An ergodic world is certainly well modellable this way. And there are parts of the world that are ergodic (to a degree). But lots that are not, which is nice, because otherwise you would not have life (Ilya Prigiogine used to stress that all the interesting stuff arises in non-equilibrium situations, essentially the same thing as non-ergodic).
That said, your post is a nice way to demonstrate the strength of the assumptions one needs to make to justify the usual actuarial stance, and rely on frequencies / probabilities...
The contrast between the comet and the life table stayed with me. I came away thinking less about how much history a forecast uses, and more about why the next event should be treated as comparable to the previous ones.
Past observations can lead to the developments of frameworks, which can be used to help forecast potential events. These frameworks need rigor, whether quantitative or qualitative, and require testing to see how accurate they are, which can only be done after the fact.
I don't believe it. :-) I reckon markets are non-ergodic. Often. I'm not alone; Paul David has made much of non-ergodicity in economics, eg https://www.scielo.br/j/rep/a/DXDDVxPMYBTZvsXwnvd4NJw/?format=pdf&lang=en
An ergodic world is certainly well modellable this way. And there are parts of the world that are ergodic (to a degree). But lots that are not, which is nice, because otherwise you would not have life (Ilya Prigiogine used to stress that all the interesting stuff arises in non-equilibrium situations, essentially the same thing as non-ergodic).
That said, your post is a nice way to demonstrate the strength of the assumptions one needs to make to justify the usual actuarial stance, and rely on frequencies / probabilities...
The contrast between the comet and the life table stayed with me. I came away thinking less about how much history a forecast uses, and more about why the next event should be treated as comparable to the previous ones.
Past observations can lead to the developments of frameworks, which can be used to help forecast potential events. These frameworks need rigor, whether quantitative or qualitative, and require testing to see how accurate they are, which can only be done after the fact.
"“Past performance is not indicative of future results” is just a simpler way of re-phrasing the riddle of induction.