P (theta | data) = P (data | theta) * P (theta) / P (data)
where
data = observations in nature,
theta = tweakable parameters of an underlying model which is implicitly assumed (but can be made explicit by adding an "M" random variable to the equation above).
To understand the equation above, consider the following background information:
- P (theta) is called the "prior" -- it is the prior probability of the theta parameters. It can be our prior belief of what those parameters should be.
- P (data | theta) is called the "likelihood" -- it is the likelihood of the data given a set of theta parameters.
- P (theta | data) is called the "posterior" -- it is the updated probability of the parameters in light of the data. In essence, we update our beliefs after seeing some data.
- P (data) is sometimes called "evidence" -- we can ignore it since it is just a normalization factor.
So we can rewrite our equation above ("~" means " approximates"):
Posterior ~ Likelihood * Prior
Now you may ask, "What does this have to do with one's views on the origins of life?" Stay tuned for the next post, since I am still in the process of formulating my ideas.