Dorothy was in a strange land and had no idea what would happen next. The good witch of the North said she should follow the scientific method to a sound forecast. Unfortunately, neither she (nor anyone else) explained what exactly the scientific method is.
As she wandered down the yellow brick forking path of endless options, Dorothy was surprised by the voice of a heuristic firmly attached to a degenerate prior. She freed the heuristic from the prior and discovered that he was amazingly swift and flexible. She suggested that with his enormous speed he could quickly reach a sound conclusion.
The disconsolate heuristic said that he could “If I only had a brain.”
And they wandered off to find a shiny extremely strong hypothesis test with a razor sharp ax. The hypothesis test was rigidly chopping down the same deadwood. Dorothy said that his great destructive power could help him clear the way to the truth. All he needed to know was a promising direction, and he could eliminate all plausible but false hypotheses leaving only the truth.
The sorrowful hypothesis test explained that he had no idea how to create hypotheses or to decide which ones were worth testing and sang that he could find the truth “If I only had a heart”.
Having heard of the wonderful Wizard of Odds who could solve all of their problems, they made a bee-line for the land of Odds. On the way they stumbled over a cowardly line. The cowardly line said he made no claim about expected values or disturbance terms, because he claimed to be nothing other than what he was, the King of the summary statistics, the OLS regression.
They said that with his daring contempt for consistency and lack of any fear of bias, he surely cold provide them with a forecast. The lion explained that he fit but didn’t forecast – that treating an OLS regression as a forecasting model might appeal to the foolish heuristic, and might follow from implausible hypotheses which were easy to test and reject, but he couldn’t do it because he didn’t have the courage.
Finally they arrived at the City of Odds where they met a wonderful wizard of odds named Thomas Bayes, who dramatically provided the probability of any conceivable event based on any conceivable data set. They were in awe until Toto barked. The Wizard boomed that they should pay no attention to the arbitrary prior behind the curtain.
So Dorothy gave up on the effort to solve the problem of induction. And Toto too.