Prof. David van Dyk (Imperial) will give gave a series of three lectures on Bayesian methods for Astronomy during February.
Bayesian statistical methods are becoming ever more popular in astronomy. The clear mathematical foundations on which Bayesian methods are based allow researchers to design statistical models that directly account for complexities in physical sources, instrumentation, and data collection, while providing a straightforward way to combine multiple information sources and/or data streams. On the other hand, Bayesian method require "prior distributions" to be specified on all unknown parameters and fitting complex Bayesian statistical models (e.g., computing parameter estimates and their uncertainties) requires sophisticated computational techniques such as Markov chain Monte Carlo (MCMC).
This course will review the mathematical foundations of Bayesian methods, discuss techniques for specifying prior distributions, and study computational techniques including MCMC. Particular attention will be paid to Bayesian multi-level models- statistical models with multiple levels of structure. These models have wide applicability in astronomy and astrophysics because information is often available on multiple "levels" that allow complex models to be represented as a sequence of simple sub-models. Hierarchical models are a particular type of multi-level model that describe a population of objects (stars, pixels, etc.) with object-level parameters following a common distribution (specified in a lower level of the multi-level model). In the course we will discuss how Bayesian hierarchical models facilitate a concept called "shrinkage," which can produce better estimates of the parameters describing the objects in populations than can simple object-by-object estimators. We will demonstrate advantages of using multi-level/hierarchical models and shrinkage estimators via examples from cosmology.
This short course will be delivered in three parts.
David van Dyk is a Professor of Statistics in the Mathematics Department at Imperial College London. After obtaining his PhD from the University of Chicago, he held academic positions at Harvard University and the University of California, Irvine before relocating to London in 2011. Professor van Dyk is an elected Fellow in the American Statistical Association (2006), the Institute of Mathematical Statistics (2010), and the International Astrostatistics Association (2016). His scholarly work focuses on methodological and computational issues involved with Bayesian analysis of highly structured statistical models and emphasizes interdisciplinary research, especially in astrophysics, solar physics, and high-energy physics. He helped found and coordinates the CHASC International Astrostatistics Center and has made numerous contributions to statistical methods used in astrophysics, including Bayesian spectral and image analysis of high-energy observations, properly calibrated methods for source and feature detection, techniques for accounting for calibration uncertainty, the analysis of color-magnitude diagrams, source classification, population studies that account for selection effects, methods to probabilistically disentangle overlapping sources, Bayesian estimates of the time delays among gravitationally lensed sources, among other topics.
David van Dyk (d . van-dyk @ imperial . ac . uk) Vinay Kashyap (vkashyap @ cfa . harvard . edu) Aneta Siemiginowska (asiemiginowska @ cfa . harvard . edu)
