TY - JOUR A1 - Lie, Han Cheng A1 - Sullivan, T. J. T1 - Quasi-invariance of countable products of Cauchy measures under non-unitary dilations JF - Electronic Communications in Probability Y1 - 2018 U6 - https://doi.org/10.1214/18-ECP113 VL - 23 IS - 8 SP - 1 EP - 6 ER - TY - JOUR A1 - Quer, Jannes A1 - Lie, Han Cheng T1 - Some connections between importance sampling and enhanced sampling methods in molecular dynamics JF - Journal of Chemical Physics N2 - Enhanced sampling methods play an important role in molecular dynamics, because they enable the collection of better statistics of rare events that are important in many physical phenomena. We show that many enhanced sampling methods can be viewed as methods for performing importance sampling, by identifying important correspondences between the language of molecular dynamics and the language of probability theory. We illustrate these connections by highlighting the similarities between the rare event simulation method of Hartmann and Schütte (J. Stat. Mech. Theor. Exp., 2012), and the enhanced sampling method of Valsson and Parrinello (Phys. Rev. Lett. 113, 090601). We show that the idea of changing a probability measure is fundamental to both enhanced sampling and importance sampling. Y1 - 2017 ER - TY - GEN A1 - Quer, Jannes A1 - Lie, Han Cheng T1 - Some connections between importance sampling and enhanced sampling methods in molecular dynamics N2 - Enhanced sampling methods play an important role in molecular dynamics, because they enable the collection of better statistics of rare events that are important in many physical phenomena. We show that many enhanced sampling methods can be viewed as methods for performing importance sampling, by identifying important correspondences between the language of molecular dynamics and the language of probability theory. We illustrate these connections by highlighting the similarities between the rare event simulation method of Hartmann and Schütte (J. Stat. Mech. Theor. Exp., 2012), and the enhanced sampling method of Valsson and Parrinello (Phys. Rev. Lett. 113, 090601). We show that the idea of changing a probability measure is fundamental to both enhanced sampling and importance sampling. T3 - ZIB-Report - 17-30 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64289 SN - 1438-0064 ER - TY - THES A1 - Lie, Han Cheng T1 - On a strongly convex approximation of a stochastic optimal control problem for importance sampling of metastable diffusions Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:188-fudissthesis000000101680-4 ER - TY - GEN A1 - Bojarovski, Stefan A1 - Hege, Hans-Christian A1 - Lie, Han Cheng A1 - Weber, Marcus T1 - Topological analysis and visualization of scalar functions characterizing conformational transitions of molecules on multiple time-scales T2 - Shape Up 2015 - Exercises in Materials Geometry and Topology, 14-18 Sept. 2015, Berlin, Germany N2 - Molecular processes such as protein folding or ligand-receptor-binding can be understood by analyzing the free energy landscape. Those processes are often metastable, i.e. the molecular systems remain in basins around local minima of the free energy landscape, and in rare cases undergo gauche transitions between metastable states by passing saddle-points of this landscape. By discretizing the configuration space, this can be modeled as a discrete Markov process. One way to compute the transition rates between conformations of a molecular system is by utilizing Transition Path Theory and the concept of committor functions. A fundamental problem from the computational point of view is that many time-scales are involved, ranging from 10^(-14) sec for the fastest motion to 10^(-6) sec or more for conformation changes that cause biological effects. The goal of our work is to provide a better understanding of such transitions in configuration space on various time-scales by analyzing characteristic scalar functions topologically and geometrically. We are developing suitable visualization and interaction techniques to support our analysis. For example, we are analyzing a transition rate indicator function by computing and visualizing its Reeb graph together with the sets of molecular states corresponding to maxima of the transition rate indicator function. A particular challenge is the high dimensionality of the domain which does not allow for a straightforward visualization of the function. The computational topology approach to the analysis of the transition rate indicator functions for a molecular system allows to explore different time scales of the system by utilizing coarser or finer topological partitioning of the function. A specific goal is the development of tools for analyzing the hierarchy of these partitionings. This approach tackles the analysis of a complex and sparse dataset from a different angle than the well-known spectral analysis of Markov State Models. Y1 - 2015 ER - TY - GEN A1 - Lie, Han Cheng A1 - Sullivan, T. J. A1 - Teckentrup, Aretha T1 - Random forward models and log-likelihoods in Bayesian inverse problems T2 - SIAM/ASA Journal on Uncertainty Quantification N2 - We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive model is approximated using a cheaper stochastic surrogate, as in Gaussian process emulation (kriging), or in the field of probabilistic numerical methods. We show that the Hellinger distance between the exact and approximate Bayesian posteriors is bounded by moments of the difference between the true and approximate log-likelihoods. Example applications of these stability results are given for randomised misfit models in large data applications and the probabilistic solution of ordinary differential equations. T3 - ZIB-Report - 18-03 KW - Bayesian inverse problem KW - random likelihood KW - surrogate model KW - posterior consistency KW - probabilistic numerics KW - uncertainty quantification KW - randomised misfit Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66324 SN - 1438-0064 VL - 6 IS - 4 SP - 1600 EP - 1629 ER - TY - JOUR A1 - Ayanbayev, Birzhan A1 - Klebanov, Ilja A1 - Lie, Han Cheng A1 - Sullivan, T. J. T1 - Γ-convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems JF - Inverse Problems Y1 - 2022 U6 - https://doi.org/10.1088/1361-6420/ac3f81 VL - 38 IS - 2 ER - TY - JOUR A1 - Ayanbayev, Birzhan A1 - Klebanov, Ilja A1 - Lie, Han Cheng A1 - Sullivan, T. J. T1 - Γ-convergence of Onsager–Machlup functionals: II. Infinite product measures on Banach spaces JF - Inverse Problems Y1 - 2022 U6 - https://doi.org/10.1088/1361-6420/ac3f82 VL - 38 IS - 2 ER - TY - JOUR A1 - Cvetkovic, Nada A1 - Conrad, Tim A1 - Lie, Han Cheng T1 - A Convergent Discretisation Method for Transition Path Theory for Diffusion Processes JF - Multiscale Modeling & Simulation Y1 - 2021 U6 - https://doi.org/10.1137/20M1329354 VL - 19 IS - 1 SP - 242 EP - 266 PB - Society for Industrial and Applied Mathematics ER -