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With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already…
This perspective chapter briefly surveys: (1) past growth in the use of Bayesian methods in astrophysics; (2) current misconceptions about both frequentist and Bayesian statistical inference that hinder wider adoption of Bayesian methods by…
There has been increasing interest by cosmologists in applying Bayesian techniques, such as Bayesian Evidence, for model selection. A typical example is in assessing whether observational data favour a cosmological constant over evolving…
We describe a hierarchical Bayesian approach for inference about a parameter $\theta$ lower-bounded by $\alpha$ with uncertain $\alpha$, derive some basic identities for posterior analysis about $(\theta,\alpha)$, and provide illustrations…
The level set approach has proven widely successful in the study of inverse problems for interfaces, since its systematic development in the 1990s. Recently it has been employed in the context of Bayesian inversion, allowing for the…
The peculiar motion of the host galaxies introduces bias in estimating cosmological parameters from supernova data. The coherent component of the peculiar motion is usually corrected for using velocity field reconstruction based on the…
An important task for any large-scale organization is to prepare forecasts of key performance metrics. Often these organizations are structured in a hierarchical manner and for operational reasons, projections of these metrics may have been…
We present a comprehensive comparison of different Markov Chain Monte Carlo (MCMC) sampling methods, evaluating their performance on both standard test problems and cosmological parameter estimation. Our analysis includes traditional…
Observed data is often contaminated by undiscovered interlopers, leading to biased parameter estimation. Here we present BEAMS (Bayesian Estimation Applied to Multiple Species) which significantly improves on the standard maximum likelihood…
Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…
Cosmological probes pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters which characterize the underlying physical system -- our Universe. Modern…
Cosmological parameter estimation from forthcoming experiments promise to reach much greater precision than current constraints. As statistical errors shrink, the required control over systematic errors increases. Therefore, models or…
The standard Bayesian model formalism comparison cannot be applied to most cosmological models as they lack well-motivated parameter priors. However, if the data-set being used is separable then it is possible to use some of the data to…
A range of Bayesian tools has become widely used in cosmological data treatment and parameter inference (see Kunz, Bassett & Hlozek (2007), Trotta (2008), Amendola, Marra & Quartin (2013)). With increasingly big datasets and higher…
We define an optimal basis system into which cosmological observables can be decomposed. The basis system can be optimised for a specific cosmological model or for an ensemble of models, even if based on drastically different physical…
These lecture notes delve into field-level inference, a framework offering a robust way to extract more information and avoid biases compared to traditional methods for cosmological data analysis. The core idea is to analyse uncompressed…
Type Ia supernovae (SNae Ia), standardisable candles that allow tracing the expansion history of the Universe, are instrumental in constraining cosmological parameters, particularly dark energy. State-of-the-art likelihood-based analyses…
We apply two Bayesian hierarchical inference schemes to infer shear power spectra, shear maps and cosmological parameters from the CFHTLenS weak lensing survey - the first application of this method to data. In the first approach, we sample…
Markov Chain Monte Carlo based Bayesian data analysis has now become the method of choice for analyzing and interpreting data in almost all disciplines of science. In astronomy, over the last decade, we have also seen a steady increase in…
We present a Bayesian hierarchical framework to analyze photometric galaxy survey data with stellar population synthesis (SPS) models. Our method couples robust modeling of spectral energy distributions with a population model and a noise…