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It's a pretty straightforward implication of bayes' law that the absence of evidence is evidence of absence. In fact, we can quite easily quantify just how stro

by smanek 16y ago

It's a pretty straightforward implication of bayes' law that the absence of evidence is evidence of absence. In fact, we can quite easily quantify just how strong the evidence it provides is. http://lesswrong.com/lw/ih/absence_of_evidence_is_evidence_of_absence/ http://lesswrong.com/lw/ih/absence_of_evidence_is_evidence_o...

PaulHoule 16y ago
But, with Bayesian methods you're feeding in prior information which can itself be flawed. When it comes to some question like 'What is reliability of the space shuttle?' the largest uncertainty in the calculation is that there is some failure mode you haven't thought of. Despite decades of changes to the space shuttle to improve safety, the official estimate of the failure probability hasn't changed since 1975. In conventional logic, we say that a reasoning method is sound if it never comes to correct conclusions. One version of 'A of E' -> 'E of A' is the "closed world assumption" which, in one variant, means that "if you haven't been presented with X, then not(X) is true." Now, we know that's not sound, not correct 100% of the time. However, when doing 'commonsense reasoning', the CWA can sometimes be a highly effective heuristic. (Note also that's there's no completely satisfactory way to deal with logical negation in knoweldge based systems at this time, so we've got to choose some poison, or otherwise deal with a system that "can't say no". Part of that is that 'commonsense reasoning' is probabilistic. For instance, an effective hold 'em player has to estimate the probability of improving his hand at drawing, have a guess about what his opponent(s) may be holding, and how the opponent may respond to his actions. From that he's able to estimate odds which help him decide what to bet. Poker's a pure example, but the same kind of probabilistic reasoning is necessary for hunting, software project management, scientific research, and many of things that people do.
amalcon 16y ago
That article is subtly wrong. Certainly it is less wrong (pun intended) than the reasoning it criticizes, but it does subtly miss the mark. Bayes' Law refers to data: specifically, it relates data to evidence. When a datum provides evidence for a hypothesis, the reverse of that datum must also provide evidence against that hypothesis. That is to say, a datum is either relevant or it's not. If it is relevant, then it will present evidence either for or against a given hypothesis, depending on its value. If you don't know that datum, however, it manages to not provide evidence either way. As such, it is easy to lack evidence either for or against a hypothesis. Through straightforward logical manipulations from there, it's possible to have "absence of evidence" while not having "evidence of absence". Therefore, they cannot be equivalent.

by smanek 16y ago

PaulHoule 16y ago

But, with Bayesian methods you're feeding in prior information which can itself be flawed. When it comes to some question like 'What is reliability of the space shuttle?' the largest uncertainty in the calculation is that there is some failure mode you haven't thought of. Despite decades of changes to the space shuttle to improve safety, the official estimate of the failure probability hasn't changed since 1975. In conventional logic, we say that a reasoning method is sound if it never comes to correct conclusions. One version of 'A of E' -> 'E of A' is the "closed world assumption" which, in one variant, means that "if you haven't been presented with X, then not(X) is true." Now, we know that's not sound, not correct 100% of the time. However, when doing 'commonsense reasoning', the CWA can sometimes be a highly effective heuristic. (Note also that's there's no completely satisfactory way to deal with logical negation in knoweldge based systems at this time, so we've got to choose some poison, or otherwise deal with a system that "can't say no". Part of that is that 'commonsense reasoning' is probabilistic. For instance, an effective hold 'em player has to estimate the probability of improving his hand at drawing, have a guess about what his opponent(s) may be holding, and how the opponent may respond to his actions. From that he's able to estimate odds which help him decide what to bet. Poker's a pure example, but the same kind of probabilistic reasoning is necessary for hunting, software project management, scientific research, and many of things that people do.

amalcon 16y ago

That article is subtly wrong. Certainly it is less wrong (pun intended) than the reasoning it criticizes, but it does subtly miss the mark. Bayes' Law refers to data: specifically, it relates data to evidence. When a datum provides evidence for a hypothesis, the reverse of that datum must also provide evidence against that hypothesis. That is to say, a datum is either relevant or it's not. If it is relevant, then it will present evidence either for or against a given hypothesis, depending on its value. If you don't know that datum, however, it manages to not provide evidence either way. As such, it is easy to lack evidence either for or against a hypothesis. Through straightforward logical manipulations from there, it's possible to have "absence of evidence" while not having "evidence of absence". Therefore, they cannot be equivalent.