Bayesian Testing and Forecasting Flashcards
Why is Bayesian analysis often called subjective? Do you find this subjectiveness a serious problem? Motivate your answer
Two answers are possible and are correct. You can either say that it is a serious
problem and come up with a good motivation or you can state that it is not a
serious problem and provide good arguments. A possible answer is:
I find it a serious problem. In small samples the posterior results depend on
the prior specification you use. You may opt for an uninformative prior but this is not allowed if you want to perform model comparison. Bayesian model
comparison can be very sensitive to the prior specification you choose. People
will always disagree about the right prior specification and hence the Bayesian
approach cannot be used to test hypothesis in an objective way.
How do different loss functions affect Bayesian point estimates, and which ones would be most suitable for certain applications?
Different loss functions affect Bayesian point estimates by determining the type of error to minimize. The quadratic loss function leads to the posterior mean, ideal for precision. The absolute loss function gives the posterior median, suited for robustness against outliers. The zero-one loss function results in the posterior mode, useful for decision-making where the most probable outcome is needed. Each function is applied based on the need for accuracy, robustness, or certainty.
