotic features) present at the site. Historically, such models have considered species individually. However, it is well-established that species interact to influence presence-absence and abundance (envisioned as biotic factors). As a result, there has been substantial recent interest in joint species distribution models with various types of response, e.g., presence-absence, continuous and ordinal data. Such models incorporate dependence between species response as a surrogate for interaction. The challenge we focus on here is how to address such modeling in the context of a large number of species (e.g., order 102) across sites numbering in the order of 102 or 103 when, in practice, only a few species are found at any observed site. Again, there is some recent literature to address this; we adopt a dimension reduction approach. The novel wrinkle we add here is spatial dependence. That is, we have a collection of sites over a relatively small spatial region so it is anticipated that species distribution at a given site would be similar to that at a nearby site. Specifically, we handle dimension reduction through Dirichlet processes joined with spatial dependence through Gaussian processes. We use both simulated data and a plant communities dataset for the Cape Floristic Region (CFR) of South Africa to demonstrate our approach. The latter consists of presence-absence measurements for 639 tree species on 662 locations. Through both data examples we are able to demonstrate improved predictive performance using the foregoing specification.

stat.ME↗

arXiv2018

Pollution State Modeling for Mexico City

Ground-level ozone and particulate matter pollutants are associated with a variety of health issues and increased mortality. For this reason, Mexican environmental agencies regulate pollutant levels. In addition, Mexico City defines pollution emergencies using thresholds that rely on regional maxima for ozone and particulate matter with diameter less than 10 micrometers ($\text{PM}_{10}$). To predict local pollution emergencies and to assess compliance to Mexican ambient air quality standards, we analyze hourly ozone and $\text{PM}_{10}$ measurements from 24 stations across Mexico City from 2017 using a bivariate spatiotemporal model. Using this model, we predict future pollutant levels using current weather conditions and recent pollutant concentrations. Using hourly pollutant projections, we predict regional maxima needed to estimate the probability of future pollution emergencies. We discuss how predicted compliance to legislated pollution limits varies across regions within Mexico City in 2017. We find that predicted probability of pollution emergencies is limited to a few time periods. In contrast, we show that predicted exceedance of Mexican ambient air quality standards is a common, nearly daily occurrence.

stat.AP↗

arXiv2017

The wrapped skew Gaussian process for analyzing spatio-temporal data

We consider modeling of angular or directional data viewed as a linear variable wrapped onto a unit circle. In particular, we focus on the spatio-temporal context, motivated by a collection of wave directions obtained as computer model output developed dynamically over a collection of spatial locations. We propose a novel wrapped skew Gaussian process which enriches the class of wrapped Gaussian process. The wrapped skew Gaussian process enables more flexible marginal distributions than the symmetric ones arising under the wrapped Gaussian process and it allows straightforward interpretation of parameters. We clarify that replication through time enables criticism of the wrapped process in favor of the wrapped skew process. We formulate a hierarchical model incorporating this process and show how to introduce appropriate latent variables in order to enable efficient fitting to dynamic spatial directional data. We also show how to implement kriging and forecasting under this model. We provide a simulation example as a proof of concept as well as a real data example. Both examples reveal consequential improvement in predictive performance for the wrapped skew Gaussian specification compared with the earlier wrapped Gaussian version.

stat.ME↗

arXiv2017

Spatio-temporal circular models with non-separable covariance structure

Circular data arise in many areas of application. Recently, there has been interest in looking at circular data collected separately over time and over space. Here, we extend some of this work to the spatio-temporal setting, introducing space-time dependence. We accommodate covariates, implement full kriging and forecasting, and also allow for a nugget which can be time dependent. We work within a Bayesian framework, introducing suitable latent variables to facilitate Markov chain Monte Carlo (MCMC) model fitting. The Bayesian framework enables us to implement full inference, obtaining predictive distributions for kriging and forecasting. We offer comparison between the less flexible but more interpretable wrapped Gaussian process and the more flexible but less interpretable projected Gaussian process. We do this illustratively using both simulated data and data from computer model output for wave directions in the Adriatic Sea off the coast of Italy.

