Bayasian Analyses of Macroevolutionary Mixtures

Brief concepts to Bayesian statistics

Briefly, Bayesian statistical methods compute a probability distribution of parameters (posterior) in a statistical model, using data and the previous knowledge (prior) about the parameters (unknown quantity of interest in a study).

For example, if we are interested in determining the size of a population, abundance is the parameter of interest. In a simple regression analysis, the slope and intercept of the regression line are the two parameters of interest.

When there are multiple parameters in an analysis, the posterior distribution of the parameters is called the joint posterior distribution (or joint posterior).

We can apply this concept to statistical models, where we describe the relationship between the parameters and data.

Using these models, we can summarize the stochastic process which produced the data, i.e. likelihood function (because it is used to compute which values of the parameters of the model are most likely to have produced the data we have observed).