8 ms·

Statistics is quite valuable and grounded in theory. It's a trusty tool if used with respect (like a knife).

candiodari 8y ago
Yeah, too bad the theory requires a number of things to be true for data and models ... that are essentially never true. Once you think about 1) is the independance assumption really applicable here ? 2) does the underlying model satisfy the law of large numbers ? (NOT your model, the underlying model, ie. "reality") 3) am I really only interested in predictions within the data range ? The answer for all these questions is almost universally "no", and the theory says that statistics is not guaranteed to work under those circumstances. Correct statistical answers: 1) which average percentage of borrowers will default ? There is no answer to that question, because many non-random influences will make borrowers default in synchronized, and therefore very much non-independent ways (say, an economic crisis, an earthquake, an epidemic). Therefore you cannot correctly even calculate an average. 2) which average percentage of borrowers will default ? A model that describes whether an individual will default is going to be non-differentiable, and therefore certainly violate the law of large numbers (there will be sudden jumps in the default rate everywhere because of a million random reasons. An idiot tv anchor declares now the time to sell, and half the town finds out their loan is underwater, say). So underlying models involving humans essentially never satisfy the law of large numbers. 3) which average percentage of borrowers will default ? The number of factors changing that value do not match between the period your data is from (ie. the past) and the period you're predicting. Because there are so many real-world factors that affect your variable you can never avoid this situation. Therefore you cannot predict. All of these issues allow one to construct realistic scenarios where even trivial statistics will fail spectacularly.
- RA_Fisher 8y ago
  It's true, statistics can't answer every question. There are some limits.

Yeah, too bad the theory requires a number of things to be true for data and models ... that are essentially never true. Once you think about 1) is the independance assumption really applicable here ? 2) does the underlying model satisfy the law of large numbers ? (NOT your model, the underlying model, ie. "reality") 3) am I really only interested in predictions within the data range ? The answer for all these questions is almost universally "no", and the theory says that statistics is not guaranteed to work under those circumstances. Correct statistical answers: 1) which average percentage of borrowers will default ? There is no answer to that question, because many non-random influences will make borrowers default in synchronized, and therefore very much non-independent ways (say, an economic crisis, an earthquake, an epidemic). Therefore you cannot correctly even calculate an average. 2) which average percentage of borrowers will default ? A model that describes whether an individual will default is going to be non-differentiable, and therefore certainly violate the law of large numbers (there will be sudden jumps in the default rate everywhere because of a million random reasons. An idiot tv anchor declares now the time to sell, and half the town finds out their loan is underwater, say). So underlying models involving humans essentially never satisfy the law of large numbers. 3) which average percentage of borrowers will default ? The number of factors changing that value do not match between the period your data is from (ie. the past) and the period you're predicting. Because there are so many real-world factors that affect your variable you can never avoid this situation. Therefore you cannot predict. All of these issues allow one to construct realistic scenarios where even trivial statistics will fail spectacularly.

RA_Fisher 8y ago
It's true, statistics can't answer every question. There are some limits.