# Welcome

I’m a software developer with a focus on backends and data analysis. Whatever you are looking for is probably in the nav bar above.

## From the Blog

### The magic of conjugate priors (for online learning)

In Bayesian reasoning, the fundamental problem is the following. Given a prior distribution $p(x)$, and some set of evidence $E$, compute a posterior distribution on $x$ namely $p(x | E)$. For example, $x$ might be the conversion rate of some email. Before you have any evidence you might expect the conversion rate to be somewhere in the range of perhaps $5\%$ and $50\%$. After you have evidence, you update your belief - if you sent out thousands of emails and observed an empirical $16.5\%$ conversion rate, you are now reasonably confident that the true conversion rate lies roughly in the range of $16\%-17\%$.

In mathematics, a conjugate prior consists of the following. Consider a family of probability distributions characterized by some parameter $\theta$ (possibly a single number, possibly a tuple). A prior is a conjugate prior if it is a member of this family and if all possible posterior distributions are also members of this family.