Monday, November 30, 2009

Probability and age

My birthday is just around the corner. It's a time for family, fun, and cake -- lots of cake. It is also a time for a quick look at the CSO mortality tables (available online).

The tables -- used in insurance and other areas -- provide a value that reflects deaths per 1000 policy holders, depending on age, sex, and smoking status. With little difficulty, I found my value.

Luckily, I am still at a less than 1 death per 1000 mortality rate ... whew ...

Nevertheless, a question remains: What is my probability of dying within the next 12 months?

Is the answer simply the rate found on the table for male, nonsmokers (blended rate since the age in the table is an issue age, which changes six months before the actual date of birth)?

The answer depends on your view of probability. If you take the standard view of probability, your answer is yes -- the rate is my probability of dying. If you take a frequency view of probability, your answer would be much different. You would state that my probability of dying is either 100% or o%. And we will not know the answer until the year is over (though God knows now).

Is this just esoteric nonsense? Not at all. Your view of probability drives how you perceive statistical conclusions. It helps you separate the statistical chaff from the statistical wheat

Note: I take a frequentist view of probability. So I'll let you know next year what my actual qx (mortality rate) was for this year. Or, just maybe, I won't.

No comments: