PRIMER SERIES
Friday, 4 May 2012
4.00pm
KB04 (Kirkwood Village)
Frank Lad (University of Canterbury)
What's it all about, Subjective Probability?
In this brief Primer I'll talk through the structure of the constructive
mathematics of operational subjective statistical methods, in the mode
of Bruno de Finetti. We'll address his constructive formulation of
probability (more generally, prevision which includes both probability
and expectation) via quantities, their realms, coherent prevision, the
fundamental theorem of prevision, coherent conditional prevision,
conditional quantities, the notion of regarding quantities exchangeably
and the representation of exchangeable distributions, sequential
forecasting, and the theory of proper scoring rules. Whew, that will be
a mouthful in a 30 minute chat!. It should allow you to get a grip on
the distinction between the objectivist conception of Statistics as a
study of empirical methods for estimating unobservable probabilistic
generating structures and the subjectivist conception of Statistics as a
procedure for learning about quantities about which you are uncertain
from the observation of quantities about which you were uncertain before
observing them.
Participating students will be offered a choice of the topic of the
seminar for the following week:
1. How big is your Mathematics? ... presenting the solution to a famous
urn problem you will be asked to solve before the seminar, and its
relevance to the fundamental theorem of probability and a billion dollar
problem on identifying asbestosis in a lung via x-ray methods. Presumes
stage two probability.
2. Why do whales strand when they do? ... presenting a subjectivist
statistical analysis of the timing of whale strandings relative to the
phases of the moon ... exhibiting an application of exchangeable
assessments to mixture trigonometric forecasting distributions based on
the New Zealand whale stranding data base. Presumes stage two
probability.
3. Completing the logarithmic scoring rule for assessing probability
distributions: presenting a leading edge reassessment of the logarithmic
scoring rule, with an analysis that motivates the discovery of extropy
as a complementary dual of entropy. Presumes stage two probability and
basic familiarity with entropy.
MOTIVATION: Why is Statistics the most universally detested and
distressing course of university students and graduate students
throughout the world? Whereas the classical subjectivists, Huyghens,
Bernoulli, Montmort, Condorcet, Laplace, and Augustus DeMorgan, who
ended the era, were content to assess probability in the words of
Laplace as merely "common-sense reduced to mathematics," ... the
objectivist revisions since the latter half of the 19th century have
constructed a forbidding metaphysical contortion driven by undefinable
relations of cause, titillated by in-principle unobservable
probabilities, ... dooming statistical practice to such Quixotic
ventures as the estimation of the in-principle-unobservable effects of
in-principle-unobservable independent variables on an unobservable
dependent variable which can only be measured with unobservable error!
The unfortunate lecturing statistician is left holding the bag, touting
our self-proclaimed powers to sort out these intricacies on the basis of
the world of X and Y in which we live, finite and discrete ... under the
questioning gaze of 18-year-olds for whom life has wildly departed from
the conjured vision of repetitions of identical conditions, and the
amazed looks of adults back to school for whom such metaphysical
contortions are never going to fly! It is not the lack of effort or
pedagogical skill ... IT'S THE CONTENT! Mainstream probability theory
and statistical practice, including its epicyclic objective Bayesian
appendages, is misleading and chimeric. Operational subjective
statistical methods provide a satisfying alternative.
What are Primers?
Primers in Mathematics and Statistics are short expository introductions
to a field of research by someone who is active in the area. Strengthen
your research; learn from your colleagues; develop a common language.
http://www.math.canterbury.ac.nz/primers
ALL WELCOME