Residual
Definition: The signed difference between an observation and a model prediction.
Why it matters here: In Model Selection and Residuals, Residual is needed to reason about weighted least squares, residuals, AIC/BIC, and posterior checks rather than merely label the phenomenon.
Relationship: It is interpreted alongside Weighted least squares and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: BIC does not replace residual diagnosis or scientific interpretation.
\(BIC=k ln(n)-2 ln(L_max)\)
Weighted least squares
Definition: A fit minimizing squared residuals scaled by their uncertainty or covariance.
Why it matters here: In Model Selection and Residuals, Weighted least squares is needed to reason about weighted least squares, residuals, AIC/BIC, and posterior checks rather than merely label the phenomenon.
Relationship: It is interpreted alongside Likelihood and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: BIC does not replace residual diagnosis or scientific interpretation.
Likelihood
Definition: The probability assigned to observed data as a function of model parameters.
Why it matters here: In Model Selection and Residuals, Likelihood is needed to reason about weighted least squares, residuals, AIC/BIC, and posterior checks rather than merely label the phenomenon.
Relationship: It is interpreted alongside BIC and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: BIC does not replace residual diagnosis or scientific interpretation.
BIC
Definition: The Bayesian information criterion, a likelihood-based score with a sample-size-dependent complexity penalty.
Why it matters here: In Model Selection and Residuals, BIC is needed to reason about weighted least squares, residuals, AIC/BIC, and posterior checks rather than merely label the phenomenon.
Relationship: It is interpreted alongside Posterior predictive check and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: BIC does not replace residual diagnosis or scientific interpretation.
Posterior predictive check
Definition: A comparison between observed structure and replicated data generated from a fitted probabilistic model.
Why it matters here: In Model Selection and Residuals, Posterior predictive check is needed to reason about weighted least squares, residuals, AIC/BIC, and posterior checks rather than merely label the phenomenon.
Relationship: It is interpreted alongside Residual and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.
Limitation or common confusion: BIC does not replace residual diagnosis or scientific interpretation.