In this paper, based on a left censored data from the twoparameter Pareto distribution, maximum likelihood and Bayes estimators for the two unknown parameters are obtained. The problem of reconstruction of the past failure times, either point or interval, in the left-censored set-up, is also considered from Bayesian and non-Bayesian approaches. Two numerical examples and a Monte Carlo simulatio...

We present a new Monte Carlo method which couples Path Integral for finite temperature protons with Quantum Monte Carlo for ground state electrons, and we apply it to metallic hydrogen for pressures beyond molecular dissociation. This method fills the gap between high temperature electron-proton Path Integral and ground state Diffusion Monte Carlo methods. Our data exhibit more structure and hi...

In this paper, we propose a method for estimating an sdimensional integral I. We define a new hybrid sequence that we call the H-mixed sequence. We obtain a probabilistic bound for the H-discrepancy of this sequence. We define a new estimator for a multidimensional integral using the H-mixed sequence. We prove a central limit theorem for this estimator. We show that by using our estimator, we o...

One of the main problems in computer graphics is to solve the global illumination problem, which is given by a Fredholm integral equation of the second kind, called the radiance equation (REQ). In order to achieve realistic images, a very complex kernel of the integral equation, modelling all physical effects of light, must be considered. Due to this complexity Monte Carlo methods seem to be an...

introduction : due to the importance of laser light penetration and propagation in biological tissues, many researchers have proposed several numerical methods such as monte carlo, finite element and green function methods. among them, the monte carlo method is an accurate method which can be applied for different tissues. however, because of its statistical nature, monte carlo simulation requi...

Introduction: The main goal of SPECT imaging is to determine activity distribution inside the organs of the body. However, due to photon attenuation, it is almost impossible to do a quantitative study. In this paper, we suggest a mathematical relationship between activity distribution and its corresponding projections using a transfer matrix. Monte Carlo simulation was used to find a precise tr...

First, the normalizing denominator in the Bayes’s Rule often has a form of integral which is typically intractable. Second, we often want an estimate of the posterior, for example the mean, the standard deviation, etc. And this estimation can be reduced to calculating integrals of the form. Monte Carlo methods can be applied to this integral computation g(θ)f(θ)λ(dθ) with high-dimensional param...