#bayesian filter

Signal to Noise: Humans as Bayesian Filters

Bayesian Filters are everywhere in Quant Trading. the most ubiquitous is the Kalman Filter. Trading without a filter is like bringing a knife (or spoon?) to a gun fight.

Humans behave a lot like collections of filters. We constantly make expectations, then revise our expectations and take actions as a result of new information. We can think of our expectations as an collection of internal beliefs.

The Kalman Filter and Pairs Trading

Imagine this scenario: you are a statistical arbitrage trader at a prop desk or HF. As such, you routinely hold an inventory of ETF exposure that you must hedge.

The previous night, you instructed your overnight traders to calculate the hedge ratios for a matrix of ETF’s.

The next morning before the market opens, your junior traders eagerly present their results for your inspection. Liking what…

Introduction to Recursive Bayesian Filters 

Let's introduce the general formula of Recursive Bayesian Filters for Hidden Markov Processes 

General Recursive Bayesian Filter 

The elements of the formula are the following ones 

$ P(x_{t} | y_{1:t}) $ State PDF given a set of Observations in different times 

$ \alpha $ Normalization Term 

$ P(y_{t} | x_{t}) $ Observation PDF given a certain State, also called Likelihood 

$ P(x_{t} | x_{t-1}) $ Process Dynamic, it is to say the PDF of the State at a certain time, given the State at the previous instant 

$ P(x_{t-1} | y_{t-1}) $ State PDF calculated at the previous iteration (it explains why this is called a Recursive Filter) 

Numerical Estimation 

In general the integral in the abovementioned formula has no closed form solution (except in very specific situations) so a numerical approximation is needed 

The Particle Filter is a Monte Carlo Method to compute a numerical approximation for this integral relying on the concept of particle 

The term Particle designate a Possible System State. 

In order to be able to adopt this solution, it is necessary to know 

the System Dynamic 

the System Likelihood 

The Particle Filter strategy so is simply as follows 

at the beginning of the iteration cycle (recursive filter) a certain amount of Particles is generated, for example by sampling a certain PDF chosen in some way 

at every iteration, the particles are evolved according to the System Dynamic thus to be able to numerically estimate the integral 

Thanksgiving 2010 was great, time to burn all these fats with more programming.

A friend of mine mentioned that he would like Cooln.es(s) better if the programming section is more accurate. He is one of the many programmers who just want to read news without participating to a community, quickly glancing on what's happening in the web.

So, what's Cooln.es(s)? It is an hourly newspaper, simple as that. The programming section is initially simple; scrape obvious sources of tech news. But as we try to expand to a lot more sources, classification becomes more tricky and less obvious.

There are endless source of news and news publishers on the web. Anyone with internet connection can publish, thanks to various (free) blog platforms. Many of these platforms use tagging as free-form way of classification. Unfortunately, most blog posts are tagged vaguely or even not at all.

This is where Bayesian filter comes in handy. We can train the filter using the obvious source of news, and slowly using it to classify incoming news.