arXiv subjects

Michael Stumpf

Publications and source records attributed to Michael Stumpf.

2 recordsLinked to original sources

arXiv2015

A closed-form approach to Bayesian inference in tree-structured graphical models

We consider the inference of the structure of an undirected graphical model in an exact Bayesian framework. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. This task would be intractable without any restriction on the considered graphs, so we limit our exploration to mixtures of spanning trees. We consider the inference of the structure of an undirected graphical model in a Bayesian framework. To avoid convergence issues and highly demanding Monte Carlo sampling, we focus on exact inference. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. To this aim, we restrict the set of considered graphs to mixtures of spanning trees. We investigate under which conditions on the priors - on both tree structures and parameters - exact Bayesian inference can be achieved. Under these conditions, we derive a fast an exact algorithm to compute the posterior probability for an edge to belong to {the tree model} using an algebraic result called the Matrix-Tree theorem. We show that the assumption we have made does not prevent our approach to perform well on synthetic and flow cytometry data.

stat.ML↗

arXiv2011

Sensitivity, robustness and identifiability in stochastic chemical kinetics models

We present a novel and simple method to numerically calculate Fisher Information Matrices for stochastic chemical kinetics models. The linear noise approximation is used to derive model equations and a likelihood function which leads to an efficient computational algorithm. Our approach reduces the problem of calculating the Fisher Information Matrix to solving a set of ordinary differential equations. {This is the first method to compute Fisher Information for stochastic chemical kinetics models without the need for Monte Carlo simulations.} This methodology is then used to study sensitivity, robustness and parameter identifiability in stochastic chemical kinetics models. We show that significant differences exist between stochastic and deterministic models as well as between stochastic models with time-series and time-point measurements. We demonstrate that these discrepancies arise from the variability in molecule numbers, correlations between species, and temporal correlations and show how this approach can be used in the analysis and design of experiments probing stochastic processes at the cellular level. The algorithm has been implemented as a Matlab package and is available from the authors upon request.

stat.AP↗