Date: 7 March 2012
Time: 13.00-14.00
Place: NJ14 3-228 (Las Vegas)
When people are first exposed to statistics, they usually learn about (un)biased estimators, confidence intervals, and p-values. These concepts (and several others) have their roots in the statistical school called classical statistics or sampling theory, and they are widely used
inference tools among students and researchers. However, the inference results obtained by classical statistics are not always sensible and are often misinterpreted.
This talk aims at demonstrating some of the problems with classical statistics and how these problems can be avoided by using Bayesian statistics instead. In particular, we consider three simple examples which are described below.
- Point Estimation: Are optimal estimators always unbiased?
Case: If you observe N IID samples from a Gaussian distribution with unknown mean and variance, what is the best way to estimate the variance? - Interval Estimation: How you should NOT interpret a confidence interval.
Case: If you observe N IID samples from a uniform distribution with unknown mean but known width, how do you find and interpret a confidence interval for the mean?> - Hypothesis testing: p-values depend on irrelevant information.
Case: If you observe the sequence HHHTHHHHTHHT of IID coin flips, do you accept or reject the hypothesis that the coin is unbiased?
We also briefly comment on the (mostly practical) problems of Bayesian statistics and give a few real world simulation examples demonstrating its usefulness.
Bio
Jesper Kjær Nielsen was born in Struer, Denmark, in 1982. He received the B.Sc and M.Sc (Cum Laude) degrees in electrical engineering from Aalborg University, Aalborg, Denmark, in 2007 and 2009, respectively. He is currently with the Department of Electronic Systems, Aalborg University, as a Ph.D. student. He has been a Visiting Scholar at the Signal Processing and Communications Laboratory, University of Cambridge and at the Department of Computer Science, University of Illinois at Urbana-Champaign. His research interests include spectral estimation, (sinusoidal) parameter estimation as well as statistical and Bayesian methods for signal processing.