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

Hi Xyroth,

You mentioned Markov Chains in a couple of forums. (Speech recognition was the other.) I did a little bit of reading after your first posting. That would be a good topic for an entry. Maybe you could share your speciality with us?

Awu.

I would love to, but unfortunately I don't know that much about them.

I do know that they are (usually) long chains of conditional probability where the interesting thing is the cumulative probability of the chain, rather than the probabilities of the individual bits of evidence.

Unfortunately, my familiarity with statistics is mostly theoretical. I tend to know when not to apply certain methods that have been considered for specific jobs I was wanting them for in the past.

as to mentioning them in a few other places, I happen to know of a few specific applications of them, with speech recognition being the most spectacular in it's results.

Markov Chains are essentially a particular application of Bayesian statistics. I could do an entry based around examples of Markoc Chains and peculiar results concerning them (such as why three-dimensional mazes are so much harder than two-dimensional ones). I may consider it after I've got this entry out of the way.

I've massaged it again. I really want to avoid terminology (other than in footnoes). Maybe there are structural improvements to be made?

That link to the .pdf file that failed - I wonder if a link to the page where the .pdf file can be found would be allright

http://www.york.ac.uk/depts/maths/histstat/lifework.htm

Alji (Member of The Guild of Wizards @ U197895)

I've read this again, and I'm happy to say, it makes sense to me. If I understand it, then anyone can.

There's a small typo:

performned > performed.

I alread put it in .

I finally got round to reading this! You have explained it all very clearly .

Typo: In the paragraph beginning "Step forward Bayesian Statistics..." there is a probability lacking a b.



Amy the Ant

Tinkle. All better, now.

I wouldn't say that radar tracking falls under 'machine learning' - it's just another application in that early assumptions about a target's whereabouts are refined with each new measurement.

You've got some first person left in the footnotes... perhaps try 'Chinese philosophers, so goes the saying, ...'
and
'this researcher is a Bayesian statistician so s/he is not entirely...'

All in all, lovely

Nice entry

I wonder has the Markov Chain Monte Carlo method you mention anything to do with the rather widely used Monte-Carlo simulations used by computational chemists in my field.
They tend to be small time scale (nano-millisecond) simulations of the behaviour of molecules after giving a computer model a computer style 'shove' as it were.
Anyway, probably rambling me...

Have an

I like it

Orcus

More shaving. Thanks for all the help.

Orcus: Does your Monte-Carlo involve talk of Gibbs samplers, Metropolis-Hastings Algorithms etc? Is it a highly computation intensive technique?

*slurp*

'Orcus: Does your Monte-Carlo involve talk of Gibbs samplers, Metropolis-Hastings Algorithms etc'

Wibble

'Is it a highly computation intensive technique?'

Yes

Sorry, not in my area really I just see it in the literature a lot. I'm not a computational bod, I'm a 'wet' chemist (which means I make stuff in a lab).

Orcus

Sounds like the right thing. How many can there be? It's also called Monto-Carlo Simulation, apparently.

Is there any rivalry between you wet guys and the ones with the simulations?

If so, you might like to tell them that MCMC is widely regarded as unreliable because there is no guarantee it will converge on the correct answer.

My work actually involves finding ways to avoid using MCMC when modelling traffic networks.

Yes it is well known that there is a problem with it. They have to specify their method of simulation and there are now a few different ones.
One that seems to be gaining favour is an 'evolutionary approach' rather than iterative methods like Monte Carlo (*hopes he's not talking complete balls here* ).

There is a certain rivalry between us but in the end they need us as we actually do make things whereas without us they would never find out if their models are correct or not. A lot of chemists remain sceptical about computer modelling as there are some rather enormous assumptions and approximations used but it *is* a highly valuable tool

I agree that it would be unlikely that there would be two methods used with the same name - although possible. I suspect they are essentially the same. I'm pretty sure that the Monte Carlo simulation gets it's name from probability - lot's of probablilty is going down in Monte Carlo itself I hear

Orcus

Of course, both evolutionary methods and numerical methods like MCMC are both Bayesian in approach. Heh heh.

And most of the probability in Monte Carlo is the injurious to your health kind...

I'm afraid the subject matter is a wee bit over my head, here - what do you reckon, Queex? Does Silverfish have a point? And should I have studied harder at statistics at school?

Great entry.

Perhaps you could add an exemplary calculation with numbers.

Like:

P(B) is the probability of dicing a 6 (1/6)
P(A,B) is the probability of dicing a 6 AND finding a parking spot (?)
P(A|B) is the prbability of dicing a 6 after I've parked my car (1/6)

Now is that correct?

Then P(A,B) = P(A|B)*P(B)
Or: 1/36 = 1/6 * 1/6

Maybe you could think of a better example?

Typo: probilities (first line after 'Use of the Theorem')

HELL

The Internet Movie Datebase uses the "True Bayesian Estimate" for the voting lists of their top 250 movies. I've always found that formula very interesting. Now has this someting to do with the theorem here? Or is this a completely different invention by Bayes?

If not, it would be a nice example of an application ...

I'd not heard of anything by that name...
An 'unbiased estimator' is common, though.

Looking at the formula, it seems to be a sensible way dealing with varying numbers of votes.

It does in fact seem to be Bayesian; the 'current answer' can be encapsulated in the number of votes for and the mean for that film, and adding new data simply change those values. It seem related to the Gamma distribution, which is often used in Bayesian statistics to model variances.

It's not terribly complex, though. Might make a good example.

Can I accept the Scout's recommendation yet?