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Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…
We present a new blind formulation of the Cosmic Microwave Background (CMB) inference problem. The approach relies on a phenomenological model of the multi-frequency microwave sky without the need for physical models of the individual…
In astronomical and cosmological studies one often wishes to infer some properties of an infinite-dimensional field indexed within a finite-dimensional metric space given only a finite collection of noisy observational data. Bayesian…
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…
Following the discovery of the brightest high-energy neutrino sources in the sky, the further detection of fainter sources is more challenging. A natural solution is to combine fainter source candidates, and instead of individual…
Using the Bayesian theory of model comparison, a new cosmological model due to John and Joseph [M. V. John and K. Babu Joseph, Phys. Rev. D 61, 87304 (2000)] is compared with the standard \Omega_{\Lambda} \neq 0 cosmological model. Their…
We perform a cosmographic analysis using several cosmological observables such as the luminosity distance moduli, the volume distance, the angular diameter distance and the Hubble parameter. These quantities are determined using different…
We present a strategy for a statistically rigorous Bayesian approach to the problem of determining cosmological parameters from the results of observations of anisotropies in the cosmic microwave background. Our strategy relies on Markov…
We discuss the constraints one can place on cosmological parameters using current cosmic microwave background data. A standard $\chi^2$--minimization over band--power estimates is first presented, followed by a discussion of the more…
The Atacama Large Millimeter/submillimeter Array with the planned electronic upgrades will deliver an unprecedented amount of deep and high resolution observations. Wider fields of view are possible with the consequential cost of image…
Inverse optimization (IO) is used to estimate unknown parameters of an optimization model from observed decisions. In the data-driven context, the estimated parameters are inherently uncertain, yet quantifying this uncertainty has received…
Using mock data for the Hubble diagrams of type Ia supernovae (SNIa) and quasars (QSOs) generated based on the standard model of cosmology, and using the least-squares method based on the Markov-Chain-Monte-Carlo (MCMC) algorithm, we first…
Star-galaxy classification is one of the most fundamental data-processing tasks in survey astronomy, and a critical starting point for the scientific exploitation of survey data. For bright sources this classification can be done with…
The ratio of Bayesian evidences is a popular tool in cosmology to compare different models. There are however several issues with this method: Bayes' ratio depends on the prior even in the limit of non-informative priors, and Jeffrey's…
Supernova cosmology without spectra will be an important component of future surveys such as LSST. This lack of supernova spectra results in uncertainty in the redshifts which, if ignored, leads to significantly biased estimates of…
Determining the physical characteristics of a star is an inverse problem consisting in estimating the parameters of models for the stellar structure and evolution, knowing certain observable quantities. We use a Bayesian approach to solve…
We introduce a Markov Chain Monte Carlo simulation and data analysis package that extends the CMBEASY software. We have taken special care in implementing an adaptive step algorithm for the Markov Chain Monte Carlo in order to improve…
It is often of interest to combine available estimates of a similar quantity from multiple data sources. When the corresponding variances of each estimate are also available, a model should take into account the uncertainty of the estimates…
Motivated by the increasing use of and rapid changes in array technologies, we consider the prediction problem of fitting a linear regression relating a continuous outcome $Y$ to a large number of covariates $\mathbf {X}$, for example,…