Related papers: An Alternative to Moment Closure
Approximations based on moment-closure (MA) are commonly used to obtain estimates of the mean molecule numbers and of the variance of fluctuations in the number of molecules of chemical systems. The advantage of this approach is that it can…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
Approximate model counting for bit-vector SMT formulas (generalizing \#SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity…
The moments of spatial probabilistic systems are often given by an infinite hierarchy of coupled differential equations. Moment closure methods are used to approximate a subset of low order moments by terminating the hierarchy at some order…
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method…
Moment approximation methods are gaining increasing attention for their use in the approximation of the stochastic kinetics of chemical reaction systems. In this paper we derive a general moment expansion method for any type of propensities…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
Closure modeling - the statistical modeling of missing dynamics in the natural sciences and engineering - is a growing and active area of research. Existing methods for closure modeling are often computationally prohibitive, lack…
This paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confidence sets for parameters are level sets of criterion functions whose boundary points may depend…
This paper introduces a new method to tackle the issue of the almost sure convergence of stochastic approximation algorithms defined from a differential inclusion. Under the assumption of slowly decaying step-sizes, we establish that the…
Model-based prediction of stochastic noise in biomolecular reactions often resorts to approximation with unknown precision. As a result, unexpected stochastic fluctuation causes a headache for the designers of biomolecular circuits. This…
MomentClosure.jl is a Julia package providing automated derivation of the time-evolution equations of the moments of molecule numbers for virtually any chemical reaction network using a wide range of moment closure approximations. It…
In this paper, novel closed-form point estimators of the beta distribution are proposed and investigated. The first estimators are a modified version of Pearson's method of moments. The underlying idea is to involve the sufficient…
We present a general numerical scheme for the practical implementation of statistical moment closures suitable for modeling complex, large-scale, nonlinear systems. Building on recently developed equation-free methods, this approach…
The use of approximate solution techniques for the Chemical Master Equation is common practice for the analysis of stochastic chemical systems. Despite their widespread use, however, many such techniques rely on unverifiable assumptions and…
Discrete-state stochastic models have become a well-established approach to describe biochemical reaction networks that are influenced by the inherent randomness of cellular events. In the last years severalmethods for accurately…
We survey a number of moment hierarchies and test their performances in computing one-dimensional shock structures. It is found that for high Mach numbers, the moment hierarchies are either computationally expensive or hard to converge,…
Stochastic modeling of gene expression is a classic problem in theoretical biophysics, and the burst approximation is widely used to simplify gene expression models formulated via the chemical master equation. However, the approximation…
Due to its simplicity and outstanding ability to generalize, stochastic gradient descent (SGD) is still the most widely used optimization method despite its slow convergence. Meanwhile, adaptive methods have attracted rising attention of…
Models phrased though moment conditions are central to much of modern inference. Here these moment conditions are embedded within a nonparametric Bayesian setup. Handling such a model is not probabilistically straightforward as the…