h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: Bayes' Theorem and Bayesian Statistics - A792560
Author: Queex Quimwrangler (level 8 ranger) - U33834

I'm not sure whether this is too brief or too long. Or neither.

I'm pretty sure that the two subjects should appear in the same entry. Interdependency, see.

Any comments?

At a quick glance this looks really good. I'll come back and have another look later on.



Amy the Ant

Typo alert > king of function < on the second line after Bayesian Statistics subheader

Alji, of the Red Dragon (Swynwr y Ddraig Goch) (conducting a sun sign poll at A712595)(Member of The Guild of Wizards U197895 looking for wiz kids to join, though you don't have to be a wiz kid just know a bit about some subject that you think will be of interest to others or just bore the pants off them. This is an equal opportunities space open to all sexes, ages and abilities)

Done.

Here's a link to the essay;

http://www.york.ac.uk/depts/maths/histstat/essay.pdf

all 24 pages of it.


Alji (Member of The Guild of Wizards U197895)

BTW you could mention that it was his friend Richard Price, who sent the essay to the R.S.

Definitely too brief.

It was looking like a really good entry, then just when it got to the interesting bit, it stopped, and just seemed to say 'Go away now, and find out for yourself'.

It was a case of probabilius interruptus, which is very frustrating.

Bels

This kind of thing goes so far over my head I'd need the Hubble Space Telescope to see it

surely this means that they are the basis of markov chains?

if so, then don't you need to include a warning about the need for keeping the variables independant?

Looks good indeed. However, you should rewrite first person style as far as possible (even if mathematical/technical papers usually are written in the 'editorial we' form to express credits for all co- and pre-workers since the times of Archimedes&Co).

typo: theroem -> theorem

Another application is in tracking radars where a target's position is being estimated by means of measurements which of course bear uncertainties or inaccurracies.

"The fact that both can be considered 'correct' by Bayesian statistics is enough to put people off"
This bears some similarities to
a) Chinese philosophy, where there is no such thing as black or white but only different shades of grey
b) Fuzzy Logic where, say, water at 90°C is, to some extend, cold

*waves at Bossel* I agree with the first person stuff, that should be reworded - easily done.

I thought that Bayes Theorem *was* fuzzy logic -isn't it?

Chinese philosophy does have black and white, but has differing amounts of white and black in each - in the extremes as 'seeds'.

I was surprised to find how long ago he lived.

I've tidied it a little. I haven't reworded the first person yet, that's a task for another day. I've also redone the closing section.

There seems to be one each way on the 'too much/too little' front. I only intended the article to be a basic introduction to the subject and some interesting implications. I could do a far more technical look, but it would only become a poor academic paper and only be of interest to mathematicians, anyway.

Where do you find these links? I Google and come back with nothing as useful as that.

Does anyone know of any useful intermediate stats references? I'm only finding Key Stage 3 and academic journals.

Try this link;

http://bidug.pnl.gov/presentations/PEP/

Alji,(Member of The H2G2 Guild of Wizards @ U197895)

Ooops! Hidden?? Did you check whether all your external links work (which, if they don't, make the Moderators hide the complete entry)?

no, bayes theorem isn't fuzzy logic.

it is firmly anchored in probability and aristotle's law of excluded middle. It work when things are definately one member of a set, but you don't know which one.

fuzzy logic relaxes this law to allow multivalent states rather than just black and white, thus extending it to cover a completely new and extra type of uncertainty.

Can't see what the problem with the link was. I'm waiting for them to get back to me.

The other link seems to centred on a specific field, I'll probably leave that for now.

I'll wait for the mods to get back to me, then reword it again.

Thanks for all the help!

Okay, apparently links to pdf files are not kosha. Strange, but there you go.

makes me wonder! I've used quite a few links to .pdf files elsewhere. Perhaps it was a commercial site?

er... forget my last posting!

I just had an entry of mine pulled because it had three 'offending' links in it. All of them are dealing with the acoustic capabilities of bats, aren't commercial or anything, and have been there since the entry was created *months* ago. I added a picture yesterday, and *bang*.

Obviously, somebody changed the rules and didn't bother to tell anyone.


Bossel

Another shakedown. Please find any new typos I've introduced.

I think this is a good entry, but there are some bits I'm not sure of, and I think there is room for improvement.

The bit about bias is one bit I'm not sure of. I can understand how you can take into account bias in data, if you know how biased it is, but I would have thought you could do that with classical statistics. For example, if the data is known to have an mean of 5 units more than what you are trying to estimate the mean of, then you take of 5 from your estimate based on the data. However, if you have unknown bias, I am not sure how bayesian statistics coped any better.

I am not a bayesian statistician by the way, but I did a module on it at university (I've finished my second year of a maths degree), when there was a module where the main thrust of it seems to be bayesian statistics. Surely, if you take large enough sample sizes, the estimate will just converge on the 'wrong' average, if the data is biased. However, please explain why I am wrong here, if I am, preferably with an example if possible.

Also, you describe the process of Bayesian statistics as starting by deciding on an initial answer. I would say that it would be an assumption, as an assumption is generally what you make before you have seen the data.

Also, I think that you could make it a bit clearly the link between Bayes theorem and Bayesian statistics. For example, you could talk about the prior probability of something happening (P(A), compares with the posterior probability of it happening, given new information B (P(A given B). Then you could link this to statistics, and talk about the initial 'answer' being the prior probability, and the posterior the final answer, when you have plugged in the data. Perhaps the terminology isn't neccesary, but it does enable you to relate the two subjects quite nicely.