Bayesian Methods Exam III Questions with 100% Correct Answers

Two advantages of standardizing predictors Correct Answer 1) It may make interpretation easier. Adding 1 to a standardized variable is equivalent to adding one standard deviation. This may be more meaningful than adding one to the natural scale. 2) Glitches that occur with large numbers are avoided. Standardizing is especially useful when the variable is squared or raised to a higher power, as in polynomial regression. Spurious relationship between predictors Correct Answer When an irrelevant predictor is correlated with a relevant predictor. Y vs X1 has a strong relationship. Y vs X1 and X2 has a strong relationship only with X2. Reason: Y and X1 both correlate well with X2 Masked relationship between predictors Correct Answer When the relationship between a predictor and the response is not significant when it is the only predictor in the regression, but it is significant when there is another predictor in the regression. Y vs X1 has a weak relationship. Y vs X1 and X2 has strong relationships with both. Often X1 and X2 are strongly correlated, Y has positive correlation with one, negative correlation with the other. Information of an outcome is defined as: Correct Answer the decrease in uncertainty from observing the outcome. 3 properties of a measure of uncertainty: Correct Answer 1) continuity - it should be a continuous function of the parameters of the distribution. 2) additivity - if we have one set of events, say hot or cold weather, and another set of events, say sun or rain, then the uncertainty of the combined set of events (hot sunny, hot rainy, cold sunny, cold rainy) should equal the sum of the uncertainty of hot/cold plus the uncertainty of sun/rain. 3) monotonicity - uncertainty should increase as the number of possible events increases. What MCMC algorithm must be tuned properly to maximize effeciciency? Correct Answer Metropolis algorithm