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Scaling of model approximation errors and expected entropy distances

Guido F. Montúfar, Johannes Rauh (2014)

Kybernetika

We compute the expected value of the Kullback-Leibler divergence of various fundamental statistical models with respect to Dirichlet priors. For the uniform prior, the expected divergence of any model containing the uniform distribution is bounded by a constant 1 - γ . For the models that we consider this bound is approached as the cardinality of the sample space tends to infinity, if the model dimension remains relatively small. For Dirichlet priors with reasonable concentration parameters the expected...

Sequential estimation of survival functions with a neutral to the right process prior

Domingo Morales, Leandro Pardo, Vicente Quesada (1994)

Applications of Mathematics

In this work, a parametric sequential estimation method of survival functions is proposed in the Bayesian nonparametric context when neutral to the right processes are used. It is proved that the mentioned method is an 1-SLA rule when Dirichlet processes are used; furthermore, asymptotically pointwise optimal procedures are obtained. Finally, an example is given.

Stable-1/2 bridges and insurance

Edward Hoyle, Lane P. Hughston, Andrea Macrina (2015)

Banach Center Publications

We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an information-based approach to the reserving problem, we derive the process of the conditional distribution of the ultimate loss. The "best-estimate ultimate loss process" is given by the conditional expectation of the ultimate loss. We derive explicit expressions for the...

Statistical analysis of periodic autoregression

Jiří Anděl (1983)

Aplikace matematiky

Methods for estimating parameters and testing hypotheses in a periodic autoregression are investigated in the paper. The parameters of the model are supposed to be random variables with a vague prior density. The innovation process can have either constant or periodically changing variances. Theoretical results are demonstrated on two simulated series and on two sets of real data.

Stochastic algorithm for Bayesian mixture effect template estimation

Stéphanie Allassonnière, Estelle Kuhn (2010)

ESAIM: Probability and Statistics

The estimation of probabilistic deformable template models in computer vision or of probabilistic atlases in Computational Anatomy are core issues in both fields. A first coherent statistical framework where the geometrical variability is modelled as a hidden random variable has been given by [S. Allassonnière et al., J. Roy. Stat. Soc.69 (2007) 3–29]. They introduce a Bayesian approach and mixture of them to estimate deformable template models. A consistent stochastic algorithm has been introduced...

The Bayes choice of an experiment in estimating a success probability

Alicja Jokiel-Rokita, Ryszard Magiera (2002)

Applicationes Mathematicae

A Bayesian method of estimation of a success probability p is considered in the case when two experiments are available: individual Bernoulli (p) trials-the p-experiment-or products of r individual Bernoulli (p) trials-the p r -experiment. This problem has its roots in reliability, where one can test either single components or a system of r identical components. One of the problems considered is to find the degree r̃ of the p r ̃ -experiment and the size m̃ of the p-experiment such that the Bayes estimator...

The Bayes sequential estimation of a normal mean from delayed observations

Alicja Jokiel-Rokita (2006)

Applicationes Mathematicae

The problem of estimating the mean of a normal distribution is considered in the special case when the data arrive at random times. Certain classes of Bayes sequential estimation procedures are derived under LINEX and reflected normal loss function and with the observation cost determined by a function of the stopping time and the number of observations up to this time.

The Bayesian approach to the combination of forecasts: some extensions into a skewed environment.

Gerrit K. Janssens (1987)

Trabajos de Estadística

Where a decision-maker has to rely on expert opinions a need for a normative model to combine these forecasts appears. This can be done using Bayes' formula and by making some assumptions on the prior distribution and the distribution of the expert assessments. We extend the case to skewed distributions of these assessments. By using an Edgeworth expansion of the density function including the skewness parameter, we are able to obtain the formula to combine the forecasts in a Bayesian way.

The importance of being the upper bound in the bivariate family.

Carles M. Cuadras (2006)

SORT

Any bivariate cdf is bounded by the Fréchet-Hoeffding lower and upper bounds. We illustrate the importance of the upper bound in several ways. Any bivariate distribution can be written in terms of this bound, which is implicit in logit analysis and the Lorenz curve, and can be used in goodness-of-fit assesment. Any random variable can be expanded in terms of some functions related to this bound. The Bayes approach in comparing two proportions can be presented as the problem of choosing a parametric...

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