Bayesian Reasoning: Gender Inference from a Specimen Measurement

Imagine that we have a population of something composed of two subset populations that, while distinct from each other, share a common characteristic that can be measured along some kind of scale. Furthermore, let’s assume that each subset population expresses this characteristic with a frequency distribution unique to each. In other words, along the scale of measurement for the characteristic, each subset displays varying levels of the characteristic among its members. Now, we choose a specimen from the larger population in an unbiased manner and measure this characteristic for this specific individual. Are we justified in inferring the subset membership of the specimen based on this measurement alone? Baye’s rule (or theorem), something you may have heard about in this age of exploding data analytics, tells us that we can be so justified as long as we assign a probability (or degree of belief) to our inference. The following discussion provides an interesting way of understanding the process for doing this. More importantly, I present how Baye’s theorem helps us overcome a common thinking failure associated with making inferences from an incomplete treatment of all the information we should use. I’ll use a bit of a fanciful example to convey this understanding along with showing the associated calculations in the R programming language.