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In recent years dynamical systems (of deterministic and stochastic nature), describing many models in mathematics, physics, engineering and finances, become more and more complex. Numerical analysis narrowed only to deterministic algorithms…
In this paper we analyze the probability of consistency of sensor data distribution systems (SDDS), and determine suitable evaluation models. This problem is typically difficult, since a reliable model taking into account all parameters and…
Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a…
Computer system simulation studies routinely rely on executing a limited number of short application regions, since full end-to-end simulation is prohibitively time-consuming. To preserve representativeness, existing methods employ either…
Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a…
We develop a new algorithm for the estimation of rare event probabilities associated with the steady-state of a Markov stochastic process with continuous state space $\mathbb R^d$ and discrete time steps (i.e. a discrete-time $\mathbb…
Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex probability distributions. The pseudo-marginal MCMC framework only requires an unbiased estimator of the unnormalized probability distribution function to construct…
In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…
When the target parameter for inference is a real-valued, continuous function of probabilities in the $k$-sample multinomial problem, variance estimation may be challenging. In small samples or when the function is nondifferentiable at the…
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.…
This paper poses a theoretical characterization of the stochastic reachability problem in terms of probability measures, capturing the probability measure of the state of the system that satisfies the reachability specification for all…
The Dynamic Monte Carlo (DMC) method is an established molecular simulation technique for the analysis of the dynamics in colloidal suspensions. An excellent alternative to Brownian Dynamics or Molecular Dynamics simulation, DMC is…
Subtask distillation is an emerging paradigm in which compact, specialized models are extracted from large, general-purpose 'foundation models' for deployment in environments with limited resources or in standalone computer systems.…
The logistic specification has been used extensively in non-Bayesian statistics to model the dependence of discrete outcomes on the values of specified covariates. Because the likelihood function is globally weakly concave estimation by…
Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the…
This paper proposes a multi-stage projection-based Lasso procedure for the semiparametric sample selection model in high-dimensional settings under a weak nonparametric restriction on the selection correction. In particular, the number of…
The safety concern for unmanned systems, namely the concern for the potential casualty caused by system abnormalities, has been a bottleneck for their development, especially in populated areas. Evidently, the collision between the unmanned…
The general synthetic iterative scheme (GSIS) has proven its efficacy in modeling rarefied gas dynamics, where the steady-state solutions are obtained after dozens of iterations of the Boltzmann equation, with minimal numerical dissipation…
We apply the sample average approximation (SAA) method to risk-neutral optimization problems governed by nonlinear partial differential equations (PDEs) with random inputs. We analyze the consistency of the SAA optimal values and SAA…
We propose approaches for testing implementations of Markov Chain Monte Carlo methods as well as of general Monte Carlo methods. Based on statistical hypothesis tests, these approaches can be used in a unit testing framework to, for…