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State-space models (SSMs) are commonly used to model time series data where the observations depend on an unobserved latent process. However, inference on the model parameters of an SSM can be challenging, especially when the likelihood of…

Power system state estimation (PSSE) is commonly formulated as weighted least-square (WLS) algorithm and solved using iterative methods such as Gauss-Newton methods. However, iterative methods have become more sensitive to system operating…

Spatio-temporal hidden Markov models are extremely difficult to estimate because their latent joint distributions are available only in trivial cases. In the estimation phase, these latent distributions are usually substituted with…

Probabilistic forecasting of time series is an important matter in many applications and research fields. In order to draw conclusions from a probabilistic forecast, we must ensure that the model class used to approximate the true…

This study introduces an integrated framework for predictive causal inference designed to overcome limitations inherent in conventional single model approaches. Specifically, we combine a Hidden Markov Model (HMM) for spatial health state…

We address the multiple testing problem under the assumption that the true/false hypotheses are driven by a Hidden Markov Model (HMM), which is recognized as a fundamental setting to model multiple testing under dependence since the seminal…

We consider two-state Non-Homogeneous Hidden Markov Models (NHHMMs) for forecasting univariate time series. Given a set of predictors, the time series are modeled via predictive regressions with state dependent coefficients and time-varying…

Hidden Markov models (HMMs) are probabilistic methods in which observations are seen as realizations of a latent Markov process with discrete states that switch over time. Moving beyond standard statistical tests, HMMs offer a statistical…

With large quantities of data typically available nowadays, forecasting models that are trained across sets of time series, known as Global Forecasting Models (GFM), are regularly outperforming traditional univariate forecasting models that…

Many multivariate statistical analysis methods and their corresponding probabilistic counterparts have been adopted to develop process monitoring models in recent decades. However, the insightful connections between them have rarely been…

The stock market presents a challenging environment for accurately predicting future stock prices due to its intricate and ever-changing nature. However, the utilization of advanced methodologies can significantly enhance the precision of…

Generative models have gained significant attention in multivariate time series forecasting (MTS), particularly due to their ability to generate high-fidelity samples. Forecasting the probability distribution of multivariate time series is…

The Pairwise Markov Chain (PMC) is a probabilistic graphical model extending the well-known Hidden Markov Model. This model, although highly effective for many tasks, has been scarcely utilized for continuous value prediction. This is…

Probabilistic model checking can provide formal guarantees on the behavior of stochastic models relating to a wide range of quantitative properties, such as runtime, energy consumption or cost. But decision making is typically with respect…

Probabilistic time series forecasting is crucial for quantifying future uncertainty, with significant applications in fields such as energy and finance. However, existing methods often rely on computationally expensive sampling or…

Generating synthetic financial time series that preserve the statistical properties of real market data is essential for stress testing, risk model validation, and scenario design. Existing approaches struggle to simultaneously reproduce…

Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…

The forecasting of Multivariate Time Series (MTS) has long been an important but challenging task. Due to the non-stationary problem across long-distance time steps, previous studies primarily adopt stationarization method to attenuate the…

Time series forecasting models are increasingly scaled through large Transformer backbones, yet most existing approaches process all series through a shared dense computation path despite substantial heterogeneity in temporal structure.…

In this paper, we develop an ensemble-based time-stepping algorithm to efficiently find numerical solutions to a group of linear, second-order parabolic partial differential equations (PDEs). Particularly, the PDE models in the group could…