1. Consider the Bradley-Terry model with home advantage (BTHA) which is defined as ύλ if i is at home, P(i beats j) = ₁ +d; Xi if j is at home, di+vdj where > 0 measures home advantage ( > 1) or disadvantage ( < 1), and A₁, A¡ are the ability parameters for competitors i and j, respectively. It can be shown that the log likelihood of A, based on results of n independent matches is K l(A, y) = H log(y) + Σw; log(A;) - ΣΣn¡j log(vλ¡ + Aj), i=1 i=1 ji K (1) where w; denotes the number of wins for i, H denotes the total number of home wins, and nij denotes the number of times that i plays at home against Derive update equations for Xi, i = 1..., K, and as part of an iterative algorithm for determining the maximum likelihood estimates Â, &.
1. Consider the Bradley-Terry model with home advantage (BTHA) which is defined as ύλ if i is at home, P(i beats j) = ₁ +d; Xi if j is at home, di+vdj where > 0 measures home advantage ( > 1) or disadvantage ( < 1), and A₁, A¡ are the ability parameters for competitors i and j, respectively. It can be shown that the log likelihood of A, based on results of n independent matches is K l(A, y) = H log(y) + Σw; log(A;) - ΣΣn¡j log(vλ¡ + Aj), i=1 i=1 ji K (1) where w; denotes the number of wins for i, H denotes the total number of home wins, and nij denotes the number of times that i plays at home against Derive update equations for Xi, i = 1..., K, and as part of an iterative algorithm for determining the maximum likelihood estimates Â, &.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter8: Polynomials
Section8.1: Adding And Subtracting Polynomials
Problem 58PPS
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Transcribed Image Text:Topic 1: Sports Modelling
1. Consider the Bradley-Terry model with home advantage (BTHA) which is defined as
ψιλι
ydi + dj
if i is at home,
if jis at home,
P(i beats j)
=
Xi
di+d,
where > 0 measures home advantage (> 1) or disadvantage ( < 1), and A₁, Aj are
the ability parameters for competitors i and j, respectively.
It can be shown that the log likelihood of A, & based on results of n independent matches
is
K
K
l(A, 4) = H log() + Σw, log(;) - Σnij log(wλ¡ + Aj),
+ Σ; kag (A) - [E
i=1
i=1 ji
(1)
where w; denotes the number of wins for i, H denotes the total number of home wins,
and ni denotes the number of times that i plays at home against j.
=
Derive update equations for Xi, i 1..., K, and as part of an iterative algorithm for
determining the maximum likelihood estimates Â, &.
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