3
Subjective probability
Revised:February 13, 2012
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
Lecture Notes for IE 544 Decision Analysis
Taner Bilgi
c
Department of Industrial Engineering
Boazii University
gc
34342 Bebek Istanbul, Turkey
[email protected]
June 1998
Revised February 13, 2012
Contents
1 Introduction
1.1 Newcombs problem . . . . . .
IE 544 Decision Analysis
Assignment 1.2
Due: March 30, Friday 5 pm
1. Construct a directed acyclic graph (DAG) with at least 10 nodes and 15 arcs.
Number nodes consecutively starting from 1. See whether each of the following
statements are true or not on
IE 544 Decision Analysis
Spring 2012
Assignment 0
A binary relation R on a set X is a subset of ordered pairs in X X , i.e., R X X . We
write xRy to mean the same thing as (x, y ) R, denoting x has relation R to y . (x, y ) R is
also written as not xRy .
Boazii University
Department of Industrial Engineering
IE544 Decision Analysis
Assignment 2
AlterNatives Inc. is an independent film producing company. They have recently
produced a feature film titled The Choices We Make. Leyla is the president of
AlterN
Bo azici University
g
Department of Industrial Engineering
IE 544 Decision Analysis
Examination Questions
April 10, 2012
1. The executives of the General Products Company (GPC) have to decide which of the three products to introduce, A, B, or C. Product C
9
Learning
Revised:March 24, 2012
Belief networks can be built based on:
Data from human experts: BNs were rst developed in the context of expert systems where
knowledge engineers are expected to interview experts and elicit from them their
domain knowled
8
Approximate Inference in BNs
Revised:March 24, 2012
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 algorith
10
Inuence Diagrams
Revised:March 24, 2012
An inuence diagram is (Heckerman and Shachter 1996)
1. a directed acyclic graph G containing decision and chance variables, and information,
and relevance arcs representing what is known at the time of a decision
7
Complexity of Exact Inference in BNs
Revised:March 24, 2012
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.
6
Inference in Bayesian Networks
Revised:March 24, 2012
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
Elimbel algorithm for the Family-out problem
For the Family-out problem with the conditional probability tables given as follows: P (F ) = (0.15, 0.85),
P (B ) = (0.01, 0.99).
f
f
d
d
P (L|F ) =
P (H |D) = h .7 .01
.6 .05
.4 .95
h .3 .99
and nally:
b
5
Dependency Models
Revised:February 13, 2012
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 as
4
Maximization of expected utility
Revised:February 13, 2012
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
2
Measurement Theory
Revised:February 13, 2012
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