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