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The quotations in this article are taken out of context and presented incomplete. For example, the article quotes The chances of something happening in the fut

The quotations in this article are taken out of context and presented incomplete. For example, the article quotes 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: Hotson v East Berkshire Health Authority [1987] AC 750. Either it has or it has not. And the judgement continues: In deciding a question of past fact the court will, of course, give the answer which it believes is more likely to be (more probably) the right answer than the wrong answer, but it arrives at its conclusion by considering on an overall assessment of the evidence (i.e. on a preponderance of the evidence) whether the case for believing that the suggested event happened is more compelling than the case for not reaching that belief (which is not necessarily the same as believing positively that it did not happen). Which is exactly the bayesian approach of 'probability as state of knowledge'.

bo1024 14y ago
The quotes are contradictory. The Bayesian approach agrees with the second and disagrees with the first. I suppose you could weasel in some sort of consistency about the wording ... something like "You cannot properly say there is a 25 percent chance that something has happened, but you can properly say you believe there is a 25 percent chance that something has happened." OK, fine, but what's the difference? You still assign a percent probability to the chance that something happened, and you still rule on the basis of those beliefs. Or do you? (It's not clear to me from those quotes.)
- lifeisstillgood 14y ago
  I am paraphrasing the two quotes: You can say there is a 25% increase in chance of dying if you smoke. You cannot say there is a 25% chance that the nurse murdered those people - she either did or did not. (what we lack is the knowledge of the past event) second para: On the preponderance of evidence, the court believes beyond a reasonable doubt that the nurse *did* kill those people. That event A *did* happen - we have used evidence to fill in the gaps of our knowledge. We are not assigning a probability to it, but we recognise that life is all probabilities, but thats what reasonable doubt it all about. I think that those two quotes (modified as I understand them) are consistent. They are also not entirely Bayesian but I would prefer to be in a court of law than a court of probability.
  - bo1024 14y ago
    Hmmm, I guess I agree. But I think a Bayesian would argue that this is an argument over wording not meaning. If we formulate beliefs and act on beliefs, then how we want to word it doesn't make a difference.
- rayiner 14y ago
  Its post facto versus a priori. There is a 25% chance of something happening, but after the fact, it either did or did not happen. Averaged over many cases we can say that after the fact there is a 25% chance it happened, but criminal trials look at one specific instance, and its accurate to say that in an instance something either did or did not happen.
  - jules 14y ago
    You should still use probability to quantify that belief. Whether it happened in the past or is going to happen in the future doesn't matter. If you throw a coin, and the coin is flying in the air, what is the probability that it lands heads? By your reasoning, the motion is already in place, and it's either going to land heads or it isn't. With a high speed camera and some physics we might even be able to predict which side it will fall. Even if we go back to a little before you threw the coin, the electrons in your brain are already in place and it's already determined which way you'll throw the coin. Would it be invalid to say that there is a 50% chance that it will land heads? So even when we are talking about the future, we use probability to quantify our belief. Or perhaps more accurately, we use it to quantify our lack of knowledge: in this case our lack of knowledge about how exactly the coin will move. Since we are already using probability not just for "fundamental randomness" but for quantifying lack of knowledge about the future, what's so special about the future vs the past? It makes total sense to apply the same reasoning to the past, even if we are talking about a specific instance.
    - rayiner 14y ago
      You're shifting the argument. Sure you should, in some cases,[1] use probabilities to determine your belief about whether something happened or not. That's precisely what the court says in the second paragraph. Your beef was ostensibly with the wording of the first paragraph, but as I pointed out that when talking about things that have happened in the past, the wording is not incorrect. [1] Of course you also shouldn't sometimes use probabilities. If we have statistics saying that witnesses lie 15% of the time, is it helpful to present expert testimony to the effect of "there is a 15% probability the witness is lying?" Such evidence is not useful and also impinges on the fundamental right of the jury to judge witness credibility.
- lolcraft 14y ago
  I actually read it as not contradictory. This was about two events: one which was a priori more probable than the other, based purely on the previous experiences of the judge. That is, he considered "X probably happened because Y has a history of happening less than X". I take that to be that the judge committed a classic fallacy: he took a frequentist, limit-in-the-long-run subjective judgement, and tried to apply it to a situation where it's really not applicable. He took his priors from a mistaken frequentist consideration, that is what I interpret the first quote to say. What he should have done, the second quote says, is to "arrive[s] at its conclusion by considering on an overall assessment of the evidence". Instead of considering what happened before, he should have taken his priors from the evidence. So, in the end, it's a sentence that supports a Bayesian methodology, in this case. Or maybe the Court of Appeal just was confused at the time, who knows.

