Bayesian methods Flashcards
Compared to Baysian methods, what are the problem with traditional statistics
- falsification (Popper)/ null hypothesis testing
- independent of alternative hypothesis
- ‘significance’ vs. sample size
- ‘significance’ vs. practical significance
- …(publication bias, effect sizes bias, false negatives common, false positives hard to correct, inflexible, limited models, …)
- ‘the emperor’s New Clothese’
widely used and accepted, esp in non-science objects
but: the word is out ‘he has nothing on’
advantage of baysian methods
flexibility
multiple models
not just significance
also: estimation
interface btw different types of models
decision (Baysian decision theory, utility function), prediction, moments
philosophical advantages
What are the problems with Popperian falsification
the magical appearance of hypothesis
not noise resistant, biases
What should be taken care when use a Bayesian prediction
- don’t use the ‘best model’
2. integrate across all models, with the appropriate probability
How to compare and decide with Baysian model is better
Occam’s razoe:
of equally good models, prefer the simpler
BUT: what if they are not equally good?
AND: what is ‘simple’ anyway
need for a numerical comparison
‘compression of space of possibilities given your data
Treat hypothesis as a parameter
State Bayers’ rule. Which part is posterior? Which part is likelihood? Which part is prior? Which part is evidence?
P(A given B)= P(B given A) * P(A) / P(B)
P(A given B) is the posterior
P(B given A) is the likelihood
P(A) is the prior
P(B) is the evidence
What is binomial distribution
How many out of n?
What is Poisson distribution?
How many out of many
What is geometric distribution
How many times do I get away with it?
How many times can the event happen before I fail to get this result?
E.g., How many round of Russian Roullite before dying
What is Cauchy distribution
Shooting in random directions, where do I hit the wall?
what is the probability of occurrence of a particular event in a random situation?
