5 ms·

I'm definitely not at all qualified to talk about this, but... aren't "uniform" and "random" antonyms?

icoder 3y ago
The article explains this quite early on, as I understand it, it means that every spot has the same chance of being picked.
bqmjjx0