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Life, the Universe and Everything
Measurement True value Obs value Inference Real World Model of World Easy stuff (e.g. Physics)
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Through a glass darkly…
Measurement H1 H3 True value Real World H2 Etc... These are statistics + so are things calculated from them (mean, etc) This is inferential statistics This is descriptive statistics Hard stuff (e.g. Biology)
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Sources of error Sampling error Evolutionary error
Imagine collecting sample again and again (from same population) Evolutionary error Imagine “collecting” population again and again from same evolutionary process (same mutational and demographic processes) Drift
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Inference by maximum likelihood
Measurement H1 H3 True value Real World H2 Etc... Data, D
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Inference by maximum likelihood
P(D|H4) Measurement P(D|H1) P(D|H3) True value Real World P(D|H2) Etc... Data, D
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Inference by maximum likelihood
P(D|H4) 0.167 Measurement P(D|H1) 0.102 P(D|H3) 0.003 True value Real World P(D|H2) 0.032 Etc... Data, D
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Inference by maximum likelihood
P(D|H4) 0.167 Measurement P(D|H1) 0.102 P(D|H3) 0.003 True value Real World P(D|H2) 0.032 Etc... Data, D
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Inference by posterior probability
H4 Measurement H1 H3 True value Real World H2 Etc... Data, D
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Inference by posterior probability
P(H4|D) Measurement P(H1|D) P(H3|D) True value Real World P(H2|D) Etc... Data, D
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Inference by posterior probability
P(D|H4) 0.145 Measurement P(D|H1) 0.187 P(D|H3) 0.033 True value Real World P(D|H2) 0.021 Etc... Data, D
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Inference by posterior probability
P(D|H4) 0.145 Measurement P(D|H1) 0.187 P(D|H3) 0.033 True value Real World P(D|H2) 0.021 Etc... Data, D
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The Null Hypothesis H4 Measurement H1 H3 True value Real H0 World H2
Etc... Null Hypothesis: “Default” “Simplest” “Most Parsimonious” “Requires least parameters” “Straw man that no-one believes in anyway”
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The infamous P-value H4 Measurement H1 H3 True value Real H0 World H2
Etc... P-value: “A P-value is the probability of obtaining similar data, by chance, that is the same or more extreme than the data observed, given that the Null Hypothesis is true.”
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Real World H0 “True” D2 P(D2|H0) Real World H0 “True” Measurement D1 (obs) P(D1|H0) Real World H0 “True” D3 P(D3|H0)
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Real World H0 “True” D2 P(D2|H0) 0.018 Real World H0 “True” Measurement D1 (obs) P-value = Σ … P(D1|H0) 0.009 Real World H0 “True” D3 P(D3|H0) 0.003
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