## Bayesian calculation of Bayesian calculation?

From Schneier’s Security blog, a lucid and highly readable commentary on security-related news, comes this comment:

The Home Secretary, John Reid, stated in December that an attempted terrorist attack in the UK over Christmas was “highly likely” … Since there wasn’t one, I think Bayes’ Theorem tells us that it is “highly likely” that Reid, and hence also MI5, either don’t know what they’re talking about, or else were lying.

From my limited experience, if nothing else, I can reason that this is not true, or at the very least not necessarily true. But what to do with such calculations, which one could argue are boundedly rational given ignorance about Bayesian matters and only a very limited amount of time to work through the logic? Is this a tolerable consequence of increasing awareness of Bayesianism?

## The start of it all

It should probably be permanently linked to on this site, for without it, this site would not exist. I am referring, of course, to

“An Essay towards solving a Problem in the Doctrine of Chances. By the late Rev. Mr. Bayes, communicated by Mr. Price, in a letter to John Canton, M. A. and F. R. S.”

a.k.a. the paper where Bayes put forth the eponymous theorem. It is available in PDF format here.

Whether Bayes was actually the first to come up with Bayes’ Theorem, or indeed Bayesian inference (Laplace has a claim to that too), for some reason (probably something to do with Stigler), Bayesian statistics is, fore sure, named after Bayes, and this paper is therefore, to all intents and purposes, the Start Of It All. It is a fascinating read, and provoked in me an awe for those who see something original and useful which everyone before them had missed.

It is very educational to read the key texts that form our most fundamental beliefs, allowing us to make sure we are not re-treading old ground, and providing inspiration for where to take our thoughts further. This paper gives an opportunity to do just that.

## Implement Bayesian inference using PHP, Part 1 – from IBM developerWorks

If you’re interested in that kind of thing, there’s a guide at IBM’s site on how to Implement Bayesian inference using PHP. It seems like a comprehensive look at an initial implementation of Bayesian techniques, and despite its being almost three years old, I recommend it. Not much excuse left not to use it on enterprise sites.

## Google search for “bayesian” — the results

As I continue to update the site, I need to find links to put in, well, the Links section. A good starting point, I’m sure you’ll agree, is to search on Google for the term “bayesian“. The first ten results, which are supposed to represent the Internet’s ten most relevant links on the subject, contain a link to the Internet Society for Bayesian Analysis, a couple of pages about Bayesian logic… and three pages about Bayesian spam filtering. Now whilst Bayesian filtering, as some call it, is a great application of Bayesian statistics (and even a pretty obvious one to my mind), it’s certainly not the only one out there. The battle ahead is thus to change public consciousness to the extent that it becomes obvious to a much larger group of people that:

1) Bayesian statistics could’ve been used to solve the spam filtering problem from the start.

2) That Bayesian statistics is not just about spam filtering.

Once that is done, we’ve won, even if people don’t know Bayes’ Theorem or how to use WinBugs, because then anyone who believes in points 1 and 2 above will logically also believe in:

1&2) Bayesian statistics can been used to solve so many problems.

And then the golden age of Bayesian statistics will be upon us, I hope.

## Polls and mass confusion

Let’s start off proceedings with a quote trying to explain one of the most pervasive yet still misunderstood usages of statistics today – polling. And with it, the whole philosophy of inference of a population by random sampling:

Polling a sample of the population has often been likened to tasting soup: if it is well stirred then you only need to have one spoonful to tell what the whole bowl is like. [Source: BBC News’ Election 2005 Guide to pollsters’ methodology]

Excellent. On the other hand, they go and mess it up by correctly – if necessarily obliquely – explaining the “3% margin of error”:

Polling companies generally claim that 95% of the time, a poll of 1,000 people will be accurate within a margin of error of +/-3%.

but then going on to say

This means that figure in the poll could be up to three percentage points higher or lower than that shown.

Well, it could also be 50% higher of lower than that shown, assuming a normal distribution for the likelihood, so that’s not really useful. This might be a minor example, but it shows how careful we must be when talking about statistics in natural, human language. All too often when the media pundits discuss these polls, someone will pipe up with something like “Oh, but Party A is only 4% ahead of Party B, so with the 3% margin of error, maybe Party B is actually ahead!”. Even if Party A has been 3-4% ahead of Party B for eight weeks in a row. Indeed, the BBC falls into this trap:

So if the Tories are on 32% and Labour is on 38%, there is a chance they could both be on 35%.

I think a Pollwatch should be set up for the most egregious implementations of or analyses of polls, if there isn’t one already. Or maybe there would be just too many examples.

## Hello world!

Welcome to the Bayesian Statistics blog. Assuming that it has been set up correctly and I update it as and when required (geddit?), you should be able to read, for the foreseeable future, posts on everything from important progress in the theory or application of Bayesian statistics, to shockingly sloppy examples of statistics usage in the media, academic journals and other blogs. Probably everything in between, too, and maybe, occasionally, stuff outside the credible interval.

The only thing I promise every post will contain is jokey, forced references to statistics, especially of the Bayesian flavour. It’s what you should expect, really.

I hope it’ll all be interesting, and I hope you write in and comment with your views and priors as required.