# What's the meaning of a posterior inclusion probability in Bayesian?

I received a script from a friend and at the end, he's keeping the values that agree to a certain threshold for the Posterior inclusion probability (PIP).

(This is coming from a GEMMA analysis calculating the effect of SNPs to explain the variance in phenotypes)

pip01       <- para.mean[which(para.mean$gamma >= 0.01),] # snps with gamma (i.e. PIP) > 0.01 pip10 <- para.mean[which(para.mean$gamma >= 0.10),] # gamma > 0.10
pip50       <- para.mean[which(para.mean\$gamma >= 0.50),] # gamma > 0.50


I'm wondering what does this mean. How can we put a posterior inclusion probability in a sentence?

Is it like, I'm 99% confident that the values that I extracted (with a pip greater than 0.01) are "significantly" having an effect?

Here is a definition of PIP:

First we calculate the posterior inclusion probability, which is the sum of all posterior probabilities of all the regressions including the specific variable (regressor). The posterior inclusion probability is a ranking measure to see how much the data favors the inclusion of a variable in the regression

In Kruschke's book:

It is the proportion of steps in the overall MCMC chain that include the predictor

Also:

While the overall inclusion probabilities provide a di erent perspective on the predictors than individual models, be careful not to think that the marginal inclusion probabilities can be multiplied to derive the model probabilities.

So is it similar to model averaging? Why talking about "individual models" in the above commentary?

• I don't think the model is using inclusion the way I do in the book, Doing Bayesian Data Analysis. When I talk about inclusion probability, I'm referring to a discrete parameter, with values 0 or 1, that marks whether or not another parameter (such as a regression coefficient) is included in a model. There is no thresholding of a continuous parameter! Jan 23, 2017 at 19:17