Conjugate priors for exponential-type processes with random initial conditions
The family of proper conjugate priors is characterized in a general exponential model for stochastic processes which may start from a random state and/or time.
Bayes sequential estimation procedures for exponential-type processes
The Bayesian sequential estimation problem for an exponential family of processes is considered. Using a weighted square error loss and observing cost involving a linear function of the process, the Bayes sequential procedures are derived.
On minimax sequential procedures for exponential families of stochastic processes
The problem of finding minimax sequential estimation procedures for stochastic processes is considered. It is assumed that in addition to the loss associated with the error of estimation a cost of observing the process is incurred. A class of minimax sequential procedures is derived explicitly for a one-parameter exponential family of stochastic processes. The minimax sequential procedures are presented in some special models, in particular, for estimating a parameter of exponential families of...
Γ-minimax sequential estimation for Markov-additive processes
The problem of estimating unknown parameters of Markov-additive processes from data observed up to a random stopping time is considered. To the problem of estimation, the intermediate approach between the Bayes and the minimax principle is applied in which it is assumed that a vague prior information on the distribution of the unknown parameters is available. The loss in estimating is assumed to consist of the error of estimation (defined by a weighted squared loss function) as well as a cost of...
Wpływ Profesora Stanisława Trybuły na rozwój teorii estymacji sekwencyjnej dla procesów stochastycznych
W artykule omówiono wkład Stanisława Trybuły w badania dotyczące sekwencyjnej estymacji dla procesów stochastycznych. Dwa jego artykuły, opublikowane w Dissertationes Mathematicae (1968, 1985), miały istotny wpływ na przyszły rozwój tej dziedziny i zainteresowały wielu statystyków matematyków. W artykule pokrótce omawiamy rezultaty uzyskane przez autorów zainspirowanych tymi dwoma fundamentalnymipracami Stanisława Trybuły.Słowa kluczowe: estymacja sekwencyjna, efektywny plan sekwencyjny, proces...
The Bayes choice of an experiment in estimating a success probability
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 -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 -experiment and the size m̃ of the p-experiment such that the Bayes estimator...
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