bo1024 14y ago

The quotes are contradictory. The Bayesian approach agrees with the second and disagrees with the first. I suppose you could weasel in some sort of consistency about the wording ... something like "You cannot properly say there is a 25 percent chance that something has happened, but you can properly say you believe there is a 25 percent chance that something has happened." OK, fine, but what's the difference? You still assign a percent probability to the chance that something happened, and you still rule on the basis of those beliefs. Or do you? (It's not clear to me from those quotes.)

lifeisstillgood 14y ago
I am paraphrasing the two quotes: You can say there is a 25% increase in chance of dying if you smoke. You cannot say there is a 25% chance that the nurse murdered those people - she either did or did not. (what we lack is the knowledge of the past event) second para: On the preponderance of evidence, the court believes beyond a reasonable doubt that the nurse *did* kill those people. That event A *did* happen - we have used evidence to fill in the gaps of our knowledge. We are not assigning a probability to it, but we recognise that life is all probabilities, but thats what reasonable doubt it all about. I think that those two quotes (modified as I understand them) are consistent. They are also not entirely Bayesian but I would prefer to be in a court of law than a court of probability.
- bo1024 14y ago
  Hmmm, I guess I agree. But I think a Bayesian would argue that this is an argument over wording not meaning. If we formulate beliefs and act on beliefs, then how we want to word it doesn't make a difference.
rayiner 14y ago
Its post facto versus a priori. There is a 25% chance of something happening, but after the fact, it either did or did not happen. Averaged over many cases we can say that after the fact there is a 25% chance it happened, but criminal trials look at one specific instance, and its accurate to say that in an instance something either did or did not happen.
- jules 14y ago
  You should still use probability to quantify that belief. Whether it happened in the past or is going to happen in the future doesn't matter. If you throw a coin, and the coin is flying in the air, what is the probability that it lands heads? By your reasoning, the motion is already in place, and it's either going to land heads or it isn't. With a high speed camera and some physics we might even be able to predict which side it will fall. Even if we go back to a little before you threw the coin, the electrons in your brain are already in place and it's already determined which way you'll throw the coin. Would it be invalid to say that there is a 50% chance that it will land heads? So even when we are talking about the future, we use probability to quantify our belief. Or perhaps more accurately, we use it to quantify our lack of knowledge: in this case our lack of knowledge about how exactly the coin will move. Since we are already using probability not just for "fundamental randomness" but for quantifying lack of knowledge about the future, what's so special about the future vs the past? It makes total sense to apply the same reasoning to the past, even if we are talking about a specific instance.
  - rayiner 14y ago
    You're shifting the argument. Sure you should, in some cases,[1] use probabilities to determine your belief about whether something happened or not. That's precisely what the court says in the second paragraph. Your beef was ostensibly with the wording of the first paragraph, but as I pointed out that when talking about things that have happened in the past, the wording is not incorrect. [1] Of course you also shouldn't sometimes use probabilities. If we have statistics saying that witnesses lie 15% of the time, is it helpful to present expert testimony to the effect of "there is a 15% probability the witness is lying?" Such evidence is not useful and also impinges on the fundamental right of the jury to judge witness credibility.
lolcraft 14y ago
I actually read it as not contradictory. This was about two events: one which was a priori more probable than the other, based purely on the previous experiences of the judge. That is, he considered "X probably happened because Y has a history of happening less than X". I take that to be that the judge committed a classic fallacy: he took a frequentist, limit-in-the-long-run subjective judgement, and tried to apply it to a situation where it's really not applicable. He took his priors from a mistaken frequentist consideration, that is what I interpret the first quote to say. What he should have done, the second quote says, is to "arrive[s] at its conclusion by considering on an overall assessment of the evidence". Instead of considering what happened before, he should have taken his priors from the evidence. So, in the end, it's a sentence that supports a Bayesian methodology, in this case. Or maybe the Court of Appeal just was confused at the time, who knows.