Related papers: Impact probability computation of Near-Earth Objec…
Importance sampling is a popular variance reduction method for Monte Carlo estimation, where a notorious question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically…
Shock-physics numerical codes are essential tools for describing the short but extreme fragmentation stage of the hypervelocity impact process on asteroids. However, accurately representing complex interior structures, surfaces, and contact…
We consider conditional tests for non-negative discrete exponential families. We develop two Markov Chain Monte Carlo (MCMC) algorithms which allow us to sample from the conditional space and to perform approximated tests. The first…
The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This…
Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic…
In this paper, we consider a Monte Carlo simulation method (MinMC) that approximates prices and risk measures for a range $\Gamma$ of model parameters at once. The simulation method that we study has recently gained popularity [HS20, FPP22,…
Markov Chain Monte Carlo (MCMC) methods are employed to sample from a given distribution of interest, whenever either the distribution does not exist in closed form, or, if it does, no efficient method to simulate an independent sample from…
A new method, based on the simulated annealing algorithm and aimed at the inverse problem in the analysis of intergalactic (interstellar) complex spectra of hydrogen and metal lines, is presented. We consider the process of line formation…
Uncertainty analysis in the outcomes of model predictions is a key element in decision-based material design to establish confidence in the models and evaluate the fidelity of models. Uncertainty Propagation (UP) is a technique to determine…
Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…
In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the…
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,…
In order to find the equilibrium geometries of molecules and solids and to perform ab initio molecular dynamics, it is necessary to calculate the forces on the nuclei. We present a correlated sampling method to efficiently calculate…
If the conclusion of a data analysis is sensitive to dropping very few data points, that conclusion might hinge on the particular data at hand rather than representing a more broadly applicable truth. How could we check whether this…
We present a new method for conducting Monte Carlo inference in graphical models which combines explicit search with generalized importance sampling. The idea is to reduce the variance of importance sampling by searching for significant…
Monte Carlo radiative transfer (MCRT) simulations are a powerful tool for determining the appearance of astrophysical objects, analyzing the prevalent physical conditions within them, and inferring their properties on the basis of real…
Markov-chain Monte Carlo sampling has become a standard technique for exploring the posterior distribution of cosmological parameters constrained by observations of CMB anisotropies. Given an infinite amount of time, any MCMC sampler will…
The detection of anisotropies with respect to a given direction in a vector field is a common problem in astronomy. Several methods have been proposed that rely on the distribution of the acute angles between the data and a reference…
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…
A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…