Related papers: What is... a Markov basis?
Smoothness has long been the dominant form of parsimony in functional data analysis, to the point of occasionally being conflated with the very notion of functional data. However, many core inferential tasks depend on the inverse…
In this work we introduce a new and richer class of finite order Markov chain models and address the following model selection problem: find the Markov model with the minimal set of parameters (minimal Markov model) which is necessary to…
Mathematical aspects of the theory of interfaces in statistical mechanics are discussed.
This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhaustive database of maps of a metric space into…
A rescaled Markov chain converges uniformly in probability to the solution of an ordinary differential equation, under carefully specified assumptions. The presentation is much simpler than those in the outside literature. The result may be…
A hidden Markov process is a well known concept in information theory and is used for a vast range of applications such as speech recognition and error correction. We bridge between two disciplines, experimental physics and advanced…
We introduce partial Markov categories as a synthetic framework for synthetic probabilistic inference, blending the work of Cho and Jacobs, Fritz, and Golubtsov on Markov categories with the work of Cockett and Lack on cartesian restriction…
In this article we give a concept of ground subgroup for finite and countable groups. By our definition such a subgroup of a group depends on a given subset of the group and on a given partition of the subset. For finite and free groups we…
The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models…
A classical problem for Markov chains is determining their stationary (or steady-state) distribution. This problem has an equally classical solution based on eigenvectors and linear equation systems. However, this approach does not scale to…
In this paper we present elementary computations for some Markov modulated counting processes, also called counting processes with regime switching. Regime switching has become an increasingly popular concept in many branches of science. In…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
The purpose of this article is to describe all possible beliefs of market participants on objective measures under Markovian environments when a risk-neutral measure is given. To achieve this, we employ the Martin integral representation of…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.
This chapter presents an introduction to Markovian modeling for the analysis of sequence data. Contrary to the deterministic approach seen in the previous sequence analysis chapters, Markovian models are probabilistic models, focusing on…
This project is going to work with one example of stochastic matrix to understand how Markov chains evolve and how to use them to make faster and better decisions only looking to the present state of the system.
In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The…
We consider stochastic thermodynamics as a theory of statistical inference for experimentally observed fluctuating time-series. To that end, we introduce a general framework for quantifying the knowledge about the dynamical state of the…
Markov processes are used in a wide range of disciplines, including finance. The transition densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available, especially for…