Media type: E-Book; Doctoral Thesis; Electronic Thesis Title: Reversible Markov State Models ; Reversible Markov Modelle Contributor: Trendelkamp-Schroer, Benjamin [Author] imprint: Freie Universität Berlin: Refubium (FU Berlin), 2016 Extent: xiii, 131 Seiten Language: English DOI: https://doi.org/10.17169/refubium-11030 Keywords: Reversibility ; Markov model ; Markov state model ; Detailed balance ; Reversible Markov model ; Reversible Markov state model Origination: Footnote: Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen. Description: 1 Introduction 2 Theory 2.1 Molecular dynamics 2.1.1 Langevin dynamics 2.1.2 Brownian dynamics 2.2 Transfer operator 2.2.1 Invariant measures 2.2.2 Detailed balance and reversibility 2.2.3 Probabilistic interpretation 2.2.4 Almost invariant sets 2.2.5 Transfer operator for molecular dynamics 2.3 Markov state models 2.4 Maximum likelihood estimation 2.5 Markov chain Monte Carlo 2.5.1 Rejection sampling 2.5.2 Metropolis Hastings algorithm 2.5.3 Gibbs sampling 2.5.4 Sampling errors 2.6 Enhanced sampling 2.6.1 Umbrella sampling 2.6.2 The weighted histogram analysis method 3 Estimation 3.1 Markov chain estimation 3.2 Dual of the reversible MLE problem 3.2.1 Scaling 3.2.2 Special cases and extensions 3.2.3 dTRAM 3.3 Convex-concave programs 3.4 The Ralph- Wright algorithm 3.5 Implementation details 3.5.1 dTRAM 3.6 Results 3.6.1 Reversible MLE 3.6.2 dTRAM 4 Uncertainty Quantification 4.1 The posterior ensemble 4.2 Sampling of nonreversible matrices 4.3 Sampling of reversible matrices 4.3.1 Prior 4.3.2 Algorithm 4.3.3 Validation 4.3.4 Application 4.3.5 Efficiency 4.4 Sampling with a fixed stationary vector 4.4.1 Prior 4.4.2 Algorithm 4.4.3 Validation 4.4.4 Application 4.4.5 Efficiency 4.5 Inference using an uncertain stationary vector 5\. Estimation of rare event kinetics 5.1 Efficient estimation via detailed balance 5.2 Finite state space Markov chain 5.3 Double-well potential 5.4 Alanine dipeptide 5.4.1 Analysis in φ and ψ dihedral angle space 5.4.2 Analysis in the φ-coordinate alone 5.5 Vesicle model 6\. Conclusion A MSM - analysis A.1 The transition kernel for the Euler- method A.2 Eigenvalues and relaxation timescales A.3 Mean first-passage times between meta-stable regions A.4 Committor functions B Transition matrix sampling B.1 Reversible sampling B.1.1 Posterior B.1.2 Beta sampling for diagonal elements B.1.3 Gamma proposal for off-diagonal elements B.1.4 Logspace random walk B.2 Reversible sampling with fixed stationary vector 109 B.2.1 Conditional expectation and likelihood B.2.2 Conditional distribution B.2.3 ... Access State: Open Access