stat.ME↗

arXiv2016

Inference for log Gaussian Cox processes using an approximate marginal posterior

The log Gaussian Cox process is a flexible class of point pattern models for capturing spatial and spatio-temporal dependence for point patterns. Model fitting requires approximation of stochastic integrals which is implemented through discretization of the domain of interest. With fine scale discretization, inference based on Markov chain Monte Carlo is computationally heavy because of the cost of repeated iteration or inversion or Cholesky decomposition (cubic order) of high dimensional covariance matrices associated with latent Gaussian variables. Furthermore, hyperparameters for latent Gaussian variables have strong dependence with sampled latent Gaussian variables. Altogether, standard Markov chain Monte Carlo strategies are inefficient and not well behaved. In this paper, we propose an efficient computational strategy for fitting and inferring with spatial log Gaussian Cox processes. The proposed algorithm is based on a pseudo-marginal Markov chain Monte Carlo approach. We estimate an approximate marginal posterior for parameters of log Gaussian Cox processes and propose comprehensive model inference strategy. We provide details for all of the above along with some simulation investigation for the univariate and multivariate settings. As an example, we present an analysis of a point pattern of locations of three tree species, exhibiting positive and negative interaction between different species.

stat.CO↗

arXiv2016

Space and circular time log Gaussian Cox processes with application to crime event data

We view the locations and times of a collection of crime events as a space-time point pattern. So, with either a nonhomogeneous Poisson process or with a more general Cox process, we need to specify a space-time intensity. For the latter, we need a \emph{random} intensity which we model as a realization of a spatio-temporal log Gaussian process. Importantly, we view time as circular not linear, necessitating valid separable and nonseparable covariance functions over a bounded spatial region crossed with circular time. In addition, crimes are classified by crime type. Furthermore, each crime event is recorded by day of the year which we convert to day of the week marks. The contribution here is to develop models to accommodate such data. Our specifications take the form of hierarchical models which we fit within a Bayesian framework. In this regard, we consider model comparison between the nonhomogeneous Poisson process and the log Gaussian Cox process. We also compare separable vs. nonseparable covariance specifications. Our motivating dataset is a collection of crime events for the city of San Francisco during the year 2012. We have location, hour, day of the year, and crime type for each event. We investigate models to enhance our understanding of the set of incidences.

stat.AP↗

arXiv2016

Disease Mapping with Generative Models

Disease mapping focuses on learning about areal units presenting high relative risk. Disease mapping models for disease counts specify Poisson regressions in relative risks compared with the expected counts. These models typically incorporate spatial random effects to accomplish spatial smoothing. Fitting of these models customarily computes expected disease counts via internal standardization. This places the data on both sides of the model, i.e., the counts are on the left side but they are also used to obtain the expected counts on the right side. As a result, these internally standardized models are incoherent and not generative; probabilistically, they could not produce the observed data. Here, we argue for adopting the direct generative model for disease counts. We model disease incidence instead of relative risks, using a generalized logistic regression. We extract relative risks post model fitting. We also extend the generative model to dynamic settings. We compare the generative models with internally standardized models through simulated datasets and a well-examined lung cancer morbidity data in Ohio. Each model is a spatial smoother and they smooth the data similarly with regard to relative risks. However, the generative models tend to provide tighter credible intervals. Since the generative specification is no more difficult to fit, is coherent, and is at least as good inferentially, we suggest it should be the model of choice for spatial disease mapping.

stat.ME↗

arXiv2016

Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This manuscript develops a class of highly scalable Nearest Neighbor Gaussian Process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive United States Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods.

stat.ME↗

arXiv2015

Spatial Process Gradients and Their Use in Sensitivity Analysis for Environmental Processes

