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A Bayesian estimate of the risk of tick-borne diseases

Marek Jiruše, Josef Machek, Viktor Beneš, Petr Zeman (2004)

Applications of Mathematics

The paper considers the problem of estimating the risk of a tick-borne disease in a given region. A large set of epidemiological data is evaluated, including the point pattern of collected cases, the population map and covariates, i.e. explanatory variables of geographical nature, obtained from GIS. The methodology covers the choice of those covariates which influence the risk of infection most. Generalized linear models are used and AIC criterion yields the decision. Further, an empirical Bayesian...

A comparison of automatic histogram constructions

Laurie Davies, Ursula Gather, Dan Nordman, Henrike Weinert (2009)

ESAIM: Probability and Statistics

Even for a well-trained statistician the construction of a histogram for a given real-valued data set is a difficult problem. It is even more difficult to construct a fully automatic procedure which specifies the number and widths of the bins in a satisfactory manner for a wide range of data sets. In this paper we compare several histogram construction procedures by means of a simulation study. The study includes plug-in methods, cross-validation, penalized maximum likelihood and the taut string...

A note on almost sure convergence and convergence in measure

P. Kříž, Josef Štěpán (2014)

Commentationes Mathematicae Universitatis Carolinae

The present article studies the conditions under which the almost everywhere convergence and the convergence in measure coincide. An application in the statistical estimation theory is outlined as well.

A note on an open problem in the foundations of statistics.

Alejandro García del Amo, David Ríos Insua (2002)

RACSAM

Estudiamos un problema abierto en los fundamentos de la estadística, el de modelizar imprecisión en preferencias y creencias dentro del marco de la utilidad esperada. Este problema fundamenta el análisis de sensibilidad en estadística bayesiana. Proporcionamos una solución en términos de utilidades esperadas dependientes del estado.

A procedure for ε-comparison of means of two normal distributions

Stanisław Jaworski, Wojciech Zieliński (2004)

Applicationes Mathematicae

For two normal distributions N(μ₁,σ²) and N(μ₂,σ²) the problem is to decide whether |μ₁-μ₂|≤ ε for a given ε. Two decision rules are given: maximin and bayesian for σ² known and unknown.

A repeated imitation model with dependence between stages: Decision strategies and rewards

Pablo J. Villacorta, David A. Pelta (2015)

International Journal of Applied Mathematics and Computer Science

Adversarial decision making is aimed at determining strategies to anticipate the behavior of an opponent trying to learn from our actions. One defense is to make decisions intended to confuse the opponent, although our rewards can be diminished. This idea has already been captured in an adversarial model introduced in a previous work, in which two agents separately issue responses to an unknown sequence of external inputs. Each agent's reward depends on the current input and the responses of both...

A review of the results on the Stein approach for estimators improvement.

Vassiliy G. Voinov, Mikhail S. Nikulin (1995)

Qüestiió

Since 1956, a large number of papers have been devoted to Stein's technique of obtaining improved estimators of parameters, for several statistical models. We give a brief review of these papers, emphasizing those aspects which are interesting from the point of view of the theory of unbiased estimation.

A sufficient condition for admissibility in linear estimation

Czesław Stępniak (1988)

Aplikace matematiky

It was recently shown that all estimators which are locally best in the relative interior of the parameter set, together with their limits constitute a complete class in linear estimation, both unbiased and biased. However, not all these limits are admissible. A sufficient condition for admissibility of a limit was given by the author (1986) for the case of unbiased estimation in a linear model with the natural parameter space. This paper extends this result to the general linear model and to biased...

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