相关论文: Estimating limits from Poisson counting data using…

In pattern recognition, handling uncertainty is a critical challenge that significantly affects decision-making and classification accuracy. Dempster-Shafer Theory (DST) is an effective reasoning framework for addressing uncertainty, and…

Evidential reasoning in expert systems has often used ad-hoc uncertainty calculi. Although it is generally accepted that probability theory provides a firm theoretical foundation, researchers have found some problems with its use as a…

Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…

Define the scaled empirical point process on an independent and identically distributed sequence $\{Y_i: i\le n\}$ as the random point measure with masses at $a_n^{-1} Y_i$. For suitable $a_n$ we obtain the weak limit of these point…

In this paper, we generalize the basic notions and results of Dempster-Shafer theory from predicates to formal concepts. Results include the representation of conceptual belief functions as inner measures of suitable probability functions,…

Inference in semi-supervised (SS) settings has gained substantial attention in recent years due to increased relevance in modern big-data problems. In a typical SS setting, there is a much larger-sized unlabeled data, containing only…

Dempster-Shafer Theory (DST) provides a powerful framework for modeling uncertainty and has been widely applied to multi-attribute classification tasks. However, traditional DST-based attribute fusion-based classifiers suffer from…

We develop dependent hierarchical normalized random measures and apply them to dynamic topic modeling. The dependency arises via superposition, subsampling and point transition on the underlying Poisson processes of these measures. The…

Count data appears in various disciplines. In this work, a new method to analyze time series count data has been proposed. The method assumes exponentially decaying covariance structure, a special class of the Mat\'ern covariance function,…

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…

We introduce a new dynamical system for sequentially observed multivariate count data. This model is based on the gamma--Poisson construction---a natural choice for count data---and relies on a novel Bayesian nonparametric prior that ties…

In this paper we use a Malliavin-Stein type method to investigate Poisson and normal approximations for the measurable functions of infinitely many independent random variables. We combine Stein's method with the difference operators in…

In reinsurance, Poisson and Negative binomial distributions are employed for modeling frequency. However, the incomplete data regarding reported incurred claims above a priority level presents challenges in estimation. This paper focuses on…

By exploiting the well-known observation that size-biasing or zero-biasing an infinitely divisible random variable may be achieved by adding an independent increment, combined with tools from Stein's method for compound Poisson and Gaussian…

This work applies modern AI tools (transformers) to solving one of the oldest statistical problems: Poisson means under empirical Bayes (Poisson-EB) setting. In Poisson-EB a high-dimensional mean vector $\theta$ (with iid coordinates…

In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived…

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…

We develop a classification method for incoming pieces of evidence in Dempster-Shafer theory. This methodology is based on previous work with clustering and specification of originally nonspecific evidence. This methodology is here put in…

We present a framework for the theoretical analysis of ensembles of low-complexity empirical risk minimisers trained on independent random compressions of high-dimensional data. First we introduce a general distribution-dependent…

In this paper we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms…