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### 3-dimensional multivertex reconstruction from 2-dimensional tracks observations using likelihood inference

Applications of Mathematics

Let ${v}_{1},{v}_{2},...,{v}_{k}$ be vertices in the $XYZ$-space, each vertex producing several tracks (straight lines) emanating from it within a narrow cone with a small angle about a fixed direction ($Z$-axis). Each track is detected (by drift chambers or other detectors) by its projections on $XY$ and $YZ$ views independently with small errors. An automated method is suggested for the reconstruction of vertices from noisy observations of the tracks projections. The procedure is based on the likelihood inference for mixtures. An illustrative...

### A Bayesian approach to cluster analysis.

Qüestiió

A general probabilistic model for describing the structure of statistical problems known under the generic name of cluster analysis, based on finite mixtures of distributions, is proposed. We analyse the theoretical and practical implications of this approach, and point out some open question on both the theoretical problem of determining the reference prior for models based on mixtures, and the practical problem of approximation that mixtures typically entail. Finally, models based on mixtures...

### A bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials

ESAIM: Probability and Statistics

In many applications, we assume that two random observations x and yare generated according to independent Poisson distributions $\left(\lambda S\right)$x1d4ab;(λS) and $\left(\mu T\right)$x1d4ab;(μT) and we are interested in performing statistical inference on the ratio φ = λ / μ of the two incidence rates. In vaccine efficacy trials, x and y are typically the numbers of cases in the vaccine and the control groups respectively, φ is called the relative risk and the statistical model is called ‘partial immunity model’. In this paper we...

### A Bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials∗

ESAIM: Probability and Statistics

In many applications, we assume that two random observations x and y are generated according to independent Poisson distributions $\left(\lambda S\right)$𝒫(λS) and $\left(\mu T\right)$𝒫(μT) and we are interested in performing statistical inference on the ratio φ = λ / μ of the two incidence rates. In vaccine efficacy trials, x and y are typically the numbers of cases in the vaccine and the control groups respectively, φ is called the relative risk...

### A Bayesian look at nuisance parameters.

Trabajos de Estadística e Investigación Operativa

The elimination of nuisance parameters has classically been tackled by various ad hoc devices, and has led to a number of attemps to define partial sufficiency and ancillarity. The Bayesian approach is clearly defined. This paper examines some classical procedures in order to see when they can be given a Bayesian justification.

### A Bayesian model for binary Markov chains.

International Journal of Mathematics and Mathematical Sciences

### A Bayesian significance test of change for correlated observations

Discussiones Mathematicae Probability and Statistics

This paper presents a Bayesian significance test for a change in mean when observations are not independent. Using a noninformative prior, a unconditional test based on the highest posterior density credible set is determined. From a Gibbs sampler simulation study the effect of correlation on the performance of the Bayesian significance test derived under the assumption of no correlation is examined. This paper is a generalization of earlier studies by KIM (1991) to not independent observations.

### A bias-robust estimate of the scale parameter of the exponential distribution under violation of the hazard function

Applicationes Mathematicae

### A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics

ESAIM: Probability and Statistics

We derive a central limit theorem for triangular arrays of possibly nonstationary random variables satisfying a condition of weak dependence in the sense of Doukhan and Louhichi [Stoch. Proc. Appl. 84 (1999) 313–342]. The proof uses a new variant of the Lindeberg method: the behavior of the partial sums is compared to that of partial sums of dependent Gaussian random variables. We also discuss a few applications in statistics which show that our central limit theorem is tailor-made for statistics...

### A choice of criterion parameters in a linearization of regression models.

Acta Mathematica Universitatis Comenianae. New Series

Kybernetika

### A collector for information without probability in a fuzzy setting

Kybernetika

In the fuzzy setting, we define a collector of fuzzy information without probability, which allows us to consider the reliability of the observers. This problem is transformed in a system of functional equations. We give the general solution of that system for collectors which are compatible with composition law of the kind “inf”.

### A comparative study of small area estimators.

SORT

It is known that direct-survey estimators of small area parameters, calculated with the data from the given small area, often present large mean squared errors because of small sample sizes in the small areas. Model-based estimators borrow strength from other related areas to avoid this problem. How small should domain sample sizes be to recommend the use of model-based estimators? How robust are small area estimators with respect to the rate sample size/number of domains?To give answers or recommendations...

### A comparison of linearization and quadratization domains

Applications of Mathematics

In a nonlinear model, the linearization and quadratization domains are considered. In the case of a locally quadratic model, explicit expressions for these domains are given and the domains are compared.

Kybernetika

### A composite Exponential-Pareto distribution.

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

Metrika

### A cooperative sensor network : optimal deployment and functioning

RAIRO - Operations Research - Recherche Opérationnelle

A network of mobile cooperative sensors is considered. The following problems are studied: (1) the “optimal“deployment of the sensors on a given territory; (2) the detection of local anomalies in the noisy data measured by the sensors. In absence of an information fusion center in the network, from “local” interactions between sensors “global“solutions of these problems are found.

### A Cooperative Sensor Network: Optimal Deployment and Functioning

RAIRO - Operations Research

A network of mobile cooperative sensors is considered. The following problems are studied: (1) the “optimal" deployment of the sensors on a given territory; (2) the detection of local anomalies in the noisy data measured by the sensors. In absence of an information fusion center in the network, from “local" interactions between sensors “global" solutions of these problems are found.