A new multipolynomial approximations algorithm the MPA algorithm is proposed for estimating the state vector θ of virtually any dynamical evolutionary system. The input of the algorithm consists of discrete-time observations Y . An adjustment of the algorithm is required to the generation of arrays of random sequences of state vectors and observations scalars corresponding to a given sequence o...

Summary We consider the problem of empirical Bayes estimation multiple variances when provided with sample variances. Assuming an arbitrary prior on variances, we derive different versions estimators using loss functions. For one particular function, resulting estimator relies marginal cumulative distribution function only. When replacing it obtain version called $F$-modelling-based provide the...

Of those things that can be estimated well in an inverse problem, which is best to estimate? Backus–Gilbert resolution theory answers a version of this question for linear (or linearized) inverse problems in Hilbert spaces with additive zero-mean errors with known, finite covariance, and no constraints on the unknown other than the data. This paper generalizes resolution: it defines the resolut...

Abstract In this paper, the estimation of R=Pr(Y < Y), when X and Y are two generalized inverted exponential distributions with different parameters is considered. The maximum likelihood estimator (MLE) of R and its asymptotic distribution are obtained. Exact and asymptotic confidence intervals of R are constructed using both exact and asymptotic distributions. Assuming that the common scale pa...

In this paper, we consider the maximum likelihood (ML) and Bayes estimation of the parameters of the generalized exponential distribution based on progressive first failure censored samples. We also consider the problem of predicting an independent future order statistics from the same distribution. However, since Bayes estimator do not exist in an explicit form for the parameters, Markov Chain...

In this paper we introduce a natural image prior that directly represents a Gaussiansmoothed version of the natural image distribution. We include our prior in a formulation of image restoration as a Bayes estimator that also allows us to solve noise-blind image restoration problems. We show that the gradient of our prior corresponds to the mean-shift vector on the natural image distribution. I...