Related papers: Distribution Estimation for Probabilistic Loops
In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential…
We present two Monte Carlo sampling algorithms for probabilistic inference that guarantee polynomial-time convergence for a larger class of network than current sampling algorithms provide. These new methods are variants of the known…
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…
We examine the extent to which random samplings from the values of a random set, determine the distribution of the random set itself. We also comment on how, given the statistics of the sampling, to detect the distribution. Several methods…
The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the…
We present a new Monte Carlo methodology for the accurate estimation of the distribution of the sum of dependent log-normal random variables. The methodology delivers statistically unbiased estimators for three distributional quantities of…
The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…
We develop a method to approximate the moments of a discrete-time stochastic polynomial system. Our method is built upon Carleman linearization with truncation. Specifically, we take a stochastic polynomial system with finitely many states…
We propose a fast algorithm for evaluating the moments of Bingham distribution. The calculation is done by piecewise rational approximation, where interpolation and Gaussian integrals are utilized. Numerical test shows that the algorithm…
Distributed systems have been widely used in practice to accomplish data analysis tasks of huge scales. In this work, we target on the estimation problem of generalized linear models on a distributed system with nonrandomly distributed…
We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an…
In this paper, we introduce a new distribution generated by Lindley random variable which offers a more flexible model for modelling lifetime data. Various statistical properties like distribution function, survival function, moments,…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…
Distributed parameter estimation for large-scale systems is an active research problem. The goal is to derive a distributed algorithm in which each agent obtains a local estimate of its own subset of the global parameter vector, based on…
The Cross Entropy method is a well-known adaptive importance sampling method for rare-event probability estimation, which requires estimating an optimal importance sampling density within a parametric class. In this article we estimate an…
Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…
Finite-precision floating point arithmetic unavoidably introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be…
We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function…
In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…
In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…