6.1 Motivation for approximations
- Remember we are trying to compute the posterior distribution:
f(θ|y)=f(θ)L(θ|y)f(y)
In previous examples (conjugate priors) we were able to do this analytically
Numerator - no issue, we specify these distributions.
Denominator - Can be difficult or intractable to compute the denominator f(y) !
f(y)=∫θ1∫θ2...∫θkf(θ)L(θ|y)dθk...dθ1dθ2
- Solution? Approximate the posterior via simulation!