The idea that you can assign probabilities to events that have already occurred, but where we are ignorant of the result, forms the basis for the Bayesian view of probability. Put very broadly, the 'classical' view of probability is in terms of genuine unpredictability about future events, popularly known as 'chance' or 'aleatory uncertainty'. The Bayesian interpretation allows probability also to be used to express our uncertainty due to our ignorance, known as 'epistemic uncertainty', and popularly expressed as betting odds. Of course there are all gradations, from pure chance (think radioactive decay) to processes assumed to be pure chance (lottery draws), to future events whose odds depend on a mixture of genuine unpredictability and ignorance of the facts (whether Oscar Pistorius will be convicted of murder), to pure epistemic uncertainty (whether Oscar Pistorius knowingly shot his girlfriend).Well, yes, that seems to be right. It's true that Bayesian probability allows you to assign probability to past events, but it is characteristic of the Bayesian approach that a probability that reaches 1 or 0 never changes thereafter.
The judges went on to say:The chances of something happening in the future may be expressed in terms of percentage. Epidemiological evidence may enable doctors to say that on average smokers increase their risk of lung cancer by X%. But you cannot properly say that there is a 25 per cent chance that something has happened. Either it has or it has not.
What does it mean to say that there was a chance of a past event going otherwise? It means saying that the past is not ruled by physics, at least not as we generally understand physics. The house burned down for physical reasons that ought to be reliable: the heat plus the fuel plus the air. Given that, and a response from the fire department slower than Y, and the house should burn.
I think the judges got this one right. Taking an alternative view requires some philosophical sophistication that is incompatible with democracy. But even given that sophistication, it seems wrong to me.
6 comments:
Interesting. Historical outcomes, are always up for interpretation, and can always be debated.
When it comes to the kind of events that can be usefully described in terms of probability, I don't think the important thing is whether they're past or future but whether they're known or unknown. Probability is just a way of talking about things we understand only partially, such that we have some knowledge about the range and frequency of results but not yet enough to pin down the exact result. We get into trouble when we start talking about probability as though it had independence existence instead of being a way to describe partial ignorance.
Well, that's one view: that the sense we have that things are "chancy" is really a function of our ignorance, because things (past or future) really will or won't happen. Thus, our sense that coin flip has a probability of 1/2 coming up heads is really wrong: it has a probability of 1 or 0, depending on the initial conditions of the flip and given the physics involved.
Of course, things in the past are settled in a way that things in the future are not. But on this view, that too is a function of ignorance: we can know what did happen, if we observed it, but not what will happen. Yet the deterministic nature of the physics is the same, if you take this view: the past is no less certain than the future.
...Bayesian probability allows you to assign probability to past events....
In my stat classes, Bayesian probabilities had nothing to say about the outcomes of past events, only about our knowledge of those outcomes given what we knew--and what we were probabilistically guessing--about surrounding events.
The judges were right that there needs to be a care about probabilities of past events--they need to be understood as probabilities driven by current knowledge of those past events, not probabilities of the events themselves.
the deterministic nature of the physics is the same, if you take this view: the past is no less certain than the future.
In chaos theory, the future is just as certain as the past. What's uncertain is how accurately we've specified the start conditions. Of course, the accuracy of chaos theory is itself, just now, a probability assessment from our ignorance.
Eric Hines
My understanding of Bayesian probability is that once your probability goes to 1 or 0, you can't move it anymore: which means that you should (given the determinism it is based upon) set your probability for past events accordingly, however you were previously calculating them.
Of course, I think (as Tex does, based on our earlier conversation) that deterministic physics needs to be discarded. It can't be right, given its consequences, and therefore it must be wrong.
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