Basin-volume notes

probability distribution

The end result of this project will be a series of volumes sampled from an unknown probability distribution. We want to determine what that distibution will be. We will have a functional form for that distribution \(P(V | \theta )\) where \(\theta\) are the unknown parameters of the distibution. In the past we’ve used a generalized Gaussian. \(P(V | \theta)\) is the biased distribution, so it will be the generalized gaussian times \(V\). This is mostly taken from

There are several ways to determine what the values of \(\theta\) should be. None of which involve histogramming.

maximum likelihood method

The likelihood is the joint probability di