Sequential Monte Carlo

$$ \mathbb{P}(X > \gamma) = \mathbb{P}(X > \gamma_1) \mathbb{P}(X > \gamma \mid X > \gamma_1) $$

for $\gamma_1 < \gamma$.

Want to solve

$$ \ell = \mathbb{P}(M > \gamma) $$

for $M = \max\{ X_1, X_2 \}$ where $X_1, X_2 \overset{\mathrm{i.i.d.}}{\sim} \mathsf{Pareto}(\alpha, \lambda)$, $\gamma=1$.

Once Loop Reflect

Once Loop Reflect