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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, &.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow
ideas from gpt, but please do not believe its answer.Very very grateful!

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, &.
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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