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We apply Markov Chain Monte Carlo (MCMC) to the problem of parametric galaxy modeling, estimating posterior distributions of galaxy properties such as ellipticity and brightness for more than 100,000 images of galaxies taken from DC2, a…
The class of $\alpha$-stable distributions enjoys multiple practical applications in signal processing, finance, biology and other areas because it allows to describe interesting and complex data patterns, such as asymmetry or heavy tails,…
We describe a novel approach to accelerating Monte Carlo Markov Chains. Our focus is cosmological parameter estimation, but the algorithm is applicable to any problem for which the likelihood surface is a smooth function of the free…
The utility of a Markov chain Monte Carlo algorithm is, in large part, determined by the size of the spectral gap of the corresponding Markov operator. However, calculating (and even approximating) the spectral gaps of practical Monte Carlo…
Let $\mathscr{P}(E)$ be the space of probability measures on a measurable space $(E,\mathcal{E})$. In this paper we introduce a class of nonlinear Markov chain Monte Carlo (MCMC) methods for simulating from a probability measure…
In this paper we build on previous work which uses inferences techniques, in particular Markov Chain Monte Carlo (MCMC) methods, to solve parameterized control problems. We propose a number of modifications in order to make this approach…
This article is a tutorial on Markov chain Monte Carlo simulations and their statistical analysis. The theoretical concepts are illustrated through many numerical assignments from the author's book on the subject. Computer code (in Fortran)…
Parametric Markov chains occur quite naturally in various applications: they can be used for a conservative analysis of probabilistic systems (no matter how the parameter is chosen, the system works to specification); they can be used to…
Estimating errors is a crucial part of any scientific analysis. Whenever a parameter is estimated (model-based or not), an error estimate is necessary. Any parameter estimate that is given without an error estimate is meaningless.…
Testing between hypotheses, when independent sampling is possible, is a well developed subject. In this paper, we propose hypothesis tests that are applicable when the samples are obtained using Markov chain Monte Carlo. These tests are…
The trace of a matrix function f(A), most notably of the matrix inverse, can be estimated stochastically using samples< x,f(A)x> if the components of the random vectors x obey an appropriate probability distribution. However such a…
Recently, global pulsar timing arrays have released results from searching for a nano-Hertz gravitational wave background signal. Although there has not been any definite evidence of the presence of such a signal in residuals of pulsar…
Estimating Monte Carlo error is critical to valid simulation results in Markov chain Monte Carlo (MCMC) and initial sequence estimators were one of the first methods introduced for this. Over the last few years, focus has been on…
Stellar oscillations can provide a wealth of information about a star, which can be extracted from observed time series of the star's brightness or radial velocity. In this paper we address the question of how to extract as much information…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC…
In this paper we study statistical methods of parameters estimation of the site percolation model. Advantages of the proposed method is demonstrated for the computing of the confidence interval of mass fractal dimension of a percolation…
This article was motivated by the desire to improve Markov chain Monte Carlo methods for spatial survival models in which the locations of individuals in space are known. For a dataset comprising information on n individuals, standard…
This paper addresses the key challenge of estimating the asymptotic covariance associated with the Markov chain central limit theorem, which is essential for visualizing and terminating Markov Chain Monte Carlo (MCMC) simulations. We focus…