Week 10 Flashcards
Lecture 28
Bayesian inference
Difference between frequentist and Bayesian
Comes down to probability
Freq: when number of experiments goes to infinity (assumes you can do large number of trials the same) REPEATABILITY is key
Bayesian: degree of belief about an event
Prove Bayes theorem
Here P(A,B) is P(A n B)
What to do if marginal probability is not available but needed
Def Bayesian parametric model
Change in notation from freq to Bayesian
As θ is a RV therefore f(x|θ) is now a distribution
Interpretation of prior dist
Represents the uncertainty about the (true value of) the parameter θ
Multi variate prior
The prior has to be
Fully specified, hyper parameters (params of prior) must be fully specified
Actualisation principle
Aka Bayes update
1) use prior dist
2) collect data
3) posterior dist
Def posterior dist
Posterior distribution analog in frequentist
Likelihood function
Prove posterior dist
Derive posterior dist using Bayes theorem
Lecture 29
Started around 2cards ago