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This work is motivated by the analysis of the extremal behavior of buoy and satellite data describing wave conditions in the North Atlantic Ocean. The available data sets consist of time series of significant wave height (Hs) with irregular…
Many models in natural language processing define probabilistic distributions over linguistic structures. We argue that (1) the quality of a model' s posterior distribution can and should be directly evaluated, as to whether probabilities…
A widely used tool in the study of risk, insurance and extreme values is the mean excess plot. One use is for validating a generalized Pareto model for the excess distribution. This paper investigates some theoretical and practical aspects…
Panel data arise in a wide range of application areas, and developing modelling methods for extreme values under such a setup is essential for reliable risk assessment and management. When choosing to model the marginal distributions of…
We present a procedure to diagnose model misspecification in situations where inference is performed using approximate Bayesian computation. We demonstrate theoretically, and empirically that this procedure can consistently detect the…
The modelling of action potentials from extracellular recordings, or spike sorting, is a rich area of neuroscience research in which latent variable models are often used. Two such models, Overfitted Finite Mixture models (OFMs) and…
The existence of large and extreme claims of a non-life insurance portfolio influences the ability of (re)insurers to estimate the reserve. The excess over-threshold method provides a way to capture and model the typical behaviour of…
Clustered data are common in practice. Clustering arises when subjects are measured repeatedly, or subjects are nested in groups (e.g., households, schools). It is often of interest to evaluate the correlation between two variables with…
With the recent growth in data availability and complexity, and the associated outburst of elaborate modelling approaches, model selection tools have become a lifeline, providing objective criteria to deal with this increasingly challenging…
The $p$-tensor Ising model is a one-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic is a multi-linear form of degree $p \geq 2$. This is a natural generalization of the matrix Ising…
In many parameter estimation problems, the exact model is unknown and is assumed to belong to a set of candidate models. In such cases, a predetermined data-based selection rule selects a parametric model from a set of candidates before the…
We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating…
The purpose of this paper is to estimate the intensity of a Poisson process $N$ by using thresholding rules. In this paper, the intensity, defined as the derivative of the mean measure of $N$ with respect to $ndx$ where $n$ is a fixed…
A $U$-statistic of a Poisson point process is defined as the sum $\sum f(x_1,\ldots,x_k)$ over all (possibly infinitely many) $k$-tuples of distinct points of the point process. Using the Malliavin calculus, the Wiener-It\^{o} chaos…
The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition…
Real count data time series often show the phenomenon of the underdispersion and overdispersion. In this paper, we develop two extensions of the first-order integer-valued autoregressive process with Poisson innovations, based on binomial…
Feature selection procedures for spatial point processes parametric intensity estimation have been recently developed since more and more applications involve a large number of covariates. In this paper, we investigate the setting where the…
For extreme value estimation we propose to use a model with a Dirichlet process mixture of gamma densities in the center and generalized Pareto densities for the tails. Due to the randomness in the center and a heavy tailed density in the…
In complex systems, events occur at irregular intervals that inherently encode the underlying dynamics of the system. Analyzing the temporal clustering of these events reveals critical insights into the non-random patterns and the temporal…
The scan statistic is widely used in spatial cluster detection applications of inhomogeneous Poisson processes. However, real data may present substantial departure from the underlying Poisson process. One of the possible departures has to…