# Latest Posts

Last edited: 2021-01-27 14:59:23

In a Bayesian inference with sampling, you learn about the model parameters through the sample taken from its *posterior distribution*, the joint probability distribution of *observing the data* with the model, a function of the model parameters values.

This post presents the Bayesian inference concepts through their application in a practical example, solving "by hand" a simple regression model in a fully Bayesian way and then using `stan`

, a tool for Bayesian inference with sampling. As we underline the steps we do with what stan does, we can deeply understand how modeling works with `stan`

and other packages that use `stan`

in the background.

Last edited: 2020-12-31 16:16:20

When I was young, I was curious to know how a computer calculates functions such as the cosine, the logarithm, or the tangent's inverse, the so-called elementary transcendental functions.

It turns out that they are calculated with the so-called *Chebyshev* polynomial approximation, where you get each polynomial coefficient by solving an integral.

In some cases, you need a couple of tens of coefficients, so there are lots of integrals to solve. It is more complicated when the function you want to approximate appears in those integrals, because you don't have how to calculate that function yet, and that's precisely why you want to have the approximation!

With patience and a little luck, I could analytically solve the approximation to some of these functions; and here I will tell you how I did it.

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