Related papers: Prediction theory in continuous time
In the paper we consider an interesting possibility of a time as a stochastic process in quantum mechanics.In order to do it we reconsider time as a mechanical quantity in classical mechanics and afterwards we quantize it. We consider…
Observations on the past provide some hints about what will happen in the future, and this can be quantified using information theory. The ``predictive information'' defined in this way has connections to measures of complexity that have…
We consider a stationary process (with either discrete or continuous time) and find an adaptive approximating stationary process combining approximation quality and supplementary good properties that can be interpreted as additional…
When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by…
We present online prediction methods for time series that let us explicitly handle nonstationary artifacts (e.g. trend and seasonality) present in most real time series. Specifically, we show that applying appropriate transformations to…
We study the spatio-temporal prediction problem and introduce a novel point-process-based prediction algorithm. Spatio-temporal prediction is extensively studied in Machine Learning literature due to its critical real-life applications such…
This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems,…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
In neuroscience, the time elapsed since the last discharge has been used to predict the probability of the next discharge. Such predictions can be improved taking into account the last two discharge times, and possibly more. Such multi-time…
Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities.…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
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…
We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We…
Under very general conditions the hitting time of a set by a stochastic process is a stopping time. We give a new simple proof of this fact. The section theorems for optional and predictable sets are easy corollaries of the proof.
Prediction is the making of statements, usually probabilistic, about future events based on current information. Retrodiction is the making of statements about past events based on current information. We present the foundations of quantum…
Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure. While classical approaches consider finite, albeit potentially huge, output spaces, in this paper we…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations which are easier to solve numerically. We demonstrate by…