A report on the Workshop Imprecise Probabilities in Statistics and Philosophy, by Seamus Bradley

A workshop on Imprecise Probabilities in Statistics and Philosophy took place at LMU Munich on the 27th and 28th of June. The workshop was co-organised by the Munich Center for Mathematical Philosophy and the LMU statistics department. There were speakers from four continents, and a broad range of views in philosophy and statistics were represented. The conference was a great success and we hope that this leads to closer ties between the philosophy and statistics communities.

The conference opened with the first keynote talk by Teddy Seidenfeld who discussed two criteria for coherence of personal probabilities and their extensions to Imprecie Probabilities (IP). Next, Carl Wagner discussed an extension of Jeffrey conditioning to more general kinds of evidence. Frank Coolen then discussed non-parametric predictive inference which naturally gives rise to sets of probabilities. Catrin Campbell-Moore showed how IP arises when attempting to give a semantics for self-referential probabilities.

Brian Hill argued that the standard dynamic choice argument against non-expected utility theories is mistaken. Arthur Paul Pedersen and Gregory Wheeler characterised the conditions under which a set of probabilities is subject to dilation. Frederik Herzberg discussed aggregation of infinitely many probability judgements. The first day of the conference closed with Arthur van Camp building bridges between approaches to rational belief based on desirable sets of gambles and choice functions.

The second keynote speaker, Fabio Cozman, opened day two of IPSP.
He discussed the difficulties with finding a concept of independence for IP that satisfies standard graph-theoretical assumptions. Yann Bennetreau-Dupin pointed out that the problem with “noninformative” (precise) priors being too informative can be overcome with IP and thereby solve paradoxes like the Doomsday paradox. Jan-Willem Romeijn discussed how to develop a theory of when statistical information sanctions full belief. Anthony Peressini used interval analysis applied to imprecise chances to avoid some problems with the discontinuous evolution of chance.

Marco Cattaneo used a measure based on likelihoods to give some content to the “reliability index” in Gärdenfors and Sahlin’s Unreliable Probabilities model. Seamus Bradley argued that two prima facie problems for updating IP aren’t problems once the proper interpretation of IP is used. Namjoong Kim discussed another problem for IP updating. The conference closed with our final keynote speaker, James M. Joyce, who discussed using scoring rules to model an agent’s epistemic values (e.g. an agent’s attitude to epistemic risk).

The workshop was supported by the Alexander von Humboldt Foundation, the LMU Statistics department and the LMU Universitätsgesellschaft.
The keynote talks were filmed and the videos are available online through the media page of the conference website.

About the author

Seamus Bradley is a postdoctoral research fellow at the Munich Center for Mathematical Philosophy at LMU Munich. His research interests are in philosophical theories of rational belief and decision, and philosophy of science. More information can be found at seamusbradley.net

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