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4.4 R Code > 4.4.1 R Code for Figure 4.1 - Pg. 69

4.4 R Code 69 that when p(D | i ) = 0 for all i = j, then, no matter how small the prior p( j ) > 0 is, the posterior p( j | D) must equal one." Somehow it sounds bet- ter the way Holmes said it. The intuition behind Holmes's deduction is clear, though: When we reduce belief in some possibilities, we necessarily increase our belief in the remaining possibilities (if our set of possibilities exhausts all conceivable options). Thus, according to Holmesian deduction, when the data make some options less believable, we increase belief in the other options. 4.3.5.2 Judicial Exoneration The reverse of Holmes's logic is also commonplace. For example, when an object d'art is found fallen from its shelf, our prior beliefs may indict the house cat, but when the visiting toddler is seen dancing next to the shelf, then the cat is exonerated. This downgrading of a hypothesis is sometimes called explaining away of a possibility by verifying a different one. This sort of exoneration also follows from Bayesian belief updating: When p(D | j ) is higher, then, even if p(D | i ) is unchanged for all i = j, p( i | D) is lower. This logic of exoneration is based on competition of mutually exclusive possibilities: If the culprit is