Related papers: On the Connection between Field-Level Inference an…
Nonparametric Bayesian approaches provide a flexible framework for clustering without pre-specifying the number of groups, yet they are well known to overestimate the number of clusters, especially for functional data. We show that a…
We analyze the consequences of models of structure formation for higher-order ($n$-point) galaxy correlation functions in the mildly non-linear regime. Several variations of the standard $\Omega=1$ cold dark matter model with…
Widefield surveys of the sky probe many clustered scalar fields -- such as galaxy counts, lensing potential, gas pressure, etc. -- that are sensitive to different cosmological and astrophysical processes. Our ability to constrain such…
Optimal estimation of signal amplitude, background level, and photocentre location is crucial to the combined extraction of astrometric and photometric information from focal plane images, and in particular from the one-dimensional…
The next generation of galaxy surveys will provide highly accurate measurements of the large-scale structure of the Universe, allowing for more stringent tests of gravity on cosmological scales. Higher order statistics are a valuable tool…
The light we receive from distant astrophysical objects carries information about their origins and the physical mechanisms that power them. The study of these signals, however, is complicated by the fact that observations are often a…
Bayesian clustering typically relies on mixture models, with each component interpreted as a different cluster. After defining a prior for the component parameters and weights, Markov chain Monte Carlo (MCMC) algorithms are commonly used to…
The space of human goals is tremendously vast; and yet, from just a few moments of watching a scene or reading a story, we seem to spontaneously infer a range of plausible motivations for the people and characters involved. What explains…
Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…
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…
The Lyman-alpha forest provides strong constraints on both cosmological parameters and intergalactic medium astrophysics, which are forecast to improve further with the next generation of surveys including eBOSS and DESI. As is generic in…
Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In…
We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over…
The absence of self averaging in mesoscopic systems is a consequence of long-range intensity correlation. Microwave measurements suggest and diagrammatic calculations confirm that the correlation function of the normalized intensity with…
We present a Bayesian hierarchical framework for a principled data analysis pipeline of peculiar velocity surveys, which makes explicit the inference problem of constraining cosmological parameters from redshift-independent distance…
Clustering attempts to partition data instances into several distinctive groups, while the similarities among data belonging to the common partition can be principally reserved. Furthermore, incomplete data frequently occurs in many…
In order to extract maximal information about cosmology from the large-scale structure of the Universe, one needs to use every bit of signal that can be observed. Beyond the spatial distributions of astronomical objects, the spatial…
A comprehensive artificial intelligence system needs to not only perceive the environment with different `senses' (e.g., seeing and hearing) but also infer the world's conditional (or even causal) relations and corresponding uncertainty.…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…
We present a Bayesian hierarchical modelling approach to infer the cosmic matter density field, and the lensing and the matter power spectra, from cosmic shear data. This method uses a physical model of cosmic structure formation to infer…