Re: [computer-go] MC - Estimating a moves true probability of winning

2007-03-03 Thread Jason House
Jacques Basaldúa wrote: Hello, Just an explanation on something I may have explained badly. I see we agree in the fundamental. Correcting bias in that estimate should lead to better sampling. This is usually called "continuity correction" http://en.wikipedia.org/wiki/Continuity_correction

Re: [computer-go] MC - Estimating a moves true probability of winning

2007-03-02 Thread steve uurtamo
> Well, the "assumption" that p is estimated from the binomial because we > are counting Bernoulli experiments of constant p is a mathematically > sound method used universally. It does not require go knowledge, that's > what i meant. When n is big enough, the binomial converges to the normal > an

Re: [computer-go] MC - Estimating a moves true probability of winning

2007-03-02 Thread Jacques Basaldúa
Hello, Just an explanation on something I may have explained badly. I see we agree in the fundamental. Correcting bias in that estimate should lead to better sampling. This is usually called "continuity correction" http://en.wikipedia.org/wiki/Continuity_correction. The estimator is not r

Re: [computer-go] MC - Estimating a moves true probability of winning

2007-03-01 Thread Jason House
I respond to various items below. Sections of the original e-mail that I'm not responding to were completely deleted. Jacques Basaldúa wrote: Hello Jason I think what you are trying to do can be done more easily. I guess the key question is "what am I trying to do?". In UCT, the next move

[computer-go] MC - Estimating a moves true probability of winning

2007-03-01 Thread Jacques Basaldúa
Hello Jason I think what you are trying to do can be done more easily. A. You have a Bernoulli random variable whose result is 0 or 1 following an unknown probability p. (Excuse me for explaining obvious things, this is for anyone who reads it.) You want to estimate p from a random sample. The e

Re: [computer-go] MC - Estimating a moves true probability of winning

2007-02-28 Thread steve uurtamo
> I'm actually kind of surprised at the dissimilarity between the > normal and multinormal. I'd expect the multinormal to boil down to the > normal, but it looks like the standard normal has additional terms. the multivariate normal has the 1-d normal as a special case, but instead of normalizi

Re: [computer-go] MC - Estimating a moves true probability of winning

2007-02-28 Thread Jason House
Actually, the example given (and the first element in the table) are exactly what I stumbled upon. In the scope of MC, I think this style of analysis is 100% correct for evaluation of leaf nodes. I guess time will tell if assuming a conjugate distribution with prior hyperparameters is a good

Re: [computer-go] MC - Estimating a moves true probability of winning

2007-02-28 Thread steve uurtamo
> Maybe other simple solutions exist, you might want to check out those distributions that magically have nice properties with respect to the bayesian integral. they're called conjugate priors, and lots of distributions have nice, easy to calculate conjugate priors. there's a table here: http:/

[computer-go] MC - Estimating a moves true probability of winning

2007-02-28 Thread Jason House
Based on my analysis, estimating a moves probability of winning by taking the number of winning simulations (w) and dividing it by the total number of simulations (n) is actually biased. I tried to break this e-mail up into sections for easy digestion by the various people who might read this