Approximate Bayesian Computation in Insurance
Patrick J. Laub and Pierre-Olivier Goffard
Just accepted to Insurance: Mathematics and Economics
Just pushed the package approxbayescomp to pip
Statistics with Likelihoods
For simple models we can write down the likelihood.
When simple rv's are combined, the resulting thing rarely has a tractable likelihood.
$$ X_1, X_2 \overset{\mathrm{i.i.d.}}{\sim} f_X(\,\cdot\,) \Rightarrow X_1 + X_2 \sim ~ \texttt{Intractable likelihood}! $$
Usually it's still possible to simulate these things...
Approximate Bayesian Computation
Example: Flip a coin a few times and get \((x_1, x_2, x_3) = (\text{H, T, H})\); what is
\pi(\theta | \boldsymbol{x}) ?
