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Published in:
2011 | OriginalPaper | Chapter
Markov Random Fields
Authors : Antonino Freno, Edmondo Trentin
Published in: Hybrid Random Fields
Publisher: Springer Berlin Heidelberg
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Let’s give Bayesian networks a break, and let us go back to our favorite topic, namely soccer. Suppose you want to develop a probabilistic model of the ranking of your team in the domestic soccer league championship at any given time
t
throughout the current season. In this setup, it is reasonable to assume that
t
is a discrete time index, denoting
t
-th game in the season and ranging from
t
= 1 (first match of the tournament) to
t
=
T
(season finale). Assuming the championship is organized as a round-robin tournament among
N
teams, then
T
= 2(
N
− 1). The ranking of your team at time
t
+ 1 is likely to change with a certain probability distribution which (
i
) accounts for the randomness of the results at the end of the corresponding matchday, and (
ii
) depends on the ranking at time
t
.