Stochastic Methods for Parameter Estimation and Design of Experiments in Systems Biology

Markov Chain Monte Carlo (MCMC) methods are sampling based techniques,
which use random numbers to approximate deterministic but unknown
values. They can be used to obtain expected values, estimate
parameters or to simply inspect the properties of a non-standard, high
dimensional probability distribution. Bayesian analysis of model
parameters provides the mathematical foundation for parameter
estimation using such probabilistic sampling.

The strengths of these stochastic methods are their robustness and
relative simplicity even for nonlinear problems with dozens of
parameters as well as a built-in uncertainty analysis. Because
Bayesian model analysis necessarily involves the notion of prior
knowledge, the estimation of unidentifiable parameters can be
regularised (by priors) in a straight forward way.

This work draws the focus on typical cases in systems biology:
relative data, nonlinear ordinary differential equation
models and few data points. It also investigates the
consequences of parameter estimation from steady state data;
consequences such as performance benefits.

In biology the data is almost exclusively relative, the raw
measurements (e.g. western blot intensities) are normalised by
control experiments or a reference value within a series and
require the model to do the same when comparing its output to the
data.

Several sampling algorithms are compared in terms of effective
sampling speed and necessary adaptations to relative and steady
state data are explained.