Related papers: Sensitivity analysis for multiscale stochastic rea…
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a…
Oscillatory systems of interacting Hawkes processes with Erlang memory kernels were introduced in Ditlevsen (2017). They are piecewise deterministic Markov processes (PDMP) and can be approximated by a stochastic diffusion. First, a strong…
We construct a stochastic fluid process with an underlying piecewise deterministic Markov process (PDMP) akin to the one used in the construction of the rational arrival process (RAP), which we call the RAP-modulated fluid process. As…
Inferring parameters of models of biochemical kinetics from single-cell data remains challenging because of the uncertainty arising from the intractability of the likelihood function of stochastic reaction networks. Such uncertainty falls…
Probabilistic model checking can provide formal guarantees on the behavior of stochastic models relating to a wide range of quantitative properties, such as runtime, energy consumption or cost. But decision making is typically with respect…
Estimation of parameters is a crucial part of model development. When models are deterministic, one can minimise the fitting error; for stochastic systems one must be more careful. Broadly parameterisation methods for stochastic dynamical…
This paper presents a novel approach to pricing American options using piecewise diffusion Markov processes (PDifMPs), a type of generalised stochastic hybrid system that integrates continuous dynamics with discrete jump processes. Standard…
Molecular motors and other complex nonequilibrium systems are controlled by large sets of design parameters, and optimizing those parameters requires computing sensitivities -- derivatives of dynamical observables with respect to the…
We consider the problem of multiple sensor scheduling for remote state estimation of multiple process over a shared link. In this problem, a set of sensors monitor mutually independent dynamical systems in parallel but only one sensor can…
This paper investigates the optimization problem of an infinite stage discrete time Markov decision process (MDP) with a long-run average metric considering both mean and variance of rewards together. Such performance metric is important…
We present a novel multiscale simulation approach for modeling stochasticity in chemical reaction networks. The approach seamlessly integrates exact-stochastic and "leaping" methodologies into a single "partitioned leaping" algorithmic…
In this paper, a new computational framework based on the topology derivative concept is presented for evaluating stochastic topological sensitivities of complex systems. The proposed framework, designed for dealing with high dimensional…
Models of reaction networks within interacting compartments (RNIC) are a generalization of stochastic reaction networks. It is most natural to think of the interacting compartments as "cells" that can appear, degrade, split, and even merge,…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
While epidemiological modeling is pivotal for informing public health strategies, a fundamental trade-off limits its predictive fidelity: exact stochastic simulations are often computationally intractable for large-scale systems, whereas…
Piecewise deterministic Markov processes (PDMPs) are a class of continuous-time Markov processes that were recently used to develop a new class of Markov chain Monte Carlo algorithms. However, the implementation of the processes is…
Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on $\mathbb Z^d_{\ge 0}$, and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes,…
A biochemical network can be simulated by a set of ordinary differential equations (ODE) under well stirred reactor conditions, for large numbers of molecules, and frequent reactions. This is no longer a robust representation when some…
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…