## The Box-Cox Transformation

The Box-Cox transformation is a family of power transform functions that are used to stabilize variance and make a dataset look more like a normal distribution. Lots of useful tools require normal-like data in order to be effective, so by using the Box-Cox transformation on your wonky-looking dataset you can then utilize some of these tools.

Here’s the transformation in its basic form. For value $x$ and parameter $\lambda$:

$\displaystyle \frac{x^{\lambda}-1}{\lambda} \quad \text{if} \quad x\neq 0$

$\displaystyle log(x) \quad \text{if} \quad x=0$

## MLE, MAP, and Naive Bayes

Suppose we are given a dataset $X$ of outcomes from some distribution parameterized by $\Theta$. How do we estimate $\Theta$?

For example, given a bent coin and a series of heads and tails outcomes from that coin, how can we estimate the probability of the coin landing heads? Continue reading “MLE, MAP, and Naive Bayes”