Approximating small probabilities using importance sampling

Update Oct 14, 2019: Michael Höhle caught a mistake and notified me on Twitter. Thanks! The problem is that I used \(\text{Unif}(-10, 10)\) as importance distribution; this does not have infinite support as the target has. This is required, see e.g. Art B. Owen (2013), “Monte Carlo theory, methods and examples”. I have now updated the post to use a normal distribution instead. Box plots are often used. They are not always the best visualisation (e.