In ‘inverse problems’ data from indirect measurements are used to estimate unknown parameters of physical systems. Uncertain data, (possibly vague) prior information on model parameters, and a physical theory relating the model parameters to the observations are the fundamental elements of any inverse problem. Using concepts from probability theory, a consistent formulation of inverse problems ...

Although knowing the time of the occurrence of the earthquakes is vital and helpful, unfortunately it is still unpredictable. By the way there is an urgent need to find a method to foresee this catastrophic event. There are a lot of methods for forecasting the time of earthquake occurrence. Another method for predicting that is to know probability density function of time interval between earth...

Conditional probability density functional theory (CP-DFT) determines the ground-state energy of a many-electron system by finding conditional from parallelizable series Kohn-Sham DFT calculations. By directly calculating densities, authors bypass need for an approximate exchange-correlation (XC) functional. CP-DFT is formally exact, but potentials are used in practice. We explore suitable appr...

Fusing probabilistic information is a fundamental task in signal and data processing with relevance to many fields of technology science. In this work, we investigate the fusion multiple probability density functions (pdfs) continuous random variable or vector. Although case variables problem pdf frequently arise multisensor processing, statistical inference, machine learning, universally accep...

2.1 The Main Theorem We first start with the simplest case where A and B are both subsets of the real line R. Let x ∈ A. The number pA(x) means that, in the infinitesimal interval [x, x+ δx), there exists pA(x)δx amount of “probability mass.” Here, δx is a “differential quantity” such that (δx) = 0. Assume that f is continuous and infinitely differentiable. The function f sends the interval [x,...

We report experimental results on the acceleration component probability distribution function at R λ = 690 to probabilities of less than 10 −7. This is an improvement of more than an order of magnitude over past measurements and allows us to conclude that the fourth moment converges and the flatness is approximately 55. We compare our probability distribution to those predicted by several mode...