spicyj 346 days ago link
Work was done in both directions. It more of a philosophical problem than math problem, although in many cases you want something specific: "I have no idea what the outcome might be but I think it either extremely on the right or left so give me priori which converges fast to one or the other). Or in a coin example: "it almost surely more or less fair, so I don want to change my views after several unlucky flips".
is sort of a really minor pet peeve of mine when people use coin flipping as an example for these things. You can have continuous or discrete event spaces.
construct a flat cylinder a couple centimeters across that you can flip fairly and achieve a 98% bias. And if you don meet those physical requirements, it not a coin. If you had a sphere shaped object and the head condition was a particular point being above the equator, maybe you could include some distribution of internal weighting that could achieve that level of bias. (Edit: clarity)If other stuff is going on, like you letting it bounce or something, then it depends on the particulars. It rather easy to load a die, for instance.
Sure. My point was that you can physically Air Max Tavas Ltr
Bayesian updating of Probability Distributions
One of the beautiful aspects of Bayesian methods is that they are subjective. As long as you have a reason, it reasonable. No amount of data can overcome that.
Once you figure out simple examples you slowly start thinking this way about the world. It beautiful. Take people for example:Someone with open mind has a priori with at least slight probability assigned to unlikely (for them!) hypothesis while on the other hand very religious people for example have 0 in Nike Air Max Tavas Size 1
Completely agreed. Your comment is a really good advertisement for normal people to learn Bayesian probability theory. Not because it useful in science or engineering, but because it useful in life.
We interested in the probability of a coin flip yielding heads before we flip any coins. Uniform is just a really common prior to choose in this situation for a few reasons: It a special case of the beta Pink And Black Air Max 2015 distribution, which is the conjugate prior for binomial problems. This means that the distribution of the probability of getting heads given the coin flips is in the same family as the prior itself (ie: beta priors with binomial likelihoods yield beta posteriors). The uniform (for this problem at least) is an "objective prior", which expresses that we don have much information about whether the flip is biased. The example you give (modeling p^2 instead of p) is a great example of when the uniform would be a bad choice. This Nike Air Max 2015 Orange And Yellow
dthunt 346 days ago link
their priori when it comes to possibility of their religion being made up so they are forced to ignore evidence to the contrary (because bayesian updating breaks for them due to division by zero and mind way to signal this exception is denial). Someone with very bad priors is un educated (in given domain) or biased or maybe just stupid, someone with good priors is an expert. I can seem like a Bayes nut at work as I mention updating my priors during debates and when discussing hypotheses for split tests.
darkxanthos 345 days ago link
yafujifide 345 days ago link
A question for people who know more about this than I do:Why was the uniform distribution on [0, 1] chosen initially? Choosing a different distribution would give a different result. (And it doesn make much sense to say, "Always choose the uniform distribution!" because the choice of variable affects the meaning of the distribution if instead we wonder about the value of p^2 and choose a uniform distribution for it on [0, 1], won we get a completely different result?)
bjterry 345 days ago link
For argumentative purposes (if trying to reach a consensus with someone who claims to be 95% sure that the coin is and accepts the heads is fair definition), you would concentrate most of your probability mass there, and find a mutually agreeable shape. You may take personal (just use all your experience) or objective (try to come up with some scheme for assigning priors to types of situations) view on this problem.
christopheraden 346 days ago link
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