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}) ?