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The algorithm of the ensemble pulsar time scale (PT$_{\rm ens}$) based on the optimal Wiener filtration method has been proposed. This algorithm allows the separation of the contributions to the post-fit pulsar timing residuals of the…

Pulsar Timing Array (PTA) collaborations recently reported evidence for the presence of a gravitational wave background (GWB) in their datasets. The main candidate that is expected to produce such a GWB is the population of supermassive…

Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…

This paper tackles the challenge presented by small-data to the task of Bayesian inference. A novel methodology, based on manifold learning and manifold sampling, is proposed for solving this computational statistics problem under the…

Pulsar timing arrays aim to detect nanohertz-frequency gravitational waves (GWs). A background of GWs modulates pulsar arrival times and manifests as a stochastic process, common to all pulsars, with a signature spatial correlation. Here we…

Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant…

Bayesian Inference is a powerful approach to data analysis that is based almost entirely on probability theory. In this approach, probabilities model {\it uncertainty} rather than randomness or variability. This thesis is composed of a…

Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

We propose a Bayesian procedure for simultaneous variable and covariance selection using continuous spike-and-slab priors in multivariate linear regression models where q possibly correlated responses are regressed onto p predictors. Rather…

A general challenge in statistics is prediction in the presence of multiple candidate models or learning algorithms. Model aggregation tries to combine all predictive distributions from individual models, which is more stable and flexible…

Linear mixed models are widely used for analyzing hierarchically structured data involving missingness and unbalanced study designs. We consider a Bayesian clustering method that combines linear mixed models and predictive projections. For…

When using incorrect or inaccurate signal models to perform parameter estimation on a gravitational wave signal, biased parameter estimates will in general be obtained. For a single event this bias may be consistent with the posterior, but…

Astronomers are often confronted with funky populations and distributions of objects: brighter objects are more likely to be detected; targets are selected based on colour cuts; imperfect classification yields impure samples. Failing to…

In 2023, after more than two decades of searching, pulsar timing array (PTA) collaborations around the world announced evidence for a stochastic gravitational wave background. It was quickly followed by work from the International Pulsar…

We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…

In Pulsar Timing Array (PTA) data analysis, noise is typically assumed to be Gaussian, and the marginalized likelihood has a well-established analytical form derived within the framework of Gaussian processes. However, this Gaussianity…

Gravitational waves are predicted by Einstein's theory of general relativity as well as other theories of gravity. The rotational stability of the fastest pulsars means that timing of an array of these objects can be used to detect and…

The phenomenon of pulsar nulling -- where pulsars occasionally turn off for one or more pulses -- provides insight into pulsar-emission mechanisms and the processes by which pulsars turn off when they cross the "death line." However, while…

Inferring the properties of colliding black holes from gravitational-wave observations is subject to systematic errors arising from modelling uncertainties. Although the accuracy of each model can be calculated through comparison to…