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

Nikolai I. Chernov, Genadij A. Ososkov, Luc Pronzato (1992)

Applications of Mathematics

Let v 1 , v 2 , . . . , v k be vertices in the X Y Z -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 X Y and Y Z 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 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 bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials

Stéphane Laurent, Catherine Legrand (2012)

ESAIM: Probability and Statistics

In many applications, we assume that two random observations x and yare generated according to independent Poisson distributions ( λ S ) x1d4ab;(λS) and ( μ T ) 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∗

Stéphane Laurent, Catherine Legrand (2012)

ESAIM: Probability and Statistics

In many applications, we assume that two random observations x and y are generated according to independent Poisson distributions ( λ S ) 𝒫(λS) and ( μ T ) 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 comparison of parametric models for mortality graduation. Application to mortality data for the Valencia Region (Spain).

Ana Debón, Francisco Montes, Ramón Sala (2005)

SORT

The parametric graduation of mortality data has as its objective the satisfactory estimation of the death rates based on mortality data but using an age-dependent function whose parameters are adjusted from the crude rates obtainable directly from the data. This paper proposes a revision of the most commonly used parametric models and compares the result obtained with each of them when they are applied to the mortality data for the Valencia Region. As a result of the comparison, we conclude that...

A copula test space model how to avoid the wrong copula choice

Frederik Michiels, Ann De Schepper (2008)

Kybernetika

We introduce and discuss the test space problem as a part of the whole copula fitting process. In particular, we explain how an efficient copula test space can be constructed by taking into account information about the existing dependence, and we present a complete overview of bivariate test spaces for all possible situations. The practical use will be illustrated by means of a numerical application based on an illustrative portfolio containing the S&P 500 Composite Index, the JP Morgan Government...

A Generalized Model of PAC Learning and its Applicability

Thomas Brodag, Steffen Herbold, Stephan Waack (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We combine a new data model, where the random classification is subjected to rather weak restrictions which in turn are based on the Mammen−Tsybakov [E. Mammen and A.B. Tsybakov, Ann. Statis. 27 (1999) 1808–1829; A.B. Tsybakov, Ann. Statis. 32 (2004) 135–166.] small margin conditions, and the statistical query (SQ) model due to Kearns [M.J. Kearns, J. ACM 45 (1998) 983–1006] to what we refer to as PAC + SQ model. We generalize the class conditional constant noise (CCCN) model introduced by Decatur...

A martingale control variate method for option pricing with stochastic volatility

Jean-Pierre Fouque, Chuan-Hsiang Han (2007)

ESAIM: Probability and Statistics

A generic control variate method is proposed to price options under stochastic volatility models by Monte Carlo simulations. This method provides a constructive way to select control variates which are martingales in order to reduce the variance of unbiased option price estimators. We apply a singular and regular perturbation analysis to characterize the variance reduced by martingale control variates. This variance analysis is done in the regime where time scales of associated driving volatility...

A method constructing density functions: the case of a generalized Rayleigh variable

Viorel Gh. Vodă (2009)

Applications of Mathematics

In this paper we propose a new generalized Rayleigh distribution different from that introduced in Apl. Mat. 47 (1976), pp. 395–412. The construction makes use of the so-called “conservability approach” (see Kybernetika 25 (1989), pp. 209–215) namely, if X is a positive continuous random variable with a finite mean-value E ( X ) , then a new density is set to be f 1 ( x ) = x f ( x ) / E ( X ) , where f ( x ) is the probability density function of X . The new generalized Rayleigh variable is obtained using a generalized form of the exponential...

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