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We consider learning continuous probabilistic graphical models in the face of missing data. For non-Gaussian models, learning the parameters and structure of such models depends on our ability to perform efficient inference, and can be…

Correlation Networks (CNs) inherently suffer from redundant information in their network topology. Bayesian Networks (BNs), on the other hand, include only non-redundant information (from a probabilistic perspective) resulting in a sparse…

Accurate uncertainty quantification in graph neural networks (GNNs) is essential, especially in high-stakes domains where GNNs are frequently employed. Conformal prediction (CP) offers a promising framework for quantifying uncertainty by…

In this paper, we present the first study that compares different models of Bayesian Neural Networks (BNNs) to predict the posterior distribution of the cosmological parameters directly from the Cosmic Microwave Background temperature and…

Seasonal forecasting is a crucial task when it comes to detecting the extreme heat and colds that occur due to climate change. Confidence in the predictions should be reliable since a small increase in the temperatures in a year has a big…

Critical decisions frequently rely on high-dimensional output from complex computer simulation models that show intricate cross-variable, spatial and temporal dependence structures, with weather and climate predictions being key examples.…

Since model bias and associated initialization shock are serious shortcomings that reduce prediction skills in state-of-the-art decadal climate prediction efforts, we pursue a complementary machine-learning-based approach to climate…

In this article, we develop fully Bayesian, copula-based, spatial-statistical models for large, noisy, incomplete, and non-Gaussian spatial data. Our approach includes novel constructions of copulas that accommodate a spatial-random-effects…

Accurately representing surface weather at the sub-kilometer scale is crucial for optimal decision-making in a wide range of applications. This motivates the use of statistical techniques to provide accurate and calibrated probabilistic…

We propose a method for post-processing an ensemble of multivariate forecasts in order to obtain a joint predictive distribution of weather. Our method utilizes existing univariate post-processing techniques, in this case ensemble Bayesian…

Projections of future climate change rely heavily on climate models, and combining climate models through a multi-model ensemble is both more accurate than a single climate model and valuable for uncertainty quantification. However,…

Forecasting the weather is an increasingly data intensive exercise. Numerical Weather Prediction (NWP) models are becoming more complex, with higher resolutions, and there are increasing numbers of different models in operation. While the…

Due to limited computational resources, medium-range temperature forecasts typically rely on low-resolution numerical weather prediction (NWP) models, which are prone to systematic and random errors. We propose a method that integrates a…

Climate change poses significant challenges for accurate climate modeling due to the complexity and variability of non-Gaussian climate systems. To address the complexities of non-Gaussian systems in climate modeling, this thesis proposes a…

We propose a new copula model for replicated multivariate spatial data. Unlike classical models that assume multivariate normality of the data, the proposed copula is based on the assumption that some factors exist that affect the joint…

Accurate estimation of the Cosmic Microwave Background (CMB) angular power spectrum is enticing due to the prospect for precision cosmology it presents. Galactic foreground emissions, however, contaminate the CMB signal and need to be…

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…

Today weather forecasting is conducted using numerical weather prediction (NWP) models, consisting of a set of differential equations describing the dynamics of the atmosphere. The output of such NWP models are single deterministic…

A data-driven model for predicting the surface temperature using neural networks was proposed to alleviate the computational burden of numerical weather prediction (NWP). Our model, named TPTNet uses only 2m temperature measured at the…

Representing and quantifying uncertainty in physical parameterisations is a central challenge in weather and climate modelling, and approaches are often developed separately for different timescales. Here, we introduce a unified framework…