Question about Effective Sample Size Formulation from Bayesian Data Analysis 3rd edition


#1

Hello,
I have an embarrassingly simple question regarding the example for Effective Sample Size calculation.

In BDA, the the first paragraph of section 11.5 states n is the number of simulation draws and m is the number of sequences.
In the last paragraph of the section (on page 287) the following is stated (Bold for emphasis)

All these calculations should be performed using only he saved iteration, after discarding the warm-up period
For example suppose we simulate 4 chains, each of length 1000 and then discard the first half of each as warm-up
Then m=8 and n=250

Why is it that m is not 4 and n is not 500 (1000 - 500 warm-up)? In other words I’m struggling to understand where the values of 4 and 250 came from.

Thank you in advance


#2

See p. 284 section “Splitting each saved sequence into two parts” . The last paragraph of that section states

For example, suppose we simulate 5 chains, each of length 1000, and then discard the
first half of each as warm-up. We are then left with 5 chains, each of length 500, and we split
each into two parts: iterations 1–250 (originally iterations 501–750) and iterations 251–500
(originally iterations 751–1000). We now have m = 10 chains, each of length n = 250.


#3

Everything makes sense now! Thank you for the quick and helpful answer