This paper develops methodology for local sensitivity analysis based on directional derivatives associated with spatial processes. Formal gradient analysis for spatial processes was elaborated in previous papers, focusing on distribution theory for directional derivatives associated with a response variable assumed to follow a Gaussian process model. In the current work, these ideas are extended to additionally accommodate a continuous covariate whose directional derivatives are also of interest and to relate the behavior of the directional derivatives of the response surface to those of the covariate surface. It is of interest to assess whether, in some sense, the gradients of the response follow those of the explanatory variable. The joint Gaussian structure of all variables, including the directional derivatives, allows for explicit distribution theory and, hence, kriging across the spatial region using multivariate normal theory. Working within a Bayesian hierarchical modeling framework, posterior samples enable all gradient analysis to occur post model fitting. As a proof of concept, we show how our methodology can be applied to a standard geostatistical modeling setting using a simulation example. For a real data illustration, we work with point pattern data, deferring our gradient analysis to the intensity surface, adopting a log-Gaussian Cox process model. In particular, we relate elevation data to point patterns associated with several tree species in Duke Forest.

math.ST↗

arXiv2013

Scaling Integral Projection Models for Analyzing Size Demography

Historically, matrix projection models (MPMs) have been employed to study population dynamics with regard to size, age or structure. To work with continuous traits, in the past decade, integral projection models (IPMs) have been proposed. Following the path for MPMs, currently, IPMs are handled first with a fitting stage, then with a projection stage. Model fitting has, so far, been done only with individual-level transition data. These data are used in the fitting stage to estimate the demographic functions (survival, growth, fecundity) that comprise the kernel of the IPM specification. The estimated kernel is then iterated from an initial trait distribution to obtain what is interpreted as steady state population behavior. Such projection results in inference that does not align with observed temporal distributions. This might be expected; a model for population level projection should be fitted with population level transitions.

stat.ME↗

arXiv2013

spBayes for large univariate and multivariate point-referenced spatio-temporal data models

In this paper we detail the reformulation and rewrite of core functions in the spBayes R package. These efforts have focused on improving computational efficiency, flexibility, and usability for point-referenced data models. Attention is given to algorithm and computing developments that result in improved sampler convergence rate and efficiency by reducing parameter space; decreased sampler run-time by avoiding expensive matrix computations, and; increased scalability to large datasets by implementing a class of predictive process models that attempt to overcome computational hurdles by representing spatial processes in terms of lower-dimensional realizations. Beyond these general computational improvements for existing model functions, we detail new functions for modeling data indexed in both space and time. These new functions implement a class of dynamic spatio-temporal models for settings where space is viewed as continuous and time is taken as discrete.

stat.CO↗

arXiv2010

Modeling large scale species abundance with latent spatial processes

Modeling species abundance patterns using local environmental features is an important, current problem in ecology. The Cape Floristic Region (CFR) in South Africa is a global hot spot of diversity and endemism, and provides a rich class of species abundance data for such modeling. Here, we propose a multi-stage Bayesian hierarchical model for explaining species abundance over this region. Our model is specified at areal level, where the CFR is divided into roughly $37{,}000$ one minute grid cells; species abundance is observed at some locations within some cells. The abundance values are ordinally categorized. Environmental and soil-type factors, likely to influence the abundance pattern, are included in the model. We formulate the empirical abundance pattern as a degraded version of the potential pattern, with the degradation effect accomplished in two stages. First, we adjust for land use transformation and then we adjust for measurement error, hence misclassification error, to yield the observed abundance classifications. An important point in this analysis is that only $28%$ of the grid cells have been sampled and that, for sampled grid cells, the number of sampled locations ranges from one to more than one hundred. Still, we are able to develop potential and transformed abundance surfaces over the entire region. In the hierarchical framework, categorical abundance classifications are induced by continuous latent surfaces. The degradation model above is built on the latent scale. On this scale, an areal level spatial regression model was used for modeling the dependence of species abundance on the environmental factors.

stat.AP↗