Browsing by Author "Mena, Ramses H."

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    Linear models for statistical shape analysis based on parametrized closed curves
    (2020) Gutierrez, Luis; Mena, Ramses H.; Diaz-Avalos, Carlos
    We develop a simple, yet powerful, technique based on linear regression models of parametrized closed curves which induces a probability distribution on the planar shape space. Such parametrization is driven by control points which can be estimated from the data. Our proposal is capable to infer about the mean shape, to predict the shape of an object at an unobserved location, and, while doing so, to consider the effect of predictors on the shape. In particular, the model is able to detect possible differences across the levels of the predictor, thus also applicable for two-sample tests. A simple MCMC algorithm for Bayesian inference is also presented and tested with simulated and real datasets. Supplementary material is available online.
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    Modeling wildfires via marked spatio-temporal Poisson processes
    (2021) Quinlan, Jose J.; Diaz-Avalos, Carlos; Mena, Ramses H.
    From a statistical viewpoint, characteristics such as ignition time, location and duration are relevant components for wildfire modeling. The observed ignition sites and starting times constitute a space-time point pattern, and a natural framework to model this type of data is via point processes. In this work, we propose a marked Poisson process to model fire patterns in space-time, considering durations as marks. The collected data correspond to fires observed in the Valencian Community, Spain, between 2010 and 2015. The methodology relies on writing the intensity function of such a process, jointly for starting times, locations and durations, as a weighted Dirichlet process mixture model. A particular choice of the kernel that determines such mixture was made, compatible with data features. We conducted posterior inference on some characteristics of interest for understanding wildfire behavior, showing high flexibility to emulate data patterns.
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    On a Dirichlet Process Mixture Representation of Phase-Type Distributions
    (2022) Ayala, Daniel; Jofre, Leonardo; Gutierrez, Luis; Mena, Ramses H.
    An explicit representation of phase-type distributions as an infinite mixture of Erlang distributions is introduced. The representation unveils a novel and useful connection between a class of Bayesian nonparametric mixture mod-els and phase-type distributions. In particular, this sheds some light on two hot topics, estimation techniques for phase-type distributions, and the availability of closed-form expressions for some functionals related to Dirichlet process mixture models. The power of this connection is illustrated via a posterior inference al-gorithm to estimate phase-type distributions, avoiding some difficulties with the simulation of latent Markov jump processes, commonly encountered in phase-type Bayesian inference. On the other hand, closed-form expressions for functionals of Dirichlet process mixture models are illustrated with density and renewal function estimation, related to the optimal salmon weight distribution of an aquaculture study.