It’s Newtonmas 2017 tomorrow!

What better way to celebrate than *talk about integration*!

The Batman Shape (sometimes called *the Batman Curve*, somewhat erroneously, I think) looks like this:

You can find details about it at Wolfram MathWorld, including its area in closed form. What’s interesting is integrating it without algebra, numerically. Quadrature would be difficult and a lot of work. Monte Carlo integration, not so much. What’s interesting is the relation between that and use of Monte Carlo integration for Bayesian computation, such as in *Markov Chain Monte Carlo* and *slice sampling*.

I was going to do the area of the Batman Shape using Monte Carlo integration and compare it with the exact value, but Jame Schloss has already done that. I might come back and do it using *slice sampling*, which will be a little interesting since it’s a two-dimensional figure. I’ll append that below if I do.

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## About hypergeometric

See http://www.linkedin.com/in/deepdevelopment/ and https://667-per-cm.net/about