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The objective of advanced topic modeling is not only to explore latent topical structures, but also to estimate relationships between the discovered topics and theoretically relevant metadata. Methods used to estimate such relationships…

Semantic compositionality (SC) refers to the phenomenon that the meaning of a complex linguistic unit can be composed of the meanings of its constituents. Most related works focus on using complicated compositionality functions to model SC…

This thesis is dedicated to the statistical analysis of multi-sub ject fMRI data, with the purpose of identifying bain structures involved in certain cognitive or sensori-motor tasks, in a reproducible way across sub jects. To overcome…

Change-point models are frequently considered when modeling phenomena where a regime shift occurs at an unknown time. In ageing research, these models are commonly adopted to estimate of the onset of cognitive decline. Yet commonly used…

Randomized controlled trials are a cornerstone of medicine and the social sciences as they enable reliable estimates of causal effects. However, they are costly and time-consuming to conduct, motivating interest in predicting causal effects…

Automated identification of protein conformational states from simulation of an ensemble of structures is a hard problem because it requires teaching a computer to recognize shapes. We adapt the naive Bayes classifier from the machine…

Given a multivariate function taking deterministic and uncertain inputs, we consider the problem of estimating a quantile set: a set of deterministic inputs for which the probability that the output belongs to a specific region remains…

Learning causal structure from sampled data is a fundamental problem with applications in various fields, including healthcare, machine learning and artificial intelligence. Traditional methods predominantly rely on observational data, but…

Clustering is commonly performed as an initial analysis step for uncovering structure in 'omics datasets, e.g. to discover molecular subtypes of disease. The high-throughput, high-dimensional nature of these datasets means that they provide…

Mediation analysis aims to separate the indirect effect through mediators from the direct effect of the exposure on the outcome. It is challenging to perform mediation analysis with neuroimaging data which involves high dimensionality,…

The early detection of Alzheimer's disease (AD) requires an understanding of the relationships between a wide range of features. Conditional independencies and partial correlations are suitable measures for these relationships, because they…

Leveraging multivariate spatial dependence to improve the precision of estimates using American Community Survey data and other sample survey data has been a topic of recent interest among data-users and federal statistical agencies. One…

We consider sequential treatment regimes where each unit is exposed to combinations of interventions over time. When interventions are described by qualitative labels, such as "close schools for a month due to a pandemic" or "promote this…

Empirical research in many social disciplines involves constructs that are not directly observable, such as behaviors. To model them, constructs must be operationalized using their relations with indicators. Structural equation modeling…

Predictive modeling using structural magnetic resonance imaging (MRI) data is a prominent approach to study brain-aging. Machine learning algorithms and feature extraction methods have been employed to improve predictions and explore…

Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures…

High dimensional and heterogeneous count data are collected in various applied fields. In this paper, we look closely at high-resolution sequencing data on the microbiome, which have enabled researchers to study the genomes of entire…

Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…

Population-based structural health monitoring (PBSHM), aims to share information between members of a population. An offshore wind (OW) farm could be considered as a population of nominally-identical wind-turbine structures. However, benign…

A Random Graph is a random object which take its values in the space of graphs. We take advantage of the expressibility of graphs in order to model the uncertainty about the existence of causal relationships within a given set of variables.…