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  "body": "\n## Summary\n\nThe Bayes factor of two models is the ratio of the probabilities that each model gives to the observed data.\nIn each model the probability is averaged over the prior of its parameters.\nIt is the factor by which the data change the odds between the two models.\nIt is the Bayesian tool to compare hypotheses and models, an alternative to [[p-values|0GGKJGZF6D]] and likelihood-ratio tests.\n\n## Explanations\n\n### L1 human\n\nTwo theories compete to explain the same data.\nEach theory predicts the data with some probability, averaged over what it leaves uncertain.\nThe Bayes factor is the ratio of these two predictions: a value of $10$ means that the data were $10$ times more expected under the first theory.\nWhatever odds you gave the theories before, you multiply them by the Bayes factor to get your odds after seeing the data.\n",
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