Is there any interest in a top-level post introducing DST? Bayesianism seems to be cited as a god of reasoning around here, but DST is strictly more powerful, since setting uncertainty to 0 in all DST formulas results in answers identical to what Bayesian probability would give. I would like to introduce Dempster-Shafer here, but only if the audience will find it worthwhile.
I would very much like an introductory post. Hopefully LW’s best statisticians would reply and a good discussion would get going. As far as human epistemic rationality is concerned, though, does it ever help to try to ‘move in harmony with the DST’ the way it seems to help when people try to ‘move in harmony with the Bayes’ by e.g. making sure to take into account prior probabilities or the like? Are there any qualitative applications of DST to one’s beliefs that are more powerful or more elegant than naive Bayesian heuristics? Also, it is just a confusion to ask what the equivalent of Bayesian networks are for DST? I’m definitely not a statistician but the application of verbalized statistical heuristics has helped me a lot in the past. It’d be cool if you could cover these questions in your post, but if not I still think you should write it. Pleaaaaaase.
I’d like to read about it, but less about the details than why we should prefer it to Bayesianism. For example, how would proponents deal with Cox’s theorem?
I’d be interested in a top-level post — I had been meaning to ask about it, in fact. I’ve read about DST briefly and had been wondering (1) if in practice it is actually useful for anything you can’t do as easily with pure Bayes, and (2) if they are theoretically isomorphic or if Bayes is strictly a special case of DST.
In my opinion, using DST usually adds unnecessary complexity to problems that can be sufficiently solved in a Bayesian framework. Then again, I think that the same thing can often be said of descending from a Bayesian to a Frequentist approach, which is to say that most problems are simple, and properly using any framework is enough to get a good answer. See neq1′s post that inspired my original comment.
That said, I work on problems that I have solved both from a Bayesian perspective and from the perspective of DST, and I have found the former lacking. There are at least a few problems that I feel like DST is much better at. If you search Google Scholar for Dempster-Shafer and look at results in the past few years, you’ll notice a really clear trend for using it to extract information from noisy sensor data. That’s what I use it for, and seems to be a strength of DST.
As to your second question, I think it is in the realm of possibility that Bayes can be used to construct DST, but I don’t know how and if it is possible, it is certainly more difficult than going the other direction. In some sense, DST is meta-Bayesian, because PDFs of PDFs of priors can be specified, but doing that with a strictly Bayesian framework misses the set-theoretic nature of Dempster’s Rule of Combination, and results in a weaker theory, that among other things, still doesn’t handle contradictions any better than Bayes does.
I would like to see it. I tried to get some idea of what it is about by Googling but failed miserably. I should disclose up front that seeing Zadeh’s name associated with it did not give me a warm and fuzzy feeling of anticipation.
I’ve been working on this, but have been swamped with other things.
Among other things, I’ve reversed my position on ata’s question about the equivalence of Bayesian probability and DST, and am reasonably sure that I can demonstrate that DST can be derived from, for instance, Jaynes’ formulation of probability. For related reasons, I’ve grown to distrust most underlying formulations of DST, and while I still trust the method (it works, after all), I think standard presentations have gotten it Wrong.
Which of course means that I feel the need to get it Less Wrong before I post it here, making this a much more monumental challenge.
I certainly wouldn’t mind. I saw your other thread and hoped someone else would reply to it and get a conversation rolling. I’ve heard a tiny bit about DST, and it sounds interesting, but I know too little about it to comment on it myself.
I was surprised that that didn’t get any responses, too. I don’t usually contribute to discussions of probability, and probably wouldn’t comment on such a post, but I’d certainly be interested in reading it.
I recently mentioned Dempster-Shafer evidentiary theory another thread. I admit, I was surprised to get no replies to that comment.
Is there any interest in a top-level post introducing DST? Bayesianism seems to be cited as a god of reasoning around here, but DST is strictly more powerful, since setting uncertainty to 0 in all DST formulas results in answers identical to what Bayesian probability would give. I would like to introduce Dempster-Shafer here, but only if the audience will find it worthwhile.
I would very much like an introductory post. Hopefully LW’s best statisticians would reply and a good discussion would get going. As far as human epistemic rationality is concerned, though, does it ever help to try to ‘move in harmony with the DST’ the way it seems to help when people try to ‘move in harmony with the Bayes’ by e.g. making sure to take into account prior probabilities or the like? Are there any qualitative applications of DST to one’s beliefs that are more powerful or more elegant than naive Bayesian heuristics? Also, it is just a confusion to ask what the equivalent of Bayesian networks are for DST? I’m definitely not a statistician but the application of verbalized statistical heuristics has helped me a lot in the past. It’d be cool if you could cover these questions in your post, but if not I still think you should write it. Pleaaaaaase.
I’d like to read about it, but less about the details than why we should prefer it to Bayesianism. For example, how would proponents deal with Cox’s theorem?
I’d be interested in a top-level post — I had been meaning to ask about it, in fact. I’ve read about DST briefly and had been wondering (1) if in practice it is actually useful for anything you can’t do as easily with pure Bayes, and (2) if they are theoretically isomorphic or if Bayes is strictly a special case of DST.
In my opinion, using DST usually adds unnecessary complexity to problems that can be sufficiently solved in a Bayesian framework. Then again, I think that the same thing can often be said of descending from a Bayesian to a Frequentist approach, which is to say that most problems are simple, and properly using any framework is enough to get a good answer. See neq1′s post that inspired my original comment.
That said, I work on problems that I have solved both from a Bayesian perspective and from the perspective of DST, and I have found the former lacking. There are at least a few problems that I feel like DST is much better at. If you search Google Scholar for Dempster-Shafer and look at results in the past few years, you’ll notice a really clear trend for using it to extract information from noisy sensor data. That’s what I use it for, and seems to be a strength of DST.
As to your second question, I think it is in the realm of possibility that Bayes can be used to construct DST, but I don’t know how and if it is possible, it is certainly more difficult than going the other direction. In some sense, DST is meta-Bayesian, because PDFs of PDFs of priors can be specified, but doing that with a strictly Bayesian framework misses the set-theoretic nature of Dempster’s Rule of Combination, and results in a weaker theory, that among other things, still doesn’t handle contradictions any better than Bayes does.
I would like to see it. I tried to get some idea of what it is about by Googling but failed miserably. I should disclose up front that seeing Zadeh’s name associated with it did not give me a warm and fuzzy feeling of anticipation.
What?! Seeing Zadeh’s name should definitely give you a “fuzzy” sensation! ;-P
Usually I am conscious of my subconscious puns. Dada Dada everywear.
Yes please!
I’ve been working on this, but have been swamped with other things.
Among other things, I’ve reversed my position on ata’s question about the equivalence of Bayesian probability and DST, and am reasonably sure that I can demonstrate that DST can be derived from, for instance, Jaynes’ formulation of probability. For related reasons, I’ve grown to distrust most underlying formulations of DST, and while I still trust the method (it works, after all), I think standard presentations have gotten it Wrong.
Which of course means that I feel the need to get it Less Wrong before I post it here, making this a much more monumental challenge.
I appreciate your commitment to quality!
I certainly wouldn’t mind. I saw your other thread and hoped someone else would reply to it and get a conversation rolling. I’ve heard a tiny bit about DST, and it sounds interesting, but I know too little about it to comment on it myself.
I was surprised that that didn’t get any responses, too. I don’t usually contribute to discussions of probability, and probably wouldn’t comment on such a post, but I’d certainly be interested in reading it.