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text: 'Let's say you have a piece of evidence $e$ and a set of hypotheses $\\mathcal H.$ Each $H_i \\in \\mathcal H$ assigns some [56v likelihood] to $e.$ The function $\\mathcal L_{e}(H_i)$ that reports this likelihood for each $H_i \\in \\mathcal H$ is known as a "likelihood function."\n\nFor example, let's say that the evidence is $e_c$ = "Mr. Boddy was killed with a candlestick," and the hypotheses are $H_S$ = "Miss Scarlett did it," $H_M$ = "Colonel Mustard did it," and $H_P$ = "Mrs. Peacock did it." Furthermore, if Miss Scarlett was the murderer, she's 20% likely to have used a candlestick. By contrast, if Colonel Mustard did it, he's 10% likely to have used a candlestick, and if Mrs. Peacock did it, she's only 1% likely to have used a candlestick. In this case, the likelihood function is\n\n$$\\mathcal L_{e_c}(h) = \n\\begin{cases}\n0.2 & \\text{if $h = H_S$} \\\\\n0.1 & \\text{if $h = H_M$} \\\\\n0.01 & \\text{if $h = H_P$} \\\\\n\\end{cases}\n$$\n\nFor an example using a continuous function, consider a possibly-biased coin whose bias $b$ to come up heads on any particular coinflip might be anywhere between $0$ and $1$. Suppose we observe the coin to come up heads, tails, and tails. We will denote this evidence $e_{HTT}.$ The likelihood function over each hypothesis $H_b$ = "the coin is biased to come up heads $b$ portion of the time" for $b \\in [0, 1]$ is:\n\n$$\\mathcal L_{e_{HTT}}(H_b) = b\\cdot (1-b)\\cdot (1-b).$$\n\nThere's no reason to [1rk normalize] likelihood functions so that they sum to 1 — they aren't probability distributions, they're functions expressing each hypothesis' propensity to yield the observed evidence. For example, if the evidence was really obvious ($e_s$ = "the sun rose this morning,") it might be the case that almost all hypotheses have a very high likelihood, in which case the sum of the likelihood function will be much more than 1.\n\nLikelihood functions carry _absolute_ likelihood information, and therefore, they contain information that [1rq relative likelihoods] do not. Namely, absolute likelihoods can be used to check a hypothesis for [227 strict confusion].',
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