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Bayesian analysis often concerns an evaluation of models with different dimensionality as is necessary in, for example, model selection or mixture models. To facilitate this evaluation, transdimensional Markov chain Monte Carlo (MCMC)…
Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In…
Particle Markov Chain Monte Carlo methods are used to carry out inference in non-linear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform…
Propagation of charged cosmic-rays in the Galaxy depends on the transport parameters, whose number can be large depending on the propagation model under scrutiny. A standard approach for determining these parameters is a manual scan,…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
In these lectures I cover a number of topics in cosmological data analysis. I concentrate on general techniques which are common in cosmology, or techniques which have been developed in a cosmological context. In fact they have very general…
We present a Bayesian approach to the problem of determining parameters for coalescing binary systems observed with laser interferometric detectors. By applying a Markov Chain Monte Carlo (MCMC) algorithm, specifically the Gibbs sampler, we…
Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…
To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. The reasoning is sound: a reduction in variance due to…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data.…
In this paper we present computational experiments with the Markov Chain Monte Carlo Matrix Inversion ($(\text{MC})^2\text{MI}$) on several accelerator architectures and investigate their impact on performance and scalability of the method.…
We made a comparative analysis of numerical methods for multidimensional optimization. The main parameter is a number of computations of the test function to reach necessary accuracy, as it is computationally "slow". For complex functions,…
Markov chain Monte Carlo (MCMC) is a sampling-based method for estimating features of probability distributions. MCMC methods produce a serially correlated, yet representative, sample from the desired distribution. As such it can be…
Monte Carlo evaluation is used to calculate heavy-ion elastic scattering including the center-of-mass correction and the Coulomb interaction.Angular distributions are presented for a number of nuclear pairs over a wide energy range using…
This paper investigates methods for estimating the optimal stochastic control policy for a Markov Decision Process with unknown transition dynamics and an unknown reward function. This form of model-free reinforcement learning comprises…
Markov chain Monte Carlo (MCMC) is a simulation method commonly used for estimating expectations with respect to a given distribution. We consider estimating the covariance matrix of the asymptotic multivariate normal distribution of a…
Owing to the remarkable photometric precision of space observatories like Kepler, stellar and planetary systems beyond our own are now being characterized en masse for the first time. These characterizations are pivotal for endeavors such…