arXiv subjects

Dani Gamerman

Publications and source records attributed to Dani Gamerman.

7 recordsLinked to original sources

arXiv2026

A Bayesian Joint Model for Multiple Point Processes with Application to Presence-Only Data

Joint modeling of multiple point processes is relevant in applications where relationships among processes are of interest, such as in ecological and archaeological studies. Statistical inference becomes particularly challenging when multiple processes are analyzed jointly and the observed data correspond to presence-only patterns, which are subject to preferential sampling and partial observability. This paper proposes a Bayesian joint model for multiple point processes, with application to the presence-only setting. The dependence between processes is explicitly incorporated into the probabilistic specification of the model using Bayesian networks. Direct use of the likelihood leads to intractable likelihood functions. Latent data processes are then introduced so that the augmented likelihood function becomes tractable and can be exactly evaluated. This formulation also enables direct inference on the number and the spatial distribution of unobserved occurrences of any of the point patterns. Inference is carried out using Markov chain Monte Carlo with blocked Gibbs sampling. Simulation studies demonstrate that the proposed inferential scheme is able to recover the true model parameters. The proposed model is applied to real presence-only data of archaeological sites and tree species from Amazonia, as part of the study of the effect that pre-Columbian Indigenous presence might have on the occurrences of relevant tree species. The results are consistent with the findings reported in the literature. They also illustrate how the proposed model enables inference on the existence and on the magnitude of the relation between processes, in addition to their association with environmental covariates.

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arXiv2025

Spatial deformation in a Bayesian spatiotemporal model for incomplete matrix-variate responses

In this paper, we propose a Bayesian matrix-variate spatiotemporal modeling framework for jointly analyzing multiple response variables observed at spatial locations over time. The approach relaxes the standard assumption of spatial isotropy by incorporating a deformation-based mechanism, allowing the covariance structure to capture directional effects and nonstationary spatial dependence. Temporal dynamics are modeled through dynamic linear models, enabling coherent uncertainty propagation within a state-space formulation. Missing observations are handled via a data augmentation strategy that preserves the joint structure of the multivariate responses. The proposed methodology is evaluated through simulation studies and an application to air quality data. Results indicate that accounting for spatial deformation leads to substantial gains in predictive performance in anisotropic settings, while cross-variable dependence plays a secondary role in improving overall fit. The framework is computationally tractable for moderate numbers of spatial locations and responses, and provides a flexible basis for modeling multivariate spatiotemporal processes under incomplete data.

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arXiv2025

Nonparametric inference for nonstationary spatial point processes

Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying intensity function. These features are difficult to capture with standard modeling approaches. This paper proposes a spatial Cox process model in which nonstationarity is induced through a random partition of the spatial domain, with conditionally independent Gaussian process priors specified across the resulting regions. This construction allows for heterogeneous spatial behavior, including sharp transitions in intensity. A discretization-free MCMC algorithm is developed to target the infinite-dimensional posterior distribution without approximation, thus ensuring exact inference. The random partition framework via Voronoi tessellation also reduces the computational burden associated with Gaussian process models. Spatial covariates can be incorporated to account for structured variation in intensity. The proposed methodology is evaluated through synthetic examples and real-world applications, demonstrating its ability to flexibly capture complex spatial structures. The model performs competitively, outperforming stationary and nonstationary alternatives in a variety of scenarios. Recent computational methods are used, enabling scalability to large datasets while preserving exactness. The paper concludes with a discussion of potential extensions and directions for future work.

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arXiv2022

Exact Bayesian Inference for Geostatistical Models under Preferential Sampling

Preferential sampling is a common feature in geostatistics and occurs when the locations to be sampled are chosen based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability law for the distribution of the locations. However, analytic intractability of the point process likelihood prevents its direct calculation. Many Bayesian (and non-Bayesian) approaches in non-parametric model specifications handle this difficulty with approximation-based methods. These approximations involve errors that are difficult to quantify and can lead to biased inference. This paper presents an approach for performing exact Bayesian inference for this setting without the need for model approximation. A qualitatively minor change on the traditional model is proposed to circumvent the likelihood intractability. This change enables the use of an augmented model strategy. Recent work on Bayesian inference for point pattern models can be adapted to the geostatistics setting and renders computational tractability for exact inference for the proposed methodology. Estimation of model parameters and prediction of the response at unsampled locations can then be obtained from the joint posterior distribution of the augmented model. Simulated studies showed good quality of the proposed model for estimation and prediction in a variety of preferentiality scenarios. The performance of our approach is illustrated in the analysis of real datasets and compares favourably against approximation-based approaches. The paper is concluded with comments regarding extensions of and improvements to the proposed methodology.

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arXiv2017

A semiparametric approach for bivariate extreme exceedances

Inference over tails is performed by applying only the results of extreme value theory. Whilst such theory is well defined and flexible enough in the univariate case, multivariate inferential methods often require the imposition of arbitrary constraints not fully justifed by the underlying theory. In contrast, our approach uses only the constraints imposed by theory. We build on previous, theoretically justified work for marginal exceedances over a high, unknown threshold, by combining it with flexible, semiparametric copulae specifications to investigate extreme dependence. Whilst giving probabilistic judgements about the extreme regime of all marginal variables, our approach formally uses the full dataset and allows for a variety of patterns of dependence, be them extremal or not. A new probabilistic criterion quantifying the possibility that the data exhibits asymptotic independence is introduced and its robustness empirically studied. Estimation of functions of interest in extreme value analyses is performed via MCMC algorithms. Attention is also devoted to the prediction of new extreme observations. Our approach is evaluated through a series of simulations, applied to real data sets and assessed against competing approaches. Evidence demonstrates that the bulk of the data does not bias and improves the inferential process for the extremal dependence.

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arXiv2015

Optimal Design in Geostatistics under Preferential Sampling

This paper analyses the effect of preferential sampling in Geostatistics when the choice of new sampling locations is the main interest of the researcher. A Bayesian criterion based on maximizing utility functions is used. Simulated studies are presented and highlight the strong influence of preferential sampling in the decisions. The computational complexity is faced by treating the new local sampling locations as a model parameter and the optimal choice is then made by analysing its posterior distribution. Finally, an application is presented using rainfall data collected during spring in Rio de Janeiro. The results showed that the optimal design is substantially changed under preferential sampling effects. Furthermore, it was possible to identify other interesting aspects related to preferential sampling effects in estimation and prediction in Geostatistics. With the Rejoinder to Comments [arXiv:1509.04817], [arXiv:1509.04819], [arXiv:1509.04821].

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arXiv2015

Exact Bayesian inference in spatio-temporal Cox processes driven by multivariate Gaussian processes

In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to allow for evolution of the intensity function over discrete time. The novelty of the method lies on the fact that no discretisation error is involved despite the non-tractability of the likelihood function and infinite dimensionality of the problem. The method is based on a Markov chain Monte Carlo algorithm that samples from the joint posterior distribution of the parameters and latent variables of the model. The models are defined in a general and flexible way but they are amenable to direct sampling from the relevant distributions, due to careful characterisation of its components. The models also allow for the inclusion of regression covariates and/or temporal components to explain the variability of the intensity function. These components may be subject to relevant interaction with space and/or time. Real and simulated examples illustrate the methodology, followed by concluding remarks.

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