A user visits my website at time t, and they may or may not click on a particular link I care about, if they do I record the fact that they clicked the link, and also the duration since t that they clicked it, call this d.
I need an algorithm that allows me to create a class like this:
class ClickProbabilityEstimate {
public void reportImpression(long id);
public void reportClick(long id);
public double estimateClickProbability(long id);
}
Every impression gets a unique id, and this is used when reporting a click to indicate which impression the click belongs to.
I need an algorithm that will return a probability, based on how much time has past since an impression was reported, that the impression will receive a click, based on how long previous clicks required. Clearly one would expect that this probability will decrease over time if there is still no click.
If necessary, we can set an upper-bound, beyond which we consider the click probability to be 0 (eg. if its been an hour since the impression occurred, we can be pretty sure there won't be a click).
The algorithm should be both space and time efficient, and hopefully make as few assumptions as possible, while being elegant. Ease of implementation would also be nice. Any ideas?
