Monday, September 10, 2007

A baysian estimate for prayer

It so happened that I went to a Church with my room mate for he had to pray. I promised not to say anything bad for an hours time. In that hour, I read some horrifying books about introducing religion to children. Some of them were written for parents and more disgustingly, some of them catered small children of age 5-10, but that's not the point here. (To understand my grief, one is referred to a chapter on religion and childhood in the 'God Delusion')

Another thing that occurred to me, my otherwise not so religious room mate had gone praying because he is applying for a residency in medical school as an oncologist (He's a Hopkins/Princeton graduate with tonnes of research and practical experience). The question was, what is the probability of succeeding when you pray, or P(success|prayer) for a general situation. As the title suggests, we define the following quntities:

Event A : is any event where you can succeed or lose. (eg, running 3 miles, getting into MIT for grad school, trying not to eat a burger for 1 month etc)

Event B : You pray for event A

For the estimate of P(success|prayer), we need the following:

P(prayer|success) i.e. the probability that you'd prayed and you actually succeeded as well. (correct me if I am wrong here) = X

P(Success) : How many times in general you succeed or in other words, how much of a loser are you? = Y

P(Prayer) : How many times do you pray before and event A occurs. = Z

then, P(Success|prayer) = X * Y / Z

I know that estimating X, Y and Z is as difficult as estimating P(Success|prayer), but we can look at interesting special cases and for the benefit of our religious friends, we will try to maximize P(Success|prayer)

First special case is a devote religious person and a devote atheist, both equally losers in life, so Y is same for both. Since the person is very religious, he prays at every event A, so X == Z, hence, his P(Success|prayer) is Y. For a devote atheist, X == Z == 0, so we can with all non-rigorousness, claim that P(success|prayer) == Y. An awesome conclusion! So a religious person and an atheist are equally likely to succeed when (and if) they pray.

Now consider the problem that you want to maximize P(Success|prayer). We assume that loser ness thus Y is a personal quality independent of the the praying statistics (which is a valid assumption in the scientific world we live in). Hence we want to maximize X and minimize Z.

A way to maximize X is to pray only when you know you are going to succeed. So you can pray before going for a small walk that you will succeed in doing so, but don't ever pray for getting into MIT which is kind of unlikely (statistically speaking). Also, try to pray only for selective events and don't go around praying for all the stupid things in life.

In summary, an atheist and a complete devote (both idealized cases) are equally likely to succeed when they pray for it. And if you want to increase your chances of success because of praying, keep on praying for stupid things at which you'll surely succeed, but don't do that in excess.

People who are more intelligent than me should correct me in the above arguments :-)


ps : I thank Mr. Varun Kanade for the maximization argument

pps : Thanks to constant pricking by Mr. Karthik Shekhar, I hereby acknowledge that the above analysis is not valid at all.

ppps : pps , the above thing was not meant for you

pppps : why do I always do that?m


Sumedh said...

perhaps you want to say "...a devout religious person..." rather than a "devote" person?
just a suggestion, no compulsion :P

shweta said...

I corrected you on phone that very day!!

You biased estimator!!

Anonymous said...

I have a problem with you assuming equal priors Y for the atheist and the pious. Though your argument about the 'scientific' world would seem reasonable to any atheist, a religious man would find it reasonable to assume a prior probability where the believers are at a vantage point. Notice that Y being unequal changes everything.


Roger Waters said...

I am talking about two people who statistically have the same Y, it's a probability which is not a prior, it's estimated based on their lives.

Anonymous said...

Let me get this right? (slightly longish)

1. By saying there are two people who statistically have the same Y, are you are saying that given a population consisting of loser believers and atheists, the average measure of 'loserness' of the population is Y?

If so, my problem is this:

In the very next statement, you have differentiated the P(prayer) of an aethist (0) from that of a believer (Z). Equivalently you have segregated the aethists from the believers and have assigned different prayer probabilities to either. But you have also assumed that the mean 'loserness' of the subdistributions remain the same the same as that of the complete one.

In other words, if I have a set of children of average height 'h' and use a threshold value h_t to segregate the kids into two 'classes' - 'short (less than h_t)' and 'tall(greater than h_t)' it does not mean that both the 'short' and the 'tall' classes would have the same mean height 'h' would it?

2. Alternatively, if you already supposed two different distributions for atheists and believers, in which case though it is reasonable to assume P(prayer) for either as you have, I don't see how 'Y' can be taken as the same.

Roger Waters said...

No, I meant that, sample people randomly from atheist and believers. The function Y is almost well defined so that it can be evaluated on each person. (I think I am right here)

Then assuming that there are infinite number of people around us, we are sure to find an atheist with loserness Y and a believer with looserness Y.

I think this answers the first part. If the first part is clear, the second part doesn't arise :-)

Rajeev said...

Too much.. Now prove that
Secularity = Theocratic..

Pritam said...

i know i'm stupid and shouldn't comment, but how come you don't worry about whether the event was caused by the prayer or not?

if you pray for something that's already certain, or that you can make certain (like going for walk), the cause is not the prayer.

however, if you do pray for mit or rain, and it happens, the religious fellow will KNOW that it happened because of his prayer while the atheist wouldn't have prayed, and if i were religious, i would say someone else had prayed :P

Roger Waters said...

The baysian estimate is a moral choice we make :-) I completely agree with your objection. But within the framework of the estimate (which is statistical and lacks any input from faith) everything is correct.

Whether the event was caused by the prayer or not is exactly the question at hand, instead of trying to come up with normative arguments about the effects of the prayer, we instead choose to learn from the statistics and evaluate the effects.

Anonymous said...

Yes ,"we are sure to find an atheist with loserness Y and a believer with looserness Y." but my only point is that your entire argument is invalid unless you can prove that there are equal number of losers who are aethists and equal believers. If you have to check correlation and prayer, you have to randomnly sample.

You seem to have implicitly assumed the above, and hence have already proven what you set out to prove. If you know who you're picking you've already chosen the correlation! And if you do randomly sample, all I say is that there is no basis to assume that the mean loserness is the same across groups.


Roger Waters said...

1. I don't see what you are saying.

2. You need beer

Anonymous said...

1. You have seen and understood my point.

2. Practise professional ethics and acknowledge it.

3. Yes I need beer. But before that I need idlis.

Cheery Cynic said...

ummm dude...i know you said analysis is not valid etc.. i just wanted to say...even if mathematically it were sound (and i have not looked carefully to see if it is) - you sitll have to prove that there is causality and not just correlation...

Roger Waters said...

That's the beauty (or drawback?) of Baysian statistics. We would intuitively assume that a high correlation (in such an otherwise random world) would imply a causality relation.

Your point well taken though. A correlation necessarily doesn't imply relation.