Hi, it is my first topic in this forum.

I’m trying **to calculate the posterior mean** with likelihood and prior distribution conjugate.

i have generated the data from N(23,10), and so i know the true standard deviation of the generator process. this sample is generated with R

i have set the prior distribution of theta like N(0,100) and the likelihood like N(\theta,10). the stan script is here.

the theory to calculate the posterior variance said that

$$\sigma_{pos}=( \frac{1}{\sigma_0}+ \frac{N}{\sigma} )^{-1}$$

i have done a script in R to calculate this, but **the variance of generated sample theta is different by the theoretical variance calculated with formula**

Can anyone help me to understand why the variance are different?

thanks for your help

Variance.R (1.3 KB)

Modello.Stan (198 Bytes)