Below is a list of ideas for potential course projects somewhere in the intersection of statistics, machine learning, and imprecise probability. Some of the ideas are on the theoretical side, some are more methodological or computational, and some are borderline philosophical. It doesn\u2019t matter though, the project can be pretty much anything—basically whatever interests you. My list is definitely not comprehensive, these are just things that (a) I know something about and (b) came to mind as I was preparing this list. So please feel free to come up with your own ideas. You\u2019re also welcome to talk with me about your interests and what you have in mind.<\/p>\n\n\n\n
I was originally planning to prepare a static PDF document that listed out some suggested project topics, references, etc., but I found the idea of listing everything out at once in a single document rather daunting. So, instead, I’m going to list out ideas and references here as I think of them. When I’ve made an update, I’ll change the “Last updated” date below. The order in which things are listed isn’t relevant. <\/p>\n\n\n\n
Last updated: 09\/26\/2022<\/strong><\/p>\n\n\n\n I have to suggest this as a possible project idea because this is specifically where my interests lie. Some new and general ideas are being developed now, but this is intended to encompass all of the approaches that have been suggested so far, so there’s no harm in investigating some of the “old” formulations. Below are some miscellaneous thoughts or things that I’ve considered before but didn’t have time to dig into myself. If anything here is of interest to you, then please talk to me—I can help you get oriented.<\/p>\n\n\n\n At the ISIPTA\u201919 meeting in Ghent, Professor Gert de Cooman was asked what is the biggest open problem in imprecise probability and he said \u201cStatistical inference.\u201d So there are lots of interesting things that can still be done. A good reference for about what was known about statistical inference and imprecise probability, around the early 2010s, is Chapter 7 of the Augustin et al Introduction to Imprecise Probability<\/em> text. Some more specifics:<\/p>\n\n\n\n Above the focus was more on specific approaches to statistical inference, etc., but a good project topic would be to pick up an interesting, practically relevant statistics or machine learning problem and explore what’s been done with this in the literature, in particular, the imprecise probability literature. One general suggestion I can make is to browse some of the recent issues of the International Journal of Approximate Reasoning<\/a><\/em> (the flagship journal of imprecise probability) to see what people are interested in; if you find a topic there that’s interesting, then you can use that paper to find some background and earlier references. Similarly, you can check out some of the recent ISIPTA (’19<\/a> and ’21<\/a>) and BELIEF conference proceedings. Below is just a list of topics, some of them I know about and some of them I don’t. I write a little bit more below about those that I know something about. <\/p>\n\n\n\n This is a project direction that I can’t provide too much general guidance on. But if you have an application area of interest, then go ahead and see what imprecise probability work is out there. I might be able to help with some suggestions if you talk to me about the specifics you have in mind. Below is just a list of things that popped into my head as I was updating the is page.<\/p>\n\n\n\n As I’m sure you already know, computation can be a challenge in the context of imprecise probability. But rather than being discouraged by this, I hope you see it as an opportunity to develop something new and impactful. Bayesian statistics faced the same challenges prior to the 1980s, but then some new ideas (and technological advances) totally changed the game. Now fitting very complex, high-dimensional Bayesian models is almost trivial. Some of those same advances can be used for imprecise probability, but there are some additional challenges, e.g., evaluating Choquet integrals involves both integration and optimization. <\/p>\n\n\n\n There is a chapter on computation in the Augustin et al book and in the Aslett et al book. Also, I know that computation has been a hot topic in the last two ISIPTA meetings, and probably has been for some time. So you could check out some of the recent conference proceedings papers for some more modern references. A former student and I have a paper<\/a> in the ISIPTA’21 proceedings about Monte Carlo\/stochastic gradient descent ideas for doing certain IM-related computations. That paper isn’t all that remarkable, but it could be a good starting point for general computational strategies for the latest version of the IM framework. There was also the recent JASA<\/em> discussion paper<\/a> on Gibbs sampler-based techniques for computations in the Dempster–Shafer framework. <\/p>\n\n\n\n Imprecise probability, like ordinary probability, is a topic in its own right, so there are interesting questions that don’t have anything directly to do with statistics, machine learning, etc. The recent journal issues and conference proceedings suggested above would be good references to see what kinds of theoretical questions people are studying these days. Below are a few topics that I think would make interesting projects.<\/p>\n\n\n\n <\/p>\n","protected":false},"excerpt":{"rendered":" Potential topics and resources Below is a list of ideas for potential course projects somewhere in the intersection of statistics, machine learning, and imprecise probability. Some of the ideas are on the theoretical side, some are more methodological or computational, and some are borderline philosophical. It doesn\u2019t matter though, the project can be pretty much […]<\/p>\n","protected":false},"author":1231,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"acf":[],"_links":{"self":[{"href":"https:\/\/wordpress-courses2223.wolfware.ncsu.edu\/st-790-001-fall-2022\/wp-json\/wp\/v2\/pages\/487"}],"collection":[{"href":"https:\/\/wordpress-courses2223.wolfware.ncsu.edu\/st-790-001-fall-2022\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/wordpress-courses2223.wolfware.ncsu.edu\/st-790-001-fall-2022\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/wordpress-courses2223.wolfware.ncsu.edu\/st-790-001-fall-2022\/wp-json\/wp\/v2\/users\/1231"}],"replies":[{"embeddable":true,"href":"https:\/\/wordpress-courses2223.wolfware.ncsu.edu\/st-790-001-fall-2022\/wp-json\/wp\/v2\/comments?post=487"}],"version-history":[{"count":28,"href":"https:\/\/wordpress-courses2223.wolfware.ncsu.edu\/st-790-001-fall-2022\/wp-json\/wp\/v2\/pages\/487\/revisions"}],"predecessor-version":[{"id":653,"href":"https:\/\/wordpress-courses2223.wolfware.ncsu.edu\/st-790-001-fall-2022\/wp-json\/wp\/v2\/pages\/487\/revisions\/653"}],"wp:attachment":[{"href":"https:\/\/wordpress-courses2223.wolfware.ncsu.edu\/st-790-001-fall-2022\/wp-json\/wp\/v2\/media?parent=487"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Inferential models (IMs)<\/h3>\n\n\n\n
Other brands of statistical inference<\/h3>\n\n\n\n
Statistics & machine learning problems<\/h3>\n\n\n\n
Applications<\/h3>\n\n\n\n
Computation<\/h3>\n\n\n\n
Imprecise-probability proper<\/h3>\n\n\n\n