# Statistics

## Understanding the Metropolis Hasting algorithm - A tutorial

The Problem Say you want to evaluate the expectation of a function over a random variable $E[f(x)] = \int p(x)f(x)dx$, or perhaps find the max of a probability distribution, typically the posterior, $\arg \max p(x|y)$, where calculating the derivate is intractable since it depends on some feature that comes from some algorithm or some unknown […]

## A short tutorial on Kernel Density Estimation (KDE)

The aim of Kernel Density Estimation(KDE) is: Given a set of $N$ samples from a random variable, $\mathbf{X}$, possibly multivariate and continuous, estimate the random variables probability density function(pdf) The univariate case To get a rough idea how one can think about the problem, we start out with a set of samples, $X=[x_1,x_2,...,x_N]$, of a […]