The Diverse Bayes Factor Case Study

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The Inverse Bayes’ Factor
The risk ratio, ρ in eEquation. (4.1), measures the odds of the null hypothesis being “true” (the party wins the election from a constituency) to it being “false” (the party loses the election from that constituency) under a particular set of data which, in this case, is that the party is the incumbent party in the constituency. In this formulation of risk, the data applicable to the different outcomes (winning or losing the election) was the same (the party was the incumbent). An alternative view of risk is obtained by posing the following question: given two rival scenarios— – in the first, a party is the incumbent in an election to a constituency while, in the second, it is a challenger— - what is the ratio of its probabilities of winning in these different situations?
In this case, the risk ratio of being the incumbent party is the ratio of the likelihood that the party wins the election if it was the incumbent to the likelihood that the party wins the election if it was a challenger. Here the outcome is the same (the party wins the election) but the data that is input is different (incumbent or challenger). In order to answer this question, the relevant risk ratio (represented by σ) is . Hereafter, σ is referred to as …show more content…

The term in eEquation. (4.3) is the inverse Bayes Factor (IBF) applied to the party that won that constituency. The inverse Bayes Factor is the odds of the null hypothesis being true (the party wins) under one set of data (the party was the incumbent), against it being true (the party wins) under the obverse set of data (the party was a challenger). If then, given that the hypothesis is true (the party wins), we are more (less) likely to observe one set data (A: the party is the incumbent party) than the complementary set of data (: the party is a

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