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Wednesday, May 25, 2011

Bayesian Inference in problem called LIFE

Ramanathan Sir has once mentioned a very nice implication of Bayesian in the real life. When we enter a new place (could be work place or educational institute), we have some prior beliefs about the people and system, as we stay there we are ought to have experience (that becomes data). That data slowly blends with the prior beliefs and we gradually come up with the posterior set of beliefs. As we go on and on, the experiences add, and we keep on updating the posterior.. and then there comes a time when (n is large) the prior beliefs are subdued by the experiences and that’s how for large n the weight is always more for the data. I liked it. 

I have a bit variation of the theory or you may say my own version or my doubt. My concern is about the data part of it. Suppose I am able to decompose my data in to two parts.. complete-past and the very latest part (recent-past). Now if my recent-past part of the data has got a bad patch, despite of the fact that the complete-past was very well behaved, then my posterior belief will obviously show a sudden negative surge (in terms of behavior) in it. Now here comes my query. How much will be the weight given to the recent past? When we have a bad experience with anyone or anything, do we remain calm enough to still account for the previous positive experiences? what remains in mind is only the negative present (or recent-past). We almost always tend to get the negative posterior belief and suddenly the weight to the complete-past decreases exponentially. Is it fair.. Do we have ways to resolve it?

What is running my mind is something like:
Posterior = W1.Prior  + W2.Data                          and for large n, W2>>W1
where  
Data = ??Recent-past + ??Complete-past


PS: Please don't take those "=" and "+" in literal sense. I ain't adding two events or sets :P

Post PS: Sorry for complicating both (life and Bayesian) :D ;)

9 comments:

Nachiket said...

Bayesian n life...nice way out!

Bayesian= complicated
life= ----

Srivats said...

It started with very interesting note of comparing the Bayesian ( learning it for the first time, thanks) with that of our assumption about others and how it changes over time. As I have exp the situation, i think its the understanding that plays a vital role here, the lesser the understanding the more the judgement based on past or recent past exp. :)

Meghana said...

Ramanathan sir always comes up with such beautiful real life examples. Hats off to him.

Your questions about dividing data into recent past and and complete past have raised more questions in my mind.(with the risk of complicating your problem rather than simplifying it)let me put them here..

Is it really ok giving weights according to recent past and complete past? What about a situation when your complete past had negative experiences and recent past is strikingly positive impression of the same person?

Disclaimer: This question could be complete non sense; given my ignorance and lack of knowledge of the topic.

Akanksha said...

Send this post to Ramanathan Sir... He will surely make a paper out of it.... :)

deep said...

@ Nachiket: I suppose life is also complicated.

@ Srivats: True..I have felt the same.

@Meghana: Your question is making sense to me.. I think if what I wrote is case of positive bias, then what you queried could be regarded as a case of negative bias (the way I interpreted your statement)..

@Akanksha: I wish one fine day he gets it on google ;)

bloody neel said...

we all have a very little memory. so lets put a zero for the complete past and a one to the recent past.

Vivek Otari said...

i think...
(??) Recent-past + (??) Complete-past =PAST

PAST (at present) is a deterministic event with known probability.
so it must be given max allowable weight...

eqn Posterior = W1.Prior + W2.Data still holds

also,-ve posterior = +(-ve posterior)
if the data is permitted with formidable df, it can yield parsimonious solution...

p.s : ofcousre "-","="&"+" in literal sense should not be considered...

deep said...

@bloody neel: its a personal choice, how we define our model.. what follows are the properties.. this one has got simplicity but looks like that it will be much harder on LIFE !!!

@Vivek Otari: too complicated to respond :|
It would be nice if you could elaborate and bring more clarity!!

Vivek Otari said...

everything which is non existent at present besides the moments to come is a part of PAST...call it recent past(recent as from last few months or years) or complete past...as a whole it's a PAST....

this will boost your eqn for
Posterior = W1.Prior + W2.Data

this helps in reducing an extra constraint on our models...if complete past is given larger share of weight it has to overpower recent past...it will allow a prudent model to operate...

(negative posterior will be feeble one)....

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