Wallet Game: Probability,Likelihood, and Extended Likelihood |
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Authors: | Yudi Pawitan Youngjo Lee |
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Affiliation: | 1. Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden;2. Department of Statistics, Seoul National University, Seoul, Korea |
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Abstract: | We propose a likelihood explanation to the two-person wallet game, a probability-related paradox, where an obviously fair game may appear favorable to both players. Yet a small variation of the game, without changing its fairness, turns it to seem unfavorable. The extended likelihood concept seems logically necessary if we want to allow the sense of uncertainty associated with a realized but still unobserved random outcome, while at the same time avoid potential probability-related paradoxes. |
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Keywords: | Exchange paradox Fisher Hierarchical generalized linear models Random effects |
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