Posted: Jan 08, 2015 6:19 pm
by Thommo
Lowpro wrote:What MLE modelling techniques have you seen? Keep this is mind right now. Probability modeling only cares about variation; more than one measurement. A sample size of 1 would be one coin, two states: Heads or Tails. You can determine likelihood without ever flipping that coin once because you know it's variation, you just will have very little confidence in it (in the case of an unfair coin). That's the point of why probability modeling is easy; the confidence is what matters though.


I'm not sure what you mean by this, yes it's easy to make a probability model with even very restricted data - we know quite a bit about a coin - we know the number of outcomes and how to label each of them, with certainty. But the accurate parts of such a model come from that knowledge, the rest is pure guesswork, we're predisposed to think of coins as fair because we encounter lots of fair coins and know quite a bit about the kinematics of coin tossing. But saying modeling is "easy" just means making any old shit up is "easy", I'm not sure it's accurate to even describe that as modeling.

It's one thing to come up with a no-confidence model where you know the underlying distribution is binomial, but what are you going to do where there's no information about the underlying distribution? You need either that information or a sample size sufficient for the central limit theorem to be applied.

Lowpro wrote:Now if there's no possibility then we have NO information. Imagine we have a coin with two states, heads and tails, but it is unfair and will NEVER land heads up. You could write a probability of 0.5 for both, but landing heads up is NOT POSSIBLE and if you tested this you'll never have the necessary variation (it will always lands tails up).


Right, I agree, the probability is somewhere between 0 and 1. The value of guessing it's 0.5 is nonexistent without wider context (which we do have for a coin, which might make the example misleading for intuitions).

Lowpro wrote:The probability works, the possible does not. God has no information, no variation, thus is impossible. Even if we had some sufficient probability of God, it would be impossible.


I'm sorry, but I don't understand what you're trying to say.

Lowpro wrote:Fun fact: N of 1 studies happen often and they're definitely modelable.


I assume you're talking about medical trials which search for cause and effect with treatments that are known to have some effectiveness. This is not the same thing at all and doesn't rely on statistical techniques in the same way.

If someone is given a treatment and their disease is cured, what can we say about the probability that the treatment was the best possible treatment? Absolutely nothing without wider information - such as whether the disease can get better on its own, and what other treatments are available.