State Model FAQ

State Model Help

This guide from the intro to POMP is very useful in understanding state based models. Getting Started with pomp

Some Term Definitions

Particle Filtering

Particle filters are methods for approximating intractable likelihoods for time series. The gist of it is that we generate examples of what the population could have been doing at each time step and then follow those examples through time, dropping particles that wander into implausible dynamics and replacing them with better ones. If we average over all the particles during a given step of a time series, we can estimate the likelihood associated with that step, and then we can combine all the steps to get a Monte Carlo estimate of the total likelihood.

Adaptive Nonlinearities

whether the model can figure out what functional form to use or if we have to assign it ourselves (e.g. we could manually evaluate a few options like log-transforming, squared terms, etc., but a something like a neural network can use the data to select a locally optimal form)

Tractable/intractable likelihood

The likelihood function describes the probability of observing the data under a specific model and set of parameters. Tractable likelihoods can be calculated easily. So, the likelihood of 10 heads and 10 tails is .5^10 * .5^10 for a fair coin, and might be .2^10 * .8^10 for a biased coin.

When things are independent and all the important bits are observed without error, likelihoods tend to be tractable. But the population dynamics might not follow those rules. Maybe the population spiked and crashed 5 times between observations. Maybe it stayed constant the whole time. Maybe it did something else. Calculating the likelihood exactly would require integrating over ​all​ of those possibilities, which is generally intractable.