Sunday, October 27, 2013

P of x given y

Hello the 12 of you that actually read the blog. In the following weeks I'll be moving over to a sports scoring and stats company for amateur sports. For those that have read the blog before, you realize that my passion lies very much in the direction of sports. I think its a great opportunity and I'm excited to be 'The Data guy / Data scientist'. For more about the company go here

What this means for the blog. Well of course there is the obvious stuff; I wont be posting my findings here (but I may post them on their blog). I also will probably tune down the sports talk, which is probably for the better. I'm going to take an approach that is stats in everyday life. I've always been big on saying P of X given Y (detailed below); so thats is going to be my new focus.

P of X given Y. (or A given B)

We basically run into this all the time, its just that generally Y is pretty complicated. Let me give you an example. I'm at a coffee shop and I have $5 in my pocket and they have 5 different coffee selections. The Y here is two steps, 1 is that I have $5 and the other being the selections. So given those conditions, which coffee am I going to purchase (event X). This is of course is Bayes theorem, the conditional probability, and one that we make ALL of our life decisions on.

Given my current condition Y, I've decided to pack my bags and move to a brand new city with brand new challenges. Now that Y is pretty complicated and more than you would like to read; but I choose X; because given the conditions of Y, this gave me (or so I hope) the highest reward.  We choose X everyday, and we dont know the optimal outcome, but we update our prior's and try again. Its from small things like trying a new type of coffee to a new root to work.

People complain that statistics are difficult and confusing; but what they don't realize is that we do these calculations daily. If I go to this dinner, what will my outcome be? Well your conditions are the date, the restaurant and a few others you probably haven't thought of. Sometimes we'll uses X's to change our conditions (maybe buy some roses or choose a fancier place). The thing is, we are constantly trying to optimize what we do, from our hairstyles to our apartments, are attempting to maximize our rewards. Whether they be subtle (building better friendships) or obvious (getting a raise at work), we are trying to optimize our lives. The core of that optimization os P(X|Y).

The Lesson:

We don't know, nor will we ever know, what would have provided the best result. The only thing we can do is look at our conditions Y, and make the best expected value of Y.

"Until the day when God shall deign to reveal the future to man, all human wisdom is summed up in these two words,--'Wait and hope'." ~ Dumas

We can only do what is statistically smartest thing to do. Other times we want to fight those odds, to prove that we can overcome them. Everyone wants to be the one that 'beat the odds' ; its why the lottery is so popular.

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