Athanasios C. Micheas

A Spatio-Temporal Point Process Model for Ambulance Demand

Ambulance demand estimation at fine time and location scales is critical for fleet management and dynamic deployment. We are motivated by the problem of estimating the spatial distribution of ambulance demand in Toronto, Canada, as it changes over discrete 2 hr intervals. This large-scale dataset is sparse at the desired temporal resolutions and exhibits location-specific serial dependence, daily, and weekly seasonality. We address these challenges by introducing a novel characterization of time-varying Gaussian mixture models. We fix the mixture component distributions across all time periods to overcome data sparsity and accurately describe Toronto’s spatial structure, while representing the complex spatio-temporal dynamics through time-varying mixture weights. We constrain the mixture weights to capture weekly seasonality, and apply a conditionally autoregressive prior on the mixture weights of each component to represent location-specific short-term serial dependence and daily seasonality. While estimation may be performed using a fixed number of mixture components, we also extend to estimate the number of components using birth-and-death Markov chain Monte Carlo. The proposed model is shown to give higher statistical predictive accuracy and to reduce the error in predicting emergency medical service operational performance by as much as two-thirds compared to a typical industry practice.

A Bayesian Hierarchical Nonoverlapping Random Disc Growth Model

A methodology is proposed to efficiently model a random set via a multistage hierarchical Bayesian model. We define a NonOverlapping Random Disk Model (NORDM), which is similar in spirit to the well-known Poisson–Boolean model. This model is formulated in a conditional setting that facilitates Bayesian sampling of important parameters in the model. This framework can accommodate any object, not just those with disk shapes, although the model can be easily extended to include any known compact convex set instead of the disc (e.g., polygons or ellipses). We further propose a growth model that is conceptually simple and allows straightforward estimation of parameters, without the need for tedious calculations of hitting or inclusion probabilities. The model is applied to severe storm cell development as obtained from weather radar.

A Unified Approach to Prior and Loss Robustness

ABSTRACT We introduce a new statistical framework in order to study Bayesian loss robustness under classes of priors distributions, thus unifying both concepts of robustness. We propose measures that capture variation with respect to both prior selection and selection of loss function and explore general properties of these measures. We illustrate the approach for the continuous exponential family. Robustness in this context is studied first with respect to prior selection where we consider several classes of priors for the parameter of interest, including unimodal and symmetric and unimodal with positive support. After prior variation has been measured we investigate robustness to loss function, using Hellinger and Linex (Linear Exponential) classes of loss functions. The methods are applied to standard examples.

Random set modelling of three-dimensional objects in a hierarchical Bayesian context

We present a Bayesian approach to modelling and estimating objects in three dimensions. A general stochastic model for object recognition based on points in the domain of observation is created via hierarchical mixtures, allowing for the inclusion of important prior information about the objects under consideration. Objects under consideration are created based on three-dimensional (3D) points in space, with each point having some probability of membership to different objects. This is the first object-oriented statistical approach that models 3D objects in a true 3D environment. A data-augmentation approach and a Birth–Death Markov Chain Monte Carlo algorithm are incorporated to provide classification probabilities of each data point to one or more of the identified objects and to obtain estimates of the parameters that describe each object. Strengths of the methodology include its ease in accommodating different data and process models, its flexibility in handling varying numbers of mixture components, and most importantly, its ability to allow for inference on individual characteristics of objects. These strengths are demonstrated on an application for a forest (tree objects) near Olympia, WA, based on remotely sensed Light Detection and Ranging point observations.

Hierarchical Bayesian modeling of marked non-homogeneous Poisson processes with finite mixtures and inclusion of covariate information

We investigate marked non-homogeneous Poisson processes using finite mixtures of bivariate normal components to model the spatial intensity function. We employ a Bayesian hierarchical framework for estimation of the parameters in the model, and propose an approach for including covariate information in this context. The methodology is exemplified through an application involving modeling of and inference for tornado occurrences.We investigate marked non-homogeneous Poisson processes using finite mixtures of bivariate normal components to model the spatial intensity function. We employ a Bayesian hierarchical framework for estimation of the parameters in the model, and propose an approach for including covariate information in this context. The methodology is exemplified through an application involving modeling of and inference for tornado occurrences.

Bayesian Procrustes analysis with applications to hydrology

In this paper, we introduce Procrustes analysis in a Bayesian framework, by treating the classic Procrustes regression equation from a Bayesian perspective, while modeling shapes in two dimensions. The Bayesian approach allows us to compute point estimates and credible sets for the full Procrustes fit parameters. The methods are illustrated through an application to radar data from short-term weather forecasts (nowcasts), a very important problem in hydrology and meteorology.

Reconciling Bayesian and Frequentist Evidence in the One-Sided Scale Parameter Testing Problem

An interesting but controversial problem arises when Bayesian as well as frequentist methodologies very often suggest similar solutions, thus creating a problem for the experimenter who wishes to make the best possible decision. For over a decade, there has been an effort by several authors to assess when Bayesian and frequentist methods provide exactly the same answers when employed. We encounter this situation in the problem of hypothesis testing, where Bayesian evidence, such as Bayes factors and prior or posterior predictive p-values are set against the classical p-values. All these measures provide a basis for rejection of a hypothesis or a model, but the selection of one over the other never comes without severe criticism. In this article, we develop prior predictive and posterior predictive p-values for one sided hypothesis testing for scale parameter problems. We reconcile Bayesian and frequentist evidence by showing that for many classes of prior distributions, the infimum of the prior predictive and posterior predictive p-values are equal to the classical p-value, for very general classes of distributions. The results are illustrated through examples relating to the one-sided testing problem for scale parameter.

On Measuring Loss Robustness Using Maximum A Posteriori Estimate

Abstract This paper investigates robustness of the loss function in a Bayesian framework. We incorporate maximum a posteriori (MAP) estimate, posterior expected loss (PEL) and introduce MAP range, in order to measure loss robustness under certain classes of loss functions, including Hellinger and LINEX loss functions. These classes of loss functions are considered for the estimation of the natural parameters of the continuous exponential family. The methods introduced are illustrated with some standard examples, including Normal and Gamma distributions. Finally, a comparison between MAP and PEL based loss robustness measures is presented to illustrate the importance of MAP estimation in measuring loss robustness.

Ranges of Posterior Expected Losses and ε-Robust Actions

Robustness of the loss functions is considered in a Bayesian framework. Variations of the posterior expected loss are studied when the loss functions belong to a certain class. Ranges of the posterior expected loss, influence function and minimax regret principles are adopted to capture the robustness and optimum choice of the loss functions. Applications include the continuous exponential family under the class of Linex loss functions, weighted squared error and Hellinger distance loss. Methods are applied to standard examples, including normal distributions. We also illustrate the use of power divergence in this framework with an application to the normal case.

Assessing shape differences in populations of shapes using the complex watson shape distribution

Abstract This paper presents a novel Bayesian method based on the complex Watson shape distribution that is used in detecting shape differences between the second thoracic vertebrae for two groups of mice, small and large, categorized according to their body weight. Considering the data provided in Johnson et al. (1988), we provide Bayesian methods of estimation as well as highest posterior density (HPD) estimates for modal vertebrae shapes within each group. Finally, we present a classification procedure that can be used in any shape classification experiment, and apply it for categorizing new vertebrae shapes in small or large groups.