Graduate Seminar

Location:  RI 209

Speaker: Nabahel Rex-Oneal

PhD Student supervised by Dianliang Deng

Title: Bounded Counts on the Boundary: Telling Structural Mass Apart from Small Samples

 Abstract:

Many datasets record a count of successes out of a known number of tries: how many people in an age group are immune to a virus, how many insects on a leaf survive a treatment, how many patients with a condition record a positive outcome. Often an unusual number of units score none of them, or all of them. Such extremes can arise for two entirely different reasons. A unit may genuinely belong to a different state, or it may be a perfectly ordinary unit that happened to land on an endpoint because only one or two tries were observed. The two are indistinguishable in the raw frequencies, yet they imply very different conclusions.

This talk introduces the Zero–One Inflated Beta–Binomial model, which keeps the sample sizes in the likelihood and carries explicit probability masses at both endpoints, so that the two explanations can be separated and each can be measured. I will describe the construction and its properties, how the model is fitted, and what it says about two datasets — confirming genuine inflation in one and ruling it out in the other. I will close with the problem I am working on now: what happens when the same units are observed repeatedly over time. No background beyond a first course in probability is assumed for the first half of the talk.