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State-space models effectively model multivariate time series by updating over time a representation of the system state from which predictions are made. The state representation is usually a vector without any explicit structure.…
We introduce a method for decomposition of trend, cycle and seasonal components in spatio-temporal models and apply it to investigate the existence of climate changes in temperature and rainfall series. The method incorporates critical…
We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…
In this paper we introduce a Non-Stationary Fuzzy Time Series (NSFTS) method with time varying parameters adapted from the distribution of the data. In this approach, we employ Non-Stationary Fuzzy Sets, in which perturbation functions are…
In the case of a linear state space model, we implement an MCMC sampler with two phases. In the learning phase, a self-tuning sampler is used to learn the parameter mean and covariance structure. In the estimation phase, the parameter mean…
We develop the methodology and a detailed case study in use of a class of Bayesian predictive synthesis (BPS) models for multivariate time series forecasting. This extends the recently introduced foundational framework of BPS to the…
This work contributes to the development of neural forecasting models with novel randomization-based learning methods. These methods improve the fitting abilities of the neural model, in comparison to the standard method, by generating…
We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space…
Predicting the response at an unobserved location is a fundamental problem in spatial statistics. Given the difficulty in modeling spatial dependence, especially in non-stationary cases, model-based prediction intervals are at risk of…
Motivated by the application to German interest rates, we propose a timevarying autoregressive model for short and long term prediction of time series that exhibit a temporary non-stationary behavior but are assumed to mean revert in the…
Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with observations. For model outputs that are distributed over space, this becomes computationally expensive because of the output size. To overcome…
A Bayesian approach is developed to analyze change points in multivariate time series and space-time data. The methodology is used to assess the impact of extended inundation on the ecosystem of the Gulf Plains bioregion in northern…
Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…
Non-stationarity is a fundamental challenge in multivariate long-term time series forecasting, often manifested as rapid changes in amplitude and phase. These variations lead to severe distribution shifts and consequently degrade predictive…
Estimation of stationary dependence structure parameters using only a single realisation of the spatial process, typically leads to inaccurate estimates and poorly identified parameters. A common way to handle this is to fix some of the…
We consider statistics of spatial averages estimated by weighting observations over an arbitrary spatial domain using identical and independent measuring devices, and derive an account of bias and variance in the presence of missing…
This paper presents a fast algorithm for estimating hidden states of Bayesian state space models. The algorithm is a variation of amortized simulation-based inference algorithms, where a large number of artificial datasets are generated at…
In this chapter, we review variance selection for time-varying parameter (TVP) models for univariate and multivariate time series within a Bayesian framework. We show how both continuous as well as discrete spike-and-slab shrinkage priors…
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…
Errors in the representation of clouds in convection-permitting numerical weather prediction models can be introduced by different sources. These can be the forcing and boundary conditions, the representation of orography, the accuracy of…