MonteCarlo and Pi

This is a post to introduce a couple of probability concepts that are useful for machine learning. To make it more interesting, I am mixing in it some MonteCarlo simulation ideas too!

To see examples in Python we need first to introduce the concept of random numbers.

Stochastic vs deterministic numbers

The English word stochastic is an adjective describing something that was randomly determined. It originally came from Greek στόχος (stokhos), meaning ‘aim, guess’.

On the other side, deterministic means that the outcome – given the same input – will always be the same. There is no unpredictability.

Random number

Randomly generated is a big area by itself, for our scope is enough to say that randomness is the lack of pattern or predictability in events. A random sequence of events therefore has no order and does not follow an intelligible combination.

Individual random events are by definition unpredictable, but in many cases the frequency of different outcomes over a large number of events is predictable.
And this is what is interesting for us: if I throw a die with six faces thousands of times, how many times in percent shall I expect to see the face number six?

Let’s see some practical examples with Python. As usual they are also available in a notebook. Continue reading “MonteCarlo and Pi”