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Googling <statistical decision theory> might help you out. My opinion is the Wikipedia page for decision theory could use a good rewrite. Someday I may get arou

Googling <statistical decision theory> might help you out. My opinion is the Wikipedia page for decision theory could use a good rewrite. Someday I may get around to it. Also, madhadron didn't quite say that Bayesian and frequentist statistics are rendered irrelevant by decision theory. Rather, statistical decision theory includes Bayesian and frequentist statistics as possible statistical decision rules. You might want to not use Bayesian or frequentist rules and instead use minimax regret or something else. I do think that it is fine that people argue about Bayes vs frequentist. I wish they'd consider everything else though.

jbay808 7y ago
>> You might want to not use Bayesian or frequentist rules and instead use minimax regret or something else. ... What? Any such decision algorithm at least in theory still takes a probability distribution as an input. You still need to approximately follow the proper rules of probability to get that distribution, there's no way around it.
- madhadron 7y ago
  How do minimax criteria not follow the"proper rules of probability"?
  - James_Henry 7y ago
    Or minimax regret
- James_Henry 7y ago
  You don't need to have a distribution to make a decision. I don't think I understand what you are saying.
  - jbay808 7y ago
    Sorry for the super late reply. I don't know if anyone will see this... But... In minimax regret, you have a set of available decisions D, and a set of possible states of nature N, and a utility U(D,N). Each state of nature also has a probability P(N) (which can be influenced by the decision too in some problems). States of nature include "interest rates rise 1%", "interest rates fall 1%", and "interest rates stay the same". Decisions include "invest in stocks" and "invest in bonds". Minimax regret proposes to ignore the probabilities P(N), instead suggesting a way to make a decision purely based on the utilities of the outcomes. But that is actually an illusion. Outside of math class word problems, we don't have N or U(D,N) handed to us on a silver platter. There is always an infinite range of possible states of nature, many of which have a probability approaching but never reaching zero, including states such as "win the lottery", "communist revolution", and "unexpected intergalactic nuclear war". In commonsense decision-making we don't include those states of nature in our decision matrix, because our common sense rules them out as being implausible before we even think about our options. You wouldn't choose to invest in bonds just because stocks have the most regret in the event of a communist takeover. So what actually happens is we intuitively apply some probability threshold that rules out states of nature falling below it from our consideration. Then we minimize max regret on the remaining "plausibly realistic" states of nature. Humans are so good at doing probability mentally that this step happens before we even realize it. But if you are writing code that makes decisions, you'll need to do it, and so you'll need to have at least a rough stab at the probability distributions.

jbay808 7y ago

>> You might want to not use Bayesian or frequentist rules and instead use minimax regret or something else. ... What? Any such decision algorithm at least in theory still takes a probability distribution as an input. You still need to approximately follow the proper rules of probability to get that distribution, there's no way around it.

madhadron 7y ago
How do minimax criteria not follow the"proper rules of probability"?
- James_Henry 7y ago
  Or minimax regret
James_Henry 7y ago
You don't need to have a distribution to make a decision. I don't think I understand what you are saying.
- jbay808 7y ago
  Sorry for the super late reply. I don't know if anyone will see this... But... In minimax regret, you have a set of available decisions D, and a set of possible states of nature N, and a utility U(D,N). Each state of nature also has a probability P(N) (which can be influenced by the decision too in some problems). States of nature include "interest rates rise 1%", "interest rates fall 1%", and "interest rates stay the same". Decisions include "invest in stocks" and "invest in bonds". Minimax regret proposes to ignore the probabilities P(N), instead suggesting a way to make a decision purely based on the utilities of the outcomes. But that is actually an illusion. Outside of math class word problems, we don't have N or U(D,N) handed to us on a silver platter. There is always an infinite range of possible states of nature, many of which have a probability approaching but never reaching zero, including states such as "win the lottery", "communist revolution", and "unexpected intergalactic nuclear war". In commonsense decision-making we don't include those states of nature in our decision matrix, because our common sense rules them out as being implausible before we even think about our options. You wouldn't choose to invest in bonds just because stocks have the most regret in the event of a communist takeover. So what actually happens is we intuitively apply some probability threshold that rules out states of nature falling below it from our consideration. Then we minimize max regret on the remaining "plausibly realistic" states of nature. Humans are so good at doing probability mentally that this step happens before we even realize it. But if you are writing code that makes decisions, you'll need to do it, and so you'll need to have at least a rough stab at the probability distributions.