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)=θ1θ2...θkf(θ)L(θ|y)dθk...dθ1dθ2

  • Solution? Approximate the posterior via simulation!