= Bayesian confirmation
{c}
{title2=$P(H\mid E,K)>P(H\mid K)$}
Evidence $E$ confirms $H$ relative to background $K$ when it increases its <conditional probability>. With $0<P(H\mid K)<1$ and positive evidence <probability>, <Bayes' theorem> gives
$$
P(H\mid E,K)>P(H\mid K)\iff P(E\mid H,K)>P(E\mid\neg H,K).
$$
Indeed, writing $p=P(H\mid K)$, $a=P(E\mid H,K)$ and $b=P(E\mid\neg H,K)$ gives the <posterior probability> $pa/(pa+(1-p)b)$; comparison with $p$ reduces to $a>b$. Thus <scientific confirmation> depends on the alternatives and background, not just on a statement's logical form.
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