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Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…
We propose to examine the predictability and the complexity characteristics of the Standard&Poor500 dynamics behaviors in a coarse-grained way using the symbolic dynamics method and under the prism of the Information theory through the…
Identification of causal structures and quantification of direct information flows in complex systems is a challenging yet important task, with practical applications in many fields. Data generated by dynamical processes or large-scale…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
Complex systems may often be characterized by their hierarchical dynamics. In this paper do we present a method and an operational algorithm that automatically infer this property in a broad range of systems; discrete stochastic processes.…
A practical and popular technique to extract the symbolic dynamics from experimentally measured chaotic time series is the threshold-crossing method, by which an arbitrary partition is utilized for determining the symbols. We address to…
For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the…
Some physical processes, including the intensity fluctuations of a chaotic laser, the detection of single photons, and the Brownian motion of a microscopic particle in a fluid are unpredictable, at least on long timescales. This…
Interpreting partial information collected from systems subject to noise is a key problem across scientific disciplines. Theoretical frameworks often focus on the dynamics of variables that result from coarse-graining the internal states of…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical…
We study sequential Bayesian inference in stochastic kinetic models with latent factors. Assuming continuous observation of all the reactions, our focus is on joint inference of the unknown reaction rates and the dynamic latent states,…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
We present some new results which relate information to chaotic dynamics. In our approach the quantity of information is measured by the Algorithmic Information Content (Kolmogorov complexity) or by a sort of computable version of it…
This paper applies probabilistic model checking techniques for discrete Markov chains to inference in Bayesian networks. We present a simple translation from Bayesian networks into tree-like Markov chains such that inference can be reduced…
In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high…
We present a general approach for computing the dynamic partition function of a continuous-time Markov process. The Ruelle topological pressure is identified with the large deviation function of a physical observable. We construct for the…