Related papers: Solving stochastic chemical kinetics by Metropolis…
The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation…
We consider the problem of efficiently simulating stochastic models of chemical kinetics. The Gillespie Stochastic Simulation algorithm (SSA) is often used to simulate these models, however, in many scenarios of interest, the computational…
This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the…
We propose an adaptive Metropolis-Hastings algorithm in which sampled data are used to update the proposal distribution. We use the samples found by the algorithm at a particular step to form the information-theoretically optimal mean-field…
At the cellular scale, biochemical processes are governed by random interactions between reactant molecules with small copy counts, leading to behavior that is inherently stochastic. Such systems are often modeled as continuous-time Markov…
Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. Motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and…
In biochemical systems some of the chemical species are present with only small numbers of molecules. In this situation discrete and stochastic simulation approaches are more relevant than continuous and deterministic ones. The fundamental…
We analyse computational efficiency of Metropolis-Hastings algorithms with stochastic AR(1) process proposals. These proposals include, as a subclass, discretized Langevin diffusion (e.g. MALA) and discretized Hamiltonian dynamics (e.g.…
A macroscopic mesoscopic, deterministic stochastic coupling strategy is proposed to accelerate the direct simulation Monte Carlo (DSMC) method for chemical reaction. First, a macroscopic synthetic equation is formulated by integrating…
The Metropolis-Hastings (MH) algorithm is one of the most widely used Markov Chain Monte Carlo schemes for generating samples from Bayesian posterior distributions. The algorithm is asymptotically exact, flexible and easy to implement.…
Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie…
Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice…
The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to conduct such sampling, but such a method can converge…
We introduce an alternative formulation of the exact stochastic simulation algorithm (SSA) for sampling trajectories of the chemical master equation for a well-stirred system of coupled chemical reactions. Our formulation is based on…
Models of reaction chemistry based on the stochastic simulation algorithm (SSA) have become a crucial tool for simulating complicated biological reaction networks due to their ability to handle extremely complicated reaction networks and to…
The quest for improved sampling methods to solve statistical mechanics problems of physical and chemical interest proceeds with renewed efforts since the invention of the Metropolis algorithm, in 1953. In particular, the understanding of…
The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to perform such sampling, but this method is known to…
There exist several methods for simulating biological and physical systems as represented by chemical reaction networks. Systems with low numbers of particles are frequently modelled as discrete-state Markov jump processes and are typically…
Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a…
Markov Chain Monte Carlo (MCMC) methods have a drawback when working with a target distribution or likelihood function that is computationally expensive to evaluate, specially when working with big data. This paper focuses on…