A homogeneous Poisson process (N(t),t ≥ 0) with the intensity function m(t)=θ is observed on the interval [0,T]. The problem consists in estimating θ with balancing the LINEX loss due to an error of estimation and the cost of sampling which depends linearly on T. The optimal T is given when the prior distribution of θ is not uniquely specified.
We consider semi-Markov control models with Borel state and action spaces, possibly unbounded costs, and holding times with a generalized exponential distribution with unknown mean θ. Assuming that such a distribution does not depend on the state-action pairs, we introduce a Bayesian estimation procedure for θ, which combined with a variant of the vanishing discount factor approach yields average cost optimal policies.
The paper concerns estimation of the rose of directions of a stationary fibre process in from the intersection counts of the process with test planes. A new approach is suggested based on Bayesian statistical techniques. The method is derived from the special case of a Poisson line process however the estimator is shown to be consistent generally. Markov chain Monte Carlo (MCMC) algorithms are used for the approximation of the posterior distribution. Uniform ergodicity of the algorithms used is...