Ph.D. course on
Fundamentals of Bayesian Reasoning
November-December 2016
The course will be given at the Department of Mathematical Sciences, Chalmers
and the University of Gothenburg. Professor in charge will be
Olle Häggström.
.
The topic of the course lies at the intersection between several
disciplines, including mathematical statistics, economics and philosophy.
We will look into the theory, developed in the 20th century by
von Neumann, Morgenstern, Savage and others, that purports to give us
reason to take a Bayesian approach to decision making and statistical
inference, and we will try to critically evaluate how strong these
reasons are. Some fundamental problems in adopting a Bayesian approach
in practice will be addressed, including how to choose a prior
distribution without invoking arbitrary subjectivity, as well as the
notorious issue of anthropic bias and observation selection effects.
The course will draw on material from various sources,
including books such as...
...as well as research articles.
The course begins on November 4, and is planned to
run until we take off for
Season's Holidays in December.
I will give lectures, and invite contributions by participants. We will meet
(some) Tuesdays at 10-12, and (some) Fridays at 10-12, always in room MVL14
at the Department of Mathematical Sciences, Chalmers. The more
precise schedule is as follows.
- Friday, November 4, at 10.00-11.45: Basic decision-theoretic
setup, utility, Pascal's wager etc. Cantor's theorem on existence of
utility (Gilboa, Section 6.1).
- Tuesday, November 8, at 10.00-11.45: The von
Neumann-Morgenstern Theorem (Gilboa, Chapter 8).
- Friday, November 11, at 10.00-11.45: De Finetti's Theorem
(Gilboa, Chapter 9).
- Tuesday, November 15, at 10.00-11.45: Savage's Theorem
(Gilboa, Chapter 10).
- Tuesday, November 22, at 10.00-11.45: Dutch book argument
for Bayesian conditionalization (very loosely based on
Stanford
Encyclopedia of Philosophy).
- Friday, December 2, at 10.00-11.45: The choice of prior.
Solomonoff's
prior (Rathmanner & Hutter, and Häggström).
- Tuesday, December 6, at 10.00-11.45: The problem
of indexical information (mostly Bostrom).
- Tuesday, December 13, at 10.00-11.45:
- Claes Andersson: Cyclical preferences.
- Rikard Isaksson: Decision-theoretic foundations of game thoery.
- Friday, December 16, at 9.00-11.45 (note the time!):
- Rasmus Einarsson: Non-black non-ravens, old evidence, and other troubles in Bayesian theory for scientific confirmation.
- Nikloas Huhnstuck: Agreeing to disagree.
- Sara Blom: Bayesianism and utilitarianism.
- Tuesday, December 20, at 10.00-11.45:
- Susanne Pettersson, Objective Bayesianism.
- Sebastian Jobjörnsson: Logical uncertainty.
Completion of the course will be rewarded by 5 hp credits, and involves
- contributing a 45-minute talk on some topic within the scope
of the course (to be determined in consultation with me), and
- writing an essay at the end of the course, bringing together
and reflecting over two or more aspects of Bayesian reasoning covered
in the course. "Does rationality require Bayesian reasoning?" would
serve well as a topic of the essay, although other topics are allowed
provided they fit with the course content.
A suitable length of the essay would be around 20 000
characters (or more). Deadline for handing it in (on paper or
in pdf format) is January 11, 2017.
As to the 45-minute oral presentations, those wishing to contribute need to
get in touch with me no later than Thursday November 10
to agree about a date and topic for the contribution.
Following are some ideas for topics, but other ideas are welcome (provided,
of course, that they are relevant to the course).
- Bayesian reasoning forbids cyclical preferences. But do we
really avoid cyclical preferences in daily life? And should we? Many
have written about this, including Lars Bergström and
Peter Fishburn.
- The 2003 book
Probability
Theory: The Logic of Science by the late E.T. Jaynes has
become a bit of a cult classic among some proponents of Bayesian reasoning.
What does he say?
- It seems that Bayesian reasoning cannot account for so-called
logical uncertainty (such as maintaining a nontrivial probability
distribution for the 347850045229:th decimal of pi). Or can it?
Scott Garrabrant and collaborators seem to have made some progress on this.
- Nobel laureate Robert Aumann's classic 1976
paper Agreeing to disagree offers a clever
and subtle argument that may have consequences for Bayesian reasoning.
For later developments, see, e.g., the paper by Tyler Cowen and
Robin Hanson.
- Philosopher Jon Williamson advocates something he calls Objective Bayesianism. In my review of his book, I claim the idea is misguided. Who (if anyone) is right?
- A recurrent theme in 20th century philosophy of statistics is
the struggle between Bayesians and frequentists. A review of
this debate might be interesting. And where does it stand today?
- Andrew Gelman's blog is
full of interesting stuff on the theory and practice of Bayesian
statistics.
- Bayesian reasoning and utilitarian ethics seem related. Much
has been written on this. Especially influential seems to be the
work on this topic by the late economist and Noble laureate
John Harsanyi.
- Is the distinction between strict and soft Bayesian approaches
that psychologists Shira Elqayam and Jonathan Evans make in their 2013
paper a valuable concept?
.