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Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
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…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…
The ability to predict the future in a given domain can be acquired by discovering empirically from experience certain temporal patterns that tend to repeat unerringly. Previous works in time series analysis allow one to make quantitative…
A prediction makes a claim about a system's future given knowledge of its past. A retrodiction makes a claim about its past given knowledge of its future. The bidirectional machine is an ambidextrous hidden Markov chain that does both…
The inference of thermodynamic quantities from the description of an only partially accessible physical system is a central challenge in stochastic thermodynamics. A common approach is coarse-graining, which maps the dynamics of such a…
From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying…
Prediction-powered inference is a framework for performing valid statistical inference when an experimental dataset is supplemented with predictions from a machine-learning system. The framework yields simple algorithms for computing…
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 system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system's state retains information about past environmental fluctuations,…
Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are…
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
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…
Statistical inference is the science of drawing conclusions about some system from data. In modern signal processing and machine learning, inference is done in very high dimension: very many unknown characteristics about the system have to…
In this article, we review selective inference, a set of techniques for inference when the statistical question asked is a function of the data. This setting often arises in contemporary scientific workflows, where hypotheses and parameters…
Inference is the task of drawing conclusions about unobserved variables given observations of related variables. Applications range from identifying diseases from symptoms to classifying economic regimes from price movements. Unfortunately,…
The scientific process is a means to turn the results of experiments into knowledge about the world in which we live. Much research effort has been directed toward automating this process. To do this, one needs to formulate the scientific…
Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling…