[Prévia] [Próxima] [Prévia por assunto] [Próxima por assunto]
[Índice cronológico] [Índice de assunto]

Prior convictions


Ola,
Aproveitando a discussao envolvendo bayesianos objetivos e subjetivos, ai vai um texto q o Tony O'Hagan escreveu para o 'Bayesian cabaret'. 

O texto estah disponivel no Bayesian Songbook em
http://www.biostat.umn.edu/~brad/cabaret.html
Mas eu recortei e colei o texto do Tony aqui, eh um pouquinho grande mas eh engracado. 

[]'s
Leo Bastos
PhD student, University of Sheffield
http://lbastos.postgrad.shef.ac.uk

---------------------------------------------

Prior Convictions
By Tony O'Hagan
First performance:  Valencia 7
[The action begins with Pilgrim entering the cave of the famous mystic Statisticus.]
Pilgrim ({\em Nicky Best}): Oh great mystic, Statisticus, I seek your help with analysing these data. 

Statisticus ({\em Tony O'Hagan, who also plays all the other parts}):
Ah, you have come to the right place. Those certainly look like interesting data. Have you brought your prior? 

Pilgrim:  My prior?
Statisticus: Yes, your prior. Didn't you bring your prior? [Getting annoyed.] You don't think I'm some kind of {\em frequentist,} do you? 
How can I analyse your data if you don't give me your prior?

Pilgrim:  I'm sorry, I didn't realise.

Statisticus:  Well, go and get your prior, and then come and see me again.

[Pilgrim enters the shop of The Objective Prior Company.]

Pilgrim:  Excuse me, I need a prior.
Shopkeeper 1: Of course, here you are. [Presents Pilgrim with a uniform prior.] 

Pilgrim:  That was quick!  Don't I get a choice?
Shopkeeper 1: Certainly not. This is a genuine objective prior, mate. None of your wishy-washy, unscientific subjective *choices* here. 

Pilgrim:  Oh, right, thank you.  [Pause.]  It's very flat, isn't it?
Shopkeeper 1: Certainly it's flat. You can't get any flatter than one of our objective priors. Look, do you want this prior or don't you? 

Pilgrim:  Well if that's all you have, I'll take it.

[Pilgrim returns to the cave of Statisticus.]

Pilgrim:  I've got a prior, now.  Here it is.

Statisticus:  [Looking at it with suspicion.]  You call that a proper prior?

Pilgrim:  Well, I don't think the shopkeeper said it was actually proper.
Statisticus: I should think not. You have been conned, O gullible one. I can't do anything with that.
[Statisticus hands Pilgrim back the prior. Pilgrim goes away again and enters the shop of Intrinsic Priors Inc.]
Pilgrim: Excuse me, I need a prior. They sold me this one at The Objective Prior Company, but it's no good.
Shopkeeper 1: [Takes prior and examines it.] I see. Well, I can give you a prior, but you'll have to tell me what sort of data you've got. 

Pilgrim:  Really?  Why?
Shopkeeper 1: Oh, it's a well-known fact that your prior depends on your data. 

Pilgrim:  Oh, OK.  My data look like this.
Shopkeeper 1: Ah, then here's your prior. I'm sure you'll be very happy with it. 

Pilgrim:  But that's the same one as before!
Shopkeeper 1: As it happens, yes it is. But that's not just any old prior, madam, that's a genuine intrinsic prior.
Pilgrim: Well, it's no good to me. I can't go back to Statisticus with that. 

[Pilgrim leaves, and goes into the shop of Reference Priors R Us.]

Pilgrim:  Good evening, I'd like a prior, please.  My data look like this.
Shopkeeper 1: OK, but you'll have to tell me what parameter you wish to learn about from these data. 

Pilgrim:  Really?  Why?
Shopkeeper 1: Oh, it's a well-known fact that your prior depends on what parameters you're interested in. 

Pilgrim:  Oh, OK.  I'm interested mainly in the location parameter.

Shopkeeper 1:  Excellent. Here's your prior, then.
Pilgrim: But that's the same flat prior I was offered by The Objective Prior Company and Intrinsic Priors Inc! 

Shopkeeper 1:  Well, that just proves it's the right one, doesn't it?

[Pilgrim leaves and goes into the shop of Default Priors for Dummies.]
Pilgrim: Look, I want a prior, please, and I ... [Pause, looks at shopkeeper closely.] You know, you look exactly the same as the man in the Objective Prior Company shop, who looked exactly the same as the one in Intrinsic Priors Inc, and he was exactly the same as in Reference Priors R Us.
Shopkeeper 1: Ah, well, that's because we're all part of one big happy chain of Berger joints. We trade under lots of different names. Anyway, here's your prior, madam. [Hands Pilgrim another flat prior.] 

Pilgrim:  I don't want that one!!  Haven't you got a proper prior?

Shopkeeper 1:  [Incredulous.]  A proper prior?  You want a real prior?

Pilgrim:  Yes.
Shopkeeper 1: You're so weird! [Patiently.] Look, our priors are really easy. You don't have to think. You don't have to worry about being different from other people. They're so nice and anonymous. 

Pilgrim:  [Insistent.]  I want a proper prior.
Shopkeeper 1: [Exasperated.] In that case you'd better go to this address. [Mimes showing an address.] 

Pilgrim:  That's a rather unfashionable part of town, isn't it?  Oh, well.

[Pilgrim leaves and then enters the shop of Conjugate Priors U Like.]

Shopkeeper 2:  Good evening, madam.
Pilgrim: Good evening. I'd like a prior please. And my data look like this. 

Shopkeeper 2:  Excellent.  I just need to take a couple of measurements.

Pilgrim:  Really?  Why?
Shopkeeper 2: Well, we could skip that bit if you like, and I could just give you the limiting form. [Shows the old flat prior again.]
Pilgrim: NO!!! That's the same prior that I was offered in all those flashy Bernardo and Berger high street shops. I want a proper prior!
Shopkeeper 2: [Soothingly.] Quite right madam, and we can offer madam the very best in user-friendly proper priors. Here on this shelf we have our very popular Normal range. 

Pilgrim:  Hmmm...  I'm not sure I'm quite Normal.
Shopkeeper 2: I see what you mean. Well, here on this other shelf we have our versatile Dirichlet range. 

Pilgrim:  That looks nice.
Shopkeeper 2: Yes, I could see when you walked in that madam was a bit simplex. 

[They mime some business, then Pilgrim goes back to Statisticus.]

Pilgrim:  [Excited.]  I've got it!  I've got a proper prior!

Statisticus:  Yes, but is it your prior?

Pilgrim:  What do you mean?  I bought it.  Doesn't that make it mine?

Statisticus:  You don't understand.  I mean, does it fit you?
Pilgrim: Well, the nice man in the Conjugate Priors U Like shop took just a few simple measurements, and then said he was giving me the Dirichlet prior that fit my specifications exactly. 

Statisticus:  Don't you think you should try it on?
Pilgrim: OK. [Mimes trying on the prior. Struggles.] Oooh ... ouch ... well, it's the right general size, but I see what you mean. It really doesn't fit. 

Statisticus:  Then it's not your prior, I'm afraid.

[Pilgrim goes back to Conjugate Priors U Like.]

Pilgrim:  Hey, this prior you sold me, it doesn't fit!!

Shopkeeper 2:  Well, madam is a rather strange shape.
Pilgrim: How dare you! That's the shape I am, and there's nothing wrong with it.
Shopkeeper 2: Well, of course, if you put it that way ... but if madam is not happy with one of our off-the-shelf convenience products, I'm afraid we can't help. You'll have to go to this place. [Mimes showing another address.]
Pilgrim: Hey, that's miles away from you! I can't believe anybody would ever want to go that far just to get a prior. [Resigned.] Still, it looks like it's my last chance. 

[Pilgrim leaves, and then we see her back at Statisticus's cave.]

Pilgrim:  I've got it!  [Doing a twirl.]  What do you think?

Statisticus:  Ah, my little pilgrim has finally found enlightenment!
Pilgrim: I had to go to this tiny craft shop down a back street, called ``Ye Olde Bespoke Prior Shoppe.'' It looked like they hadn't had any customers for years. Anyway, they took loads of measurements, and kept asking me what I thought. They wouldn't let me go until I was completely satisfied. It took absolutely ages, but here it is!
Statisticus: And a very fine prior it is, too. So ``you,'' if I may say so. Yes, that is definitely your prior. 

Pilgrim:  Right, so you can analyse my data now?

Statisticus:  Well, not straight away.

Pilgrim:  Why not?
Statisticus: Well, that's a beautiful prior, but I'm afraid it doesn't make the computation very easy. No, I'll have to get out my MCMC machine, you see, and that will take a little while. Come back here in another four years and we'll see if it's converged. 

[Pilgrim throws down script and stamps foot in disgust.]