22 Lecture 13 - 2019
22.2 Poisson
Binomial events with N trials large/unknown and probability of event is small
Poisson with varied exposure/offset
22.3 Generalized linear madness
Example of oceanic tool complexity
Modeled with a poisson link
The model outcomes are terrible - though they fit the data, the intercepts don’t pass through origin
Wouldn’t we expect zero population = zero tools?
Solution is a scientific model
22.4 Scientific model
The relationship can be thought of as a change in tools per unit time
Change in time = alpha P ^ beta
Alpha: innovation rate, P: population per person = each person has some change of inventing something
Beta: diminishing returns, saturation effect, “someone else will invent it for you”
TODO: read more about this, highlight it, etc
The resulting model using this function based in the scientific model is not perfect, but meanings are clearer, the intercept actually goes through 0
This is an ad hoc function, not a link
22.5 Survival analysis
Estimate rates by modeling time-to-event
Can’t ignore censored cases
- Left censored: don’t when when time started
- Right censored: something else cut off end
Example cats
Time to adoption for observed adoptions is simplest, an exponential function
For censored cats
- use the cumulative distribution
- take the complement
- calculate probability no event yet
22.7 Mixtures
Blends of stochastic processes
eg. varying means, probabilities, rates
eg. zero-inflation, hurdles
Example monks
Number of manuscripts per day
Can we infer the number of days they get drunk?
Drunkenness is a hidden state
There is a probability that they drink or work, and within the work, a probability that they produce 0 or 1+ manuscripts