Saturday, March 22, 2014

Whose confidence interval is this?

This week, yet again, I was confronted by yet another facet of the nonsensical nature of the frequentist approach to statistics. The blog of Andrew Gelman drew my attention to a recent peer-reviewed paper studying the extent of misunderstanding of the meaning of confidence intervals, among students and researchers. What shocked me, though, was not the only findings of the study. 

Confidence intervals are a relatively simple idea in statistics, used to quantify the precision of a measurement. When a measurement is subject to statistical noise, the result is not going to be exactly equal to the parameter under investigation. For a high quality measurement, where the impact of the noise is relatively low, we can expect the result of the measurement to be close to the true value. We can express this expected closeness to the truth by supplying a narrow confidence interval. If the noise is more dominant, then the confidence interval will be wider - we will be less sure that truth is close to the result of the measurement. Confidence intervals are also known as error bars.

Thursday, February 27, 2014

The Full Adder Circuit

I recently wrote a very brief introduction to Boolean algebra for the glossary, so I thought it would be worth describing a very simple but important application example. There are two main reasons why I'm interested in Boolean algebra. The first is that in probability theory, the hypotheses we investigate are assumed to be Boolean in character (true or false, with no intermediates allowed). The second is that Boolean algebra is an important branch of logic, and therefore intimately linked to science and rationality.

In an earlier post, I discussed how all transfer of information comes down to a sequence of answers to yes/no questions. In this spirit, therefore, consider the following:
By answering only yes/no type questions, calculate the sum 234 + 111. In other words, if you were a digital computer, how would you perform this calculation?

Monday, February 3, 2014

Practical Morality, Part 2

It has been said that democracy is the worst form of government, except all those others that have been tried.
Winston Churchill 

(The second of two parts. Read the first installment here.)

Politics & Science

I have a funny little feeling that Churchill actually knew a small bit about politics. According to dear, old Winston, democracy sucks. But why does it suck? And does it necessarily suck?

A full analysis of these questions could run into thousands of pages, and obviously stretches far beyond any area in which I could claim expertise, but for now at least, I want to point out just one aspect of democracy's poor performance to date that can most definitely be fixed. That is, the failure so far of both politicians and the electorate to explicitly recognize the necessarily rational basis for morality.

Wednesday, January 29, 2014

Practical Morality, Part 1

(The first of two parts. Part 2 is here.)

The Social Contract

Where-ever you are right now, take a quick look around. Do a quick survey of all the stuff you can see. Think about the number of things you have around you that other people have made. If you are in your own home, then great, the experiment works even better - the things around you probably belong to you, you make some kind of use of them, and quite possibly your life would be less satisfying without them. Some of these things may even be, if not essential for life, indispensable for a comfortable modern existence.

Thursday, January 16, 2014

The Dennett Tennis Test

This is a simple little tactic to consider employing next time you find yourself in conversation with somebody who doubts the efficacy of scientific method, particularly anybody who wants to propose any kind of alternative.

You know the sort, I’m sure. The kind of person who says “sure, scientific data argues that acupuncture is total and utter garbage, but maybe acupuncture is one of those things science isn’t equipped to investigate.” Or the kind of person who says “absolutely, you’re right, I have no evidence that my god exists, but frankly I’m offended at your crass insistence that everything has to come down to evidence.” Or “how ridiculous to suggest that science has anything to say about the supernatural.”

Sunday, December 22, 2013

Confounded Koalas

Koalas are not as exclusive as kangaroos. At least, when it comes to their drinking habits. As I explained before, kangaroos drink beer or whisky, but not both. Koalas like to mix things up a bit more, when it comes to their choice of drink, but how much exactly? What is the probability, for example, that any given koala who drinks beer on any given night will also drink whisky on the same night? These are the sorts of urgent questions that science must seek to answer with the utmost speed and accuracy.

Saturday, November 16, 2013

The Acid Test of Indifference

In recent posts, I've looked at the interpretation of the Shannon entropy, and the justification for the maximum entropy principle in inference under uncertainty. In the latter case, we looked at how mathematical investigation of the entropy function can help with establishing prior probability distributions from first principles. 

There are some prior distributions, however, that we know automatically, without having to give the slightest thought to entropy. If the maximum entropy principle is really going to work, the first thing it has got to be able to do is to reproduce those distributions that we can deduce already, using other methods.