LPS 240: Seminar on Evidence
Introduction. The purpose of
this seminar is to study how we do (and/or should) transition from
various bodies of evidence to assessments about how and how well they
support or undermine various aspects of a given scientific theory. We
will be primarily concerned with the typical case where the evidence at
hand is indeterminate, because there is error in our measurements, our
models are simplifications of complex phenomena, etc. In particular, we
will examine some ways in which evidence in its most basic form is
manipulated and transformed into some more useful mathematical
object(s) that then bear(s) on a precise question in a precise way.
Mathematical requirements.
There are no formal requirements for this course, although students
should be willing to pick up some basic techniques on the fly. The
first part of the course will be largely quantitative in nature, and
certain assumptions may have to be taken on faith by some. I will try,
though, to make the centrally important points accessible to those
whose background in linear algebra and real analysis is largely limited
to what they've acquired in this course. (Although not all of our
authors will use them, all integrals may be assumed to be Riemann
integrals,
except when explicitly noted otherwise.)
Expectations. Those enrolled in
the course will be expected to be actively engaged in the discussion
components of the course. They will also be expected to give at least
one in-class presentation, and to submit a term paper of the usual
length and maturity.
Presentations. A major point of
giving presentations is as preparation for giving professional talks
and presentations. For this reason, I offer the following
recommendations. Those presenting technical material
should try to relate it to some relevant conceptual issues. In
particular, the presentation should be accessible to persons without a
technical background, so that they can see what the relevant issues are
and why they matter. Those presenting more conceptual material should
try to relate it to the nitty-gritty details of actual
practices/methods, so as to illustrate how some philosophical idea(s)
are (or are not) realized in real life.
The course is divided into two main parts, described below. A
preliminary and provisionary syllabus can be found here.
Part A: Some theoretical aspects of
statistical methods.
In this first part of the course, we will examine some foundational
aspects
of ordinary statistical methods. Many of these methods (e.g.,
correlation, regression, anova, statistical inference) can be usefully
viewed as phenomena occurring in high-dimensional Euclidean space. We
will see why this is so, and also establish some parallel results that
place the evidence in other (unique) geometries when it contains
different kinds of uncertainty or randomness. Although this
presentation does not resemble how such methods are introduced in
undergraduate textbooks, it is, I believe, a vastly more powerful and
flexible framework from which to understand and utilize statistical
methods. In this overview, I will tack heavily towards a theoretical
understanding of the methods, and away from many of the practical
issues of implementing them. However, throughout the course, we will
frequently examine the multifaceted space between cases where these
methods do Good Works, and cases where they are in bondage to sin, and
cannot free themselves. Readings will be drawn from selections from:
- Wickens, Thomas D. 1995. The Geometry of
Multivariate Statistics. Hillsdale, NJ: Lawrence
Erlbaum Associates.
- Bulmer, M. G. 1979. Principles
of Statistics. New York: Dover
Publications.
- Hogg, Robert V., Joseph W. McKean, and Allen T. Craig.
2005. Introduction to Mathematical
Statistics. 6th ed. Upper Saddle River, NJ: Pearson
Prentice
Hall.
- Stuart, Alan, Keith Ord, and Steven Arnold 1999. Kendall’s Advanced
Theory of Statistics: Volume 2a:
Classical Inference and the Linear Model (6th ed.).
London:
Hodder Arnold
- O’Hagan, Anthony, and Jonathan Forster 2004. Kendall’s Advanced Theory of
Statistics: Volume 2B:
Bayesian Inference (2nd ed.). London: Hodder Arnold.
You will want to obtain a copy of Wickens 1995 and Bulmer 1979. I will
upload
pdfs of the relevant portions of the other texts.
Part B: Topics. In this second
part of the course, we will examine a variety of issues of
philosophical relevance from a mathematically informed empirical
perspective. What material we cover in this part will be partly
determined by the interests of the participants. The readings break
into three general topics: (i) using/analyzing statistical methods in
philosophical contexts, (ii) further statistical theory of relevance to
philosophy, (iii) expert decision making (i.e., do we really need all
these methods, or are we better off just training ourselves to make
informal, holistic professional judgments?).