I am interested in learning about my son’s cell phone use. Suppose the mean number of text messages that he sends and receives per day is equal to

How do I construct a prior density on

There are two distinct ways of assessing your prior. One can think about plausible values of the mean number of daily text messages

Personally, I think it is easier to think about the number of text messages

If one matches my guesses with these expressions, one can show

To see if these values make any sense, I plot my predictive density. This density is a special case of a negative binomial density where (using the R notation)

size = a, prob = b /(b + 1).

I graph using the following R commands. One can compute P(5 <= y <= 15) = 0.89 which means that on 89% of the days, I believe Steven will send between 5 and 15 messages.

a = 44.4; b = 4.4

plot(0:30,dnbinom(0:30,size=a,prob=b/(b+1)),type=”h”,

xlab=”y”, ylab=”Predictive Prob”, col=”red”, lwd=2)