# Characterize distribution of the output of probabilistic model

Dataset: each row is a patient. Categorical covariates $x$ (often with many categories) include patient information, one binary outcome variable indicating survival.

Background: I fitted a probabilistic model to the data described above in order to calculate the probability of survival. I then calculated with the fitted model the probability of survival for each sample $P(survival|x)$ in the dataset and plotted the distribution of this estimated probability. The distribution has many peaks (see attached picture).

Question: I would like to "characterize" the peaks of the distribution. The outcome of this characterization* would be a statistical description of each peak. Is this achievable with existing statistical methods?

Example: The outcome of one such characterization would be

• Peak 1: Samples in this peak have mostly diag_1_4 either equal to 4,5,6 and are men (not shown)
• Peak 2: Samples in this peak have mostly diag_1_4 either equal to 0,8,NA and are women (not shown)
• Peak 3: Samples in this peak have mostly diag_1_4 either equal to 1,2,3 and are unemployed (not shown)

My approach so far: For each covariate, I have stratified the distribution of estimated survival risk according to each level of the covariate (see attached picture). By visual inspection I could Identify some covariates that seemed to explain the observed peaks. In the attached picture one can see that the peaks seem to be explained by the diag_1_4 covariate.

* I know my description of "characterization" is vague. Probably part of the solution is to define exactly what I mean with "characterization". Any help with this definition is welcome!