Bayesian (stupid) Stats: Flashcards
(11 cards)
What are Bayesians ABCs?
- Take a guess of your parameter
- Generate simulate data from the guess using a model
- Compare the simulated data to you real data. Does it match? Yes - store this guess as a success, no - throw that guess away
Repeat 1-3 A LOT - Look at the distribution of your success
What is an a priori distribution?
The distribution of the parameter -> what we know before the inference
What is the likelihood distribution?
How likely it is to observe our real data given a value of the parameter. This does not depend on the prior.
What is the posterior distribution?
A combination of the likelihood and the prior. It is the probability of the parameter given the data and the prior.
What are three ways of drawing a prior distribution?
Uninformative, empirical, subjective
What are the benefits and disadvantages of an uninformative prior?
Assume almost nothing, which is good if you know nothing, but make a big parameter space quickly
What are the benefits and disadvantages of an empirical prior distribution?
Allows you to incorporate knowledge and decreases the size of the parameter space, but becomes a weighting game and your assumptions may be wrong
What is a generative model (MCMC)?
It compares the likelihood of current position to likelihood of old position and then makes a move according to a set of riles.
What is the benefit of an MCMC?
It is an effective way of exploring the parameter space, by moving towards areas of higher likelihood and recording parameter values to draw posteriors.
What does a successful MCMC trace look like?
A fat, hairy caterpillar
Why is this trace indicating a successful MCMC run?
Uniform
No trends
Covers the full range of values
Indicates good mixing and convergence
It does not have the initial burn-in period (exploration)
