Stochastic methods for parameter estimation and design of experiments in systems biology / vorgelegt von Andrei Kramer.

Format:

Book

Thesis/Dissertation

Author/Creator:

Kramer, Andrei, author.

Language:

English

Subjects (All):

Stochastic analysis--Mathematical models.

Stochastic analysis.

Systems biology--Statistical mehods.

Systems biology.

Biological systems--Data processing.

Biological systems.

Physical Description:

1 online resource (xii,137 pages) : illustrations

Edition:

1st ed.

Place of Publication:

Berlin, Germany : Logos Verlag, [2016]

Summary:

Long description: 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.

Contents:

Intro

1. Motivation and Background

1.1. Contribution

1.2. Probability

2. Introduction

2.1. Available Data in Relation to Modelling Frameworks

2.2. Modelling Using Ordinary Differential Equations

2.3. Measurement and Prediction Uncertainty

3. Existing Methods for Parameter Estimation via Markov Chain Monte Carlo

3.1. Monte Carlo

3.2. Markov Chains in the Reals

3.3. Geometry of Parameter Spaces

3.4. MCMC Algorithm Type Overview

3.5. Metropolis-Hastings Type Algorithms

3.6. Hamiltonian Type Algorithms

3.7. Riemannian Manifold Hamiltonian Monte Carlo

3.8. Sensitivity Analysis for Steady States

4. Discussion on Tuning

4.1. Comparing Two Algorithms from Different Families Requires Careful Tuning

4.2. Algorithm-Independent Tuning

5. Algorithm Development

5.1. Calculation of Steady States

5.2. Near Steady State Sensitivity Approximation

5.3. Discussion

5.4. Model Assisted Design of Experiments

6. Software Development

6.1. MCMC Package Written in C

6.2. mcmc_clib - Usage Structure

6.3. mcmc_clib Is Capable of Dealing with Large Models

7. Conclusions 101A. Modelling in Systems Biology

A.1. Scale and Granularity

A.2. Stochastic and Dynamic Modelling

B. Models

B.1. Test-Model for the mcmc_clib Package

B.2. Test-Model for the Comparison of smmala Type Algorithms

B.3. Models Used in the matlab Study of rmhmc and smmala

C. Treatment of Special Cases in Measurement Setups

C.1. Measurement Times Can Be Different between Experiments

C.2. Log-Normal Measurement Errors and Poor Data

Bibliography.

Notes:

"Von der Fakultät Konstruktions-, Produktions- und Fahrzeugtechnik der Universität Stuttgart zur Erlangung der Würde eines Doktor- Ingenieurs (Dr.-Ing.) genehmigte Abhandlung."

Ph.D. Universität Stuttgart 2015.

Includes bibliographical references (pages 127-137).

Description based on print version record.

ISBN:

3-8325-8795-0

9783832587956