When people say that advertising doesn't work on them they are generally only focused on being immediately motivated to action by the ad. However advertising serves a wide range of functions beyond that. No one sees one Mercedes ad and goes out to purchase a $75k car. That doesn't mean that Mercedes is stupid for still buying TV ads. The ad is instead meant to do things like keep consumers updated on the latest product line, establish the brand of the company, and to keep that brand in the back of consumer's mind when an eventual buy decision does come up potentially years down the road.
Aspiration is a large part of advertising.
It's not just that you won't go out but that Mercades, most of us never will be able to afford one, but we all know its a luxurious product, a sign of wealth and 'doing well'. That's in large part because of the brand image, if you bought the same car with a Ford badge would they be able to charge as much?
Yes, and it would be good to try to measure that effect also, and for that the statistics and optimization stand to be more difficult and advanced. E.g., the main input is not just some ads and clicks but a stochastic process, that is, random variables indexed by time.
Uh, go measure something and get a number. You now have the value of a random variable. The sense in which the number is random or unknowable in advance, unpredictable, independent of something else, etc. is left open. Collect such data once, say, over 3 months, and now have a sample path of the stochastic process. Do it again and get another sample path, etc.
