SLIDE 6 Maximum likelihood
How will the frequentist estimate the parameter? Answer: maximum likelihood.
Basic idea
Our best estimate of the parameter(s) are the one(s) that make our observed data most likely. We know what we have
- bserved so far (our data). Our best “guess” would therefore
be to select parameters that make our observations most likely. Binomial distribution: P(Y = y) = n y
Slide 10— PhD (Aug 23rd 2011) — Frequentist and Bayesian statistics
Bayesians
Each investigator is entitled to his/hers personal belief ... the prior information. No fixed values for parameters but a distribution. All distributions are subjective. Yours is as good as mine. Can still talk about the mean — but it is the mean of my distribution. In many cases trying to circumvent by using vague priors. Thumb tack pin pointing down:
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Theta Prior distribution
Slide 11— PhD (Aug 23rd 2011) — Frequentist and Bayesian statistics
Credibility intervals
Bayesians have an altogether different world-view. They say that only the data are real. The population mean is an abstraction, and as such some values are more believable than others based on the data and their prior beliefs.
Slide 12— PhD (Aug 23rd 2011) — Frequentist and Bayesian statistics
