Search results for "markov chains"
showing 10 items of 73 documents
Importance sampling for Lambda-coalescents in the infinitely many sites model
2011
We present and discuss new importance sampling schemes for the approximate computation of the sample probability of observed genetic types in the infinitely many sites model from population genetics. More specifically, we extend the 'classical framework', where genealogies are assumed to be governed by Kingman's coalescent, to the more general class of Lambda-coalescents and develop further Hobolth et. al.'s (2008) idea of deriving importance sampling schemes based on 'compressed genetrees'. The resulting schemes extend earlier work by Griffiths and Tavar\'e (1994), Stephens and Donnelly (2000), Birkner and Blath (2008) and Hobolth et. al. (2008). We conclude with a performance comparison o…
Convergence of Markov Chains
2020
We consider a Markov chain X with invariant distribution π and investigate conditions under which the distribution of X n converges to π as n→∞. Essentially it is necessary and sufficient that the state space of the chain cannot be decomposed into subspaces that the chain does not leave, or that are visited by the chain periodically; e.g., only for odd n or only for even n.
Non-equilibrium Markov state modeling of periodically driven biomolecules
2019
Molecular dynamics simulations allow to study the structure and dynamics of single biomolecules in microscopic detail. However, many processes occur on time scales beyond the reach of fully atomistic simulations and require coarse-grained multiscale models. While systematic approaches to construct such models have become available, these typically rely on microscopic dynamics that obey detailed balance. In vivo, however, biomolecules are constantly driven away from equilibrium in order to perform specific functions and thus break detailed balance. Here we introduce a method to construct Markov state models for systems that are driven through periodically changing one (or several) external p…
Income distribution dynamics: monotone Markov chains make light work
1995
This paper considers some aspects of the dynamics of income distributions by employing a simple Markov chain model of income mobility. The main motivation of the paper is to introduce the techniques of “monotone” Markov chains to this field. The transition matrix of a discrete Markov chain is called monotone if each row stochastically dominates the row above it. It will be shown that by embedding the dynamics of the income distribution in a monotone Markov chain, a number of interesting results may be obtained in a straightforward and intuitive fashion.
Levy targeting and the principle of detailed balance
2011
We investigate confining mechanisms for Lévy flights under premises of the principle of detailed balance. In this case, the master equation of the jump-type process admits a transformation to the Lévy-Schrödinger semigroup dynamics akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation. This sets a correspondence between above two stochastic dynamical systems, within which we address a (stochastic) targeting problem for an arbitrary stability index μ ε (0,2) of symmetric Lévy drivers. Namely, given a probability density function, specify the semigroup potential, and thence the jump-type dynamics for which this PDF is actually a long-time asymptotic (target) …
The pianigiani-yorke measure for topological markov chains
1997
We prove the existence of a Pianigiani-Yorke measure for a Markovian factor of a topological Markov chain. This measure induces a Gibbs measure in the limit set. The proof uses the contraction properties of the Ruelle-Perron-Frobenius operator.
Context Trees, Variable Length Markov Chains and Dynamical Sources
2012
Infinite random sequences of letters can be viewed as stochastic chains or as strings produced by a source, in the sense of information theory. The relationship between Variable Length Markov Chains (VLMC) and probabilistic dynamical sources is studied. We establish a probabilistic frame for context trees and VLMC and we prove that any VLMC is a dynamical source for which we explicitly build the mapping. On two examples, the "comb" and the "bamboo blossom", we find a necessary and sufficient condition for the existence and the uniqueness of a stationary probability measure for the VLMC. These two examples are detailed in order to provide the associated Dirichlet series as well as the genera…
QUANTITATIVE CONVERGENCE RATES FOR SUBGEOMETRIC MARKOV CHAINS
2015
We provide explicit expressions for the constants involved in the characterisation of ergodicity of subgeometric Markov chains. The constants are determined in terms of those appearing in the assumed drift and one-step minorisation conditions. The results are fundamental for the study of some algorithms where uniform bounds for these constants are needed for a family of Markov kernels. Our results accommodate also some classes of inhomogeneous chains.
A study on forecasting electricity production and consumption in smart cities and factories
2019
Abstract The electrical power sector must undergo a thorough metamorphosis to achieve the ambitious targets in greenhouse gas reduction set forth in the Paris Agreement of 2015. Reducing uncertainty about demand and, in case of renewable electricity generation, supply is important for the determination of spot electricity prices. In this work we propose and evaluate a context-based technique to anticipate the electricity production and consumption in buildings. We focus on a household with photovoltaics and energy storage system. We analyze the efficiency of Markov chains, stride predictors and also their combination into a hybrid predictor in modelling the evolution of electricity producti…
Comparison of different uncertainty techniques in urban stormwater quantity and quality modelling
2011
Abstract Urban drainage models are important tools used by both practitioners and scientists in the field of stormwater management. These models are often conceptual and usually require calibration using local datasets. The quantification of the uncertainty associated with the models is a must, although it is rarely practiced. The International Working Group on Data and Models, which works under the IWA/IAHR Joint Committee on Urban Drainage, has been working on the development of a framework for defining and assessing uncertainties in the field of urban drainage modelling. A part of that work is the assessment and comparison of different techniques generally used in the uncertainty assessm…