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 o
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
Co
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 wheth
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 re
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 title
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
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 inte
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 .
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 ar
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 (thr
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 probabilit
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
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 triple
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
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 qualit