Related papers: Statistical Depth for Point Process via the Isomet…

Many real objects are modeled as discrete sets of points, such as corners or other salient features. For our main applications in chemistry, points represent atomic centers in a molecule or a solid material. We study the problem of…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

Univariate isotonic regression (IR) has been used for nonparametric estimation in dose-response and dose-finding studies. One undesirable property of IR is the prevalence of piecewise-constant stretches in its estimates, whereas the…

This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise…

We propose a model for multiclass classification of time series to make a prediction as early and as accurate as possible. The matrix sequential probability ratio test (MSPRT) is known to be asymptotically optimal for this setting, but…

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…

In this work, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distributions). Unlike the traditional DL and SC framework, our new…

Recognizing subtle historical patterns is central to modeling and forecasting problems in time series analysis. Here we introduce and develop a new approach to quantify deviations in the underlying hidden generators of observed data…

The study of time-inhomogeneous Markov jump processes is a traditional topic within probability theory that has recently attracted substantial attention in various applications. However, their flexibility also incurs a substantial…

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often…

In this paper, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distributions). Unlike the traditional DL and SC framework, our new…

We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical…

Selecting important spatial-dependent variables under the nonhomogeneous spatial Poisson process model is an important topic of great current interest. In this paper, we use the Deviance Information Criterion (DIC) and Logarithm of the…

Data assimilation is the process of estimating the state of a dynamical system over time by combining model predictions with measurements. This task becomes challenging when the system is nonlinear and high-dimensional. To address this,…

In the literature, a large body of work advocates the use of log-ratio transformation for multivariate statistical analysis of compositional data. In contrast, few studies have looked at how data transformation changes the efficacy of…

For point patterns observed in natura, spatial heterogeneity is more the rule than the exception. In numerous applications, this can be mathematically handled by the flexible class of log Gaussian Cox processes (LGCPs); in brief, a LGCP is…

Building upon the one-step replica symmetry breaking formalism, duly understood and ramified, we show that the sequence of ordered extreme values of a general class of Euclidean-space logarithmically correlated random energy models…

The problem of parameter estimation by i.i.d. observations of an inhomogeneous Poisson process is considered in situation of misspecification. The model is that of a Poissonian signal observed in presence of a homogeneous Poissonian noise.…

This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…

Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…