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Importance sampling in R course notes and code.

Importance sampling a Monte Carlo method to speed up the convergence of the MC estimates.

We start by approximating an integral of interest, namely

$$ \theta = \int_{0}^{1} (cos(x) + sin(x))^{2} $$

with crude Monte Carlo estimation. We get the following result

Then we take another example to approximate the following integral

$$ \int_{0}^{1} \frac{e^{-x}}{1 - x^{2}} dx $$

and we show that the convergence is more stable and achieved faster with importance sampling, as seen on this graph.

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