"PRINCIPLES OF PHYLOGENETICS: ECOLOGY AND EVOLUTION" Integrative Biology 200B University of California, Berkeley Lab for Jan 27, 2009, Introduction to Statistical Thinking A. Concepts: • A way of making inferences in the face of uncertainty (epistemology). • The statistical universe (ontology) • Inductive vs. deductive reasoning • Descriptive statistics vs. hypothesis testing • What is a hypothesis? • What is a null hypotheses? • What is "error"? Type I & Type II error • Precision vs. accuracy • Sampling (and the concept of "randomness" and "bias") • What is an experiment? How does it differ from an observation? • Experimental Design - observations planned in advance • Experimental and sample units • Replication vs. pseudoreplication • Control • Causality B. Data • Population • Sample • Parameters • Scales of measurement: - Nominal (only a name) - Ordinal (ranking of categories) - Interval or Ratio (continuous values) • Central tendency: - mean - median• Dispersion (why is this important?): - range - standard deviation and variance - standard error - quartiles C. Liklihood, Bayes, and frequentist approaches Likelihood = P(Data | Model & Parameters) P(A&B)=P(A|B)P(B) P(A&B)=P(B|A)P(A) Maximum likelihood – pick the best model Bayesian – calculate the posterior probability of each model Estimate with MCMC Nuisance parameters ML: Joint estimation-Maximize likelihood for all parameters at once Bayes: Marginal estimation–Sum over all possible values of nuisance parameters Frequentist – Does the data support the given model over another? Nested hypotheses Compare 2*LRT to C2 to calculate p-value Can also compare non-nested hypotheses (i.e. AIC) Bayesian – How much does the data support this model relative to another? MCMC calculates uncertainty as a product of the
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