Related papers: What is... a Markov basis?
Developing satisfactory methodology for the analysis of Markov random field is a very challenging task. Indeed, due to the Markovian dependence structure, the normalizing constant of the fields cannot be computed using standard analytical…
The aim of this paper is to provide Markov-type inequalities in the setting of weighted Sobolev spaces when the considered weights are generalized classical weights. Also, as results of independent interest, some basic facts about Sobolev…
The question in the title is discussed briefly, with emphasis on a few basic examples and their properties.
We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene…
This short note reviews the basic theory for quantifying both the asymptotic and preasymptotic convergence of Markov chain Monte Carlo estimators.
A construction is given of Markov partitions for some rational maps, which persist over regions of parameter space, not confined to single hyperbolic components. The set on which the Markov partition exists, and its boundary, are analysed.
These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory.…
The analysis of high-dimensional time series data has become increasingly important across a wide range of fields. Recently, a method for constructing the minimum information Markov kernel on finite state spaces was established. In this…
The purpose of this paper is to introduce a notion of causality in Markov decision processes based on the probability-raising principle and to analyze its algorithmic properties. The latter includes algorithms for checking cause-effect…
The aim of this paper is to present a self contained introduction to the Hubbard model and some of its applications.The paper consists of two parts: the first will introduce the basic notions of the Hubbard model starting from the…
It is known that a Markov basis of the binary graph model of a graph $G$ corresponds to a set of binomial generators of cut ideals $I_{\widehat{G}}$ of the suspension $\widehat{G}$ of $G$. In this paper, we give another application of cut…
A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…
A brief presentation of basic definitions and notation used in permutation patterns research.
Classical linear regression is considered for a case when regression parameters depend on the external random environment. The last is described as a continuous time Markov chain with finite state space. Here the expected sojourn times in…
The theory of causal fermion systems is an approach to describe fundamental physics. We here introduce the mathematical framework and give an overview of the objectives and current results.
Our goal in this short note is to briefly and succinctly describe some basic concepts and properties of Ergodic Optimization for readers unfamiliar with the subject. We avoid technical issues in order to provide a global overview of this…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
This work introduces a novel cause-effect relation in Markov decision processes using the probability-raising principle. Initially, sets of states as causes and effects are considered, which is subsequently extended to regular path…
A statistical test is presented to decide whether data are adequately described by probabilistic functions of finite state Markov chains (''hidden Markov models'') as applied in the analysis of ion channel data. Particularly, the test can…