NCRA Astronomy Seminar

Speaker  :  Mihir Arjunwadkar (Centre for Modelling and Simulation, University of Pune)
Title :  Nonparametric Inference for the Cosmic Microwave Background

Abstract:
The  cosmic microwave  background  (CMB), which  permeates the  entire Universe, is the radiation left over from just 380,000 years after the Big Bang.  Fluctuations in  the CMB over  small length  scales provide clues to  the Universe's structure  and composition shortly  after the Big Bang.   These clues are critical for  testing cosmological models. Cosmologists often summarize these fluctuations through what is called the  power   spectrum,  which essentially  gives  the   variance  of fluctuations  as a  function of  multipole moment.   The shape  of the power  spectrum, and  in particular  the  location and  height of  its peaks, relates directly to parameters in cosmological models.  Thus, a critical statistical  question is how accurately can  this spectrum be estimated.

Traditionally, cosmologists have used, almost exclusively, model-based parametric statistical  methods -- e.g.,  likelihood-based or Bayesian -- for  this  problem.   I  will first  describe  a  model-independent nonparametric method for estimating a function from data together with confidence  set  around  the  fit.   I  will  then  describe  our  own comparative  analysis  of  the  WMAP (Wilkinson  microwave  anisotropy probe) 1-, 3-, 5-, and 7-year data using this methodology.