Lecture Notes for IE544 Decision Analysis
Taner Bilgi
c
Department of Industrial Engineering
Boazii University
gc
34342 Bebek Istanbul, Turkey
[email protected]
June 1998
Revised February 24, 2004
Contents
1 Introduction
1.1 Newcombs problem . . . . . . .
2
Measurement Theory
Revised:February 24, 2004
The theory of measurement deals with representing qualitative structures with numerical
ones . The aim is to assign numbers to the elements of the qualitative structure such that
the properties of the qualita
7
Complexity of Exact Inference in BNs
Revised:April 1, 2004
We follow Cooper (1990) and reduce a decision problem version of the inference in BN
problem to a well known NP-complete problem 3SAT (three satisability).
We start by dening the 3SAT problem. C
5
Dependency Models
Revised:March 16, 2004
Denition 5.1 A dependency model, M over a nite set of elements U is any subset of
triplets (X, Y, Z ) where X, Y, Z are disjoint subsets of U . The triplets in M represent independencies, i.e., (X, Y, Z ) M asser
8
Approximate Inference in BNs
Revised:April 1, 2004
Since exact inference in belief networks is NP-hard we do not expect to nd an ecient
algorithm to solve the exact inference problem unless P N P .
In this case we can think of an approximation algorithm
6
Inference in Bayesian Networks
Revised:March 17, 2004
6.1
Representation
A Probabilistic Network (aka causal graph, Bayesian belief network, etc.) is a graphical
representation of a joint probability function.
Denition 6.1 G = cfw_N, A is a directed gra
3
Subjective probability
Revised:February 24, 2004
3.1
Interpretations of probability
The interpretation of what probability means is still a subject of intense debate. One major division is between objective and epistemological understandings of what P r
4
Maximization of expected utility
Revised:March 17, 2004
Denition 4.1 Let X = cfw_x1 , x2 , , xr be a nite set of possible prizes, let
= p1 , x1 ; p2 , x2 ; ; pr , xr
be a simple lottery where pi 0 is the probability of winning xi , i = 1, 2, , r and r=