Related papers: Estimation of the Parameters of Multivariate Stabl…
Uncertainty quantification (UQ) includes the characterization, integration, and propagation of uncertainties that result from stochastic variations and a lack of knowledge or data in the natural world. Monte Carlo (MC) method is a…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
Multifidelity Monte Carlo methods rely on a hierarchy of possibly less accurate but statistically correlated simplified or reduced models, in order to accelerate the estimation of statistics of high-fidelity models without compromising the…
Analysis of a probabilistic system often requires to learn the joint probability distribution of its random variables. The computation of the exact distribution is usually an exhaustive precise analysis on all executions of the system. To…
We propose an algorithm for evaluation of the cumulative bivariate normal distribution, building upon Marsaglia's ideas for evaluation of the cumulative univariate normal distribution. The algorithm is mathematically transparent, delivers…
We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…
This article describes two Monte Carlo methods for calculating confidence intervals on cumulative density function (CDF) based multivariate normal quantiles that allows for controlling the tail regions of a multivariate distribution where…
In this paper, we discuss computational aspects to obtain accurate inferences for the parameters of the generalized gamma (GG) distribution. Usually, the solution of the maximum likelihood estimators (MLE) for the GG distribution have no…
This paper proposes an efficient method for the simultaneous estimation of the state of a quantum system and the classical parameters that govern its evolution. This hybrid approach benefits from efficient numerical methods for the…
We devise a Monte Carlo based method for detecting whether a non-negative Markov chain is stable for a given set of parameter values. More precisely, for a given subset of the parameter space, we develop an algorithm that is capable of…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…
In this paper we introduce a new class of multivariate unimodal distributions, motivated by Khintchine's representation. We start by proposing a univariate model, whose support covers all the unimodal distributions on the real line. The…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
We provide a simple method to estimate the parameters of multivariate stochastic volatility models with latent factor structures. These models are very useful as they alleviate the standard curse of dimensionality, allowing the number of…
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…
Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…
We propose an unbiased Monte-Carlo estimator for $\mathbb{E}[g(X_{t_1}, \cdots, X_{t_n})]$, where $X$ is a diffusion process defined by a multi-dimensional stochastic differential equation (SDE). The main idea is to start instead from a…
In this paper we study the problem of statistical inference on the parameters of the semiparametric variance-mean mixtures. This class of mixtures has recently become rather popular in statistical and financial modelling. We design a…