Related papers: Inferring the shape of data: A probabilistic frame…
Focusing on a specific crowd dynamics situation, including real life experiments and measurements, our paper targets a twofold aim: (1) we present a Bayesian probabilistic method to estimate the value and the uncertainty (in the form of a…
Mathematical models are invaluable for understanding and predicting how biological systems behave, although their construction requires specifying mechanisms and relationships that are often not perfectly known. In the presence of multiple…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
Design of experiments has traditionally relied on the frequentist hypothesis testing framework where the optimal size of the experiment is specified as the minimum sample size that guarantees a required level of power. Sample size…
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…
This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…
Forecasting techniques for assessing the power of future experiments to discriminate between theories or discover new laws of nature are of great interest in many areas of science. In this paper, we introduce a Bayesian forecasting method…
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…
In any other circumstance, it might make sense to define the extent of the terrain (Data Science) first, and then locate and describe the landmarks (Principles). But this data revolution we are experiencing defies a cadastral survey. Areas…
Shape information is of great importance in many applications. For example, the oil-bearing capacity of sand bodies, the subterranean remnants of ancient rivers, is related to their cross-sectional shapes. The analysis of these shapes is…
A population quantity of interest in statistical shape analysis is the location of landmarks, which are points that aid in reconstructing and representing shapes of objects. We provide an automated, model-based approach to inferring…
Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of…
Incorporating shape information is essential for the delineation of many organs and anatomical structures in medical images. While previous work has mainly focused on parametric spatial transformations applied on reference template shapes,…
Bayesian nonparametric models offer a flexible and powerful framework for statistical model selection, enabling the adaptation of model complexity to the intricacies of diverse datasets. This survey intends to delve into the significance of…
Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model's…
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…
We present a general probabilistic formalism for cross-identifying astronomical point sources in multiple observations. Our Bayesian approach, symmetric in all observations, is the foundation of a unified framework for object matching,…
Current theories of perception suggest that the brain represents features of the world as probability distributions, but can such uncertain foundations provide the basis for everyday vision? Perceiving objects and scenes requires knowing…