Bayesian inference is applied to the level fluctuations of two coupled microwave billiards in order to extract the coupling strength. The coupled resonators provide a model of a chaotic quantum system containing two coupled symmetry classes of levels. The number variance is used to quantify the level fluctuations as a function of the coupling and to construct the conditional probability distrib...

In this paper, we develop a method for playing variants of spatial games like chess or checkers, where the state of the opponent is only partially observable. Each side has a number of hidden pieces invisible to opposition. An estimate of the opponent state probability distribution is made assuming moves are made to maximize the entropy of subsequent state distribution or belief. The belief sta...

Morphological features are used to estimate the state of a random pattern (set) governed by a multivariate probability distribution. The feature vector is composed of granulometric moments and pattern estimation involves feature-based estimation of the parameter vector governing the random set. Under such circumstances, the joint density of the features and parameters is a generalized function ...

：A new distribution called the exponentiated Burr XII Weibull(EBW) distributions is proposed and presented. This contains several known such as log-logistic Weibull, Rayleigh, exponential, Lomax Exponential, Rayleigh exponential special cases. A comprehensive investigation of properties this generalized including series expansion probability density function cumulative function, hazard reverse ...

We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the ‘0 − 1’ loss function and a constant cost of observation per unit of time for general prior distributions. The statistical problem is reformulated as an optimal stopping problem with the current conditional probability that the drift is non-negative as the und...

We present a deep neural network for a model-free prediction of a chaotic dynamical system from noisy observations. The proposed deep learning model aims to predict the conditional probability distribution of a state variable. The Long Short-Term Memory network (LSTM) is employed to model the nonlinear dynamics and a softmax layer is used to approximate a probability distribution. The LSTM mode...

For the first time, we formulate a flexible density function from the selection mechanism viewpoint (see, for example, Bayarri & DeGroot (1992) and ArellanoValle et al. (2006)) which possesses nice biological and physical interpretations. The new density function contains as special cases many models that have been proposed recently in the literature. In our model, we assume that the number of ...