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In practice, several time series exhibit long-range dependence or persistence in their observations, leading to the development of a number of estimation and prediction methodologies to account for the slowly decaying autocorrelations. The…

Two standard models for probabilistic systems are Markov chains (MCs) and Markov decision processes (MDPs). Classic objectives for such probabilistic models for control and planning problems are reachability and stochastic shortest path.…

This paper develops a framework for quantile regression in binary longitudinal data settings. A novel Markov chain Monte Carlo (MCMC) method is designed to fit the model and its computational efficiency is demonstrated in a simulation…

Time series forecasting has seen many methods attempted over the past few decades, including traditional technical analysis, algorithmic statistical models, and more recent machine learning and artificial intelligence approaches. Recently,…

Linear dynamical systems are the foundational statistical model upon which control theory is built. Both the celebrated Kalman filter and the linear quadratic regulator require knowledge of the system dynamics to provide analytic…

Data assimilation techniques are widely used to predict complex dynamical systems with uncertainties, based on time-series observation data. Error covariance matrices modelling is an important element in data assimilation algorithms which…

A machine-learning-based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of high-dimensional regression techniques (e.g., random forests, LASSO)…

Automatic differentiation (AD) has driven recent advances in machine learning, including deep neural networks and Hamiltonian Markov Chain Monte Carlo methods. Partially observed nonlinear stochastic dynamical systems have proved resistant…

Most long memory forecasting studies assume that the memory is generated by the fractional difference operator. We argue that the most cited theoretical arguments for the presence of long memory do not imply the fractional difference…

This article introduces a novel dynamic framework to Bayesian model averaging for time-varying parameter quantile regressions. By employing sequential Markov chain Monte Carlo, we combine empirical estimates derived from dynamically chosen…

Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering…

We present a simulation methodology for Bayesian estimation of rate parameters in Markov jump processes arising for example in stochastic kinetic models. To handle the problem of missing components and measurement errors in observed data,…

The increasing interest in renewable energy, particularly in wind, has given rise to the necessity of accurate models for the generation of good synthetic wind speed data. Markov chains are often used with this purpose but better models are…

Dynamic factor models are often estimated by point-estimation methods, disregarding parameter uncertainty. We propose a method accounting for parameter uncertainty by means of posterior approximation, using variational inference. Our…

In this work, we will investigate a Bayesian approach to estimating the parameters of long memory models. Long memory, characterized by the phenomenon of hyperbolic autocorrelation decay in time series, has garnered significant attention.…

We combine high-dimensional factor models with fractional integration methods and derive models where nonstationary, potentially cointegrated data of different persistence is modelled as a function of common fractionally integrated factors.…

We propose a novel Markov chain Monte-Carlo (MCMC) method for reverse engineering the topological structure of stochastic reaction networks, a notoriously challenging problem that is relevant in many modern areas of research, like…

Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as…

The probability prediction of multivariate time series is a notoriously challenging but practical task. On the one hand, the challenge is how to effectively capture the cross-series correlations between interacting time series, to achieve…

Current time-series forecasting models are primarily based on transformer-style neural networks. These models achieve long-term forecasting mainly by scaling up the model size rather than through genuinely autoregressive (AR) rollout. From…