5,203 research outputs found
On-the-fly Uniformization of Time-Inhomogeneous Infinite Markov Population Models
This paper presents an on-the-fly uniformization technique for the analysis
of time-inhomogeneous Markov population models. This technique is applicable to
models with infinite state spaces and unbounded rates, which are, for instance,
encountered in the realm of biochemical reaction networks. To deal with the
infinite state space, we dynamically maintain a finite subset of the states
where most of the probability mass is located. This approach yields an
underapproximation of the original, infinite system. We present experimental
results to show the applicability of our technique
Lie algebra solution of population models based on time-inhomogeneous Markov chains
Many natural populations are well modelled through time-inhomogeneous
stochastic processes. Such processes have been analysed in the physical
sciences using a method based on Lie algebras, but this methodology is not
widely used for models with ecological, medical and social applications. This
paper presents the Lie algebraic method, and applies it to three biologically
well motivated examples. The result of this is a solution form that is often
highly computationally advantageous.Comment: 10 pages; 1 figure; 2 tables. To appear in Applied Probabilit
A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics
We propose a new sensitivity analysis methodology for complex stochastic
dynamics based on the Relative Entropy Rate. The method becomes computationally
feasible at the stationary regime of the process and involves the calculation
of suitable observables in path space for the Relative Entropy Rate and the
corresponding Fisher Information Matrix. The stationary regime is crucial for
stochastic dynamics and here allows us to address the sensitivity analysis of
complex systems, including examples of processes with complex landscapes that
exhibit metastability, non-reversible systems from a statistical mechanics
perspective, and high-dimensional, spatially distributed models. All these
systems exhibit, typically non-gaussian stationary probability distributions,
while in the case of high-dimensionality, histograms are impossible to
construct directly. Our proposed methods bypass these challenges relying on the
direct Monte Carlo simulation of rigorously derived observables for the
Relative Entropy Rate and Fisher Information in path space rather than on the
stationary probability distribution itself. We demonstrate the capabilities of
the proposed methodology by focusing here on two classes of problems: (a)
Langevin particle systems with either reversible (gradient) or non-reversible
(non-gradient) forcing, highlighting the ability of the method to carry out
sensitivity analysis in non-equilibrium systems; and, (b) spatially extended
Kinetic Monte Carlo models, showing that the method can handle high-dimensional
problems
Computing Battery Lifetime Distributions
The usage of mobile devices like cell phones, navigation systems, or laptop computers, is limited by the lifetime of the included batteries. This lifetime depends naturally on the rate at which energy is consumed, however, it also depends on the usage pattern of the battery. Continuous drawing of a high current results in an excessive drop of residual capacity. However, during \ud
intervals with no or very small currents, batteries do recover to a certain extend. We model this complex behaviour with an inhomogeneous Markov reward model, following the approach of the so-called Kinetic battery Model (KiBaM). \ud
The state-dependent reward rates thereby correspond to the power consumption of the attached device and to the available charge, respectively. We develop a tailored numerical algorithm for the computation of the distribution of the consumed energy and show how different workload patterns influence the overall lifetime of a battery
Explicit formulas for a continuous stochastic maturation model. Application to anticancer drug pharmacokinetics/pharmacodynamics
We present a continuous time model of maturation and survival, obtained as
the limit of a compartmental evolution model when the number of compartments
tends to infinity. We establish in particular an explicit formula for the law
of the system output under inhomogeneous killing and when the input follows a
time-inhomogeneous Poisson process. This approach allows the discussion of
identifiability issues which are of difficult access for finite compartmental
models. The article ends up with an example of application for anticancer drug
pharmacokinetics/pharmacodynamics.Comment: Revised version, accepted for publication in Stochastic Models
(Taylor & Francis
Fast MCMC sampling for Markov jump processes and extensions
Markov jump processes (or continuous-time Markov chains) are a simple and
important class of continuous-time dynamical systems. In this paper, we tackle
the problem of simulating from the posterior distribution over paths in these
models, given partial and noisy observations. Our approach is an auxiliary
variable Gibbs sampler, and is based on the idea of uniformization. This sets
up a Markov chain over paths by alternately sampling a finite set of virtual
jump times given the current path and then sampling a new path given the set of
extant and virtual jump times using a standard hidden Markov model forward
filtering-backward sampling algorithm. Our method is exact and does not involve
approximations like time-discretization. We demonstrate how our sampler extends
naturally to MJP-based models like Markov-modulated Poisson processes and
continuous-time Bayesian networks and show significant computational benefits
over state-of-the-art MCMC samplers for these models.Comment: Accepted at the Journal of Machine Learning Research (JMLR
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