Simulation and Inference - Two Sides of the Same Coin
Today's measurement devices have literally opened up entire new worlds for us to explore. Recent satellite measurements of the Cosmic Microwave Background (CMB) are able to not only detect, but map out in great detail, details of the universe in its infancy. Many other astrophysical processes of interest after "last scattering" are also being probed from a variety of space or ground based platforms. Each of these instruments return observations with their own unique insight into the universe we want to understand, as well as their own peculiar response to the signal they are deigned to detect. As a result, we are faced with the increasingly important challenge of attempting to analyze and interpret observations from a wide variety of instruments to form a coherent view of the universe. How can we make inferences about our universe from observations returned from a diverse collection of instruments spanning a wide range of frequencies and spatial scales? In this review, we will discuss a general, Bayesian, approach to ANY model based problem of inference - it is general and automatic, and only requires one to think about how to get a computer to simulate what is being measured - inference given actual observations follows literally "automatically" - in principle. This talk will review applications of this framework to CMB analysis but also demonstrate how to formulate inference for a wide range of other problems including state estimation for noisy observations of nonlinear dynamical systems.