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.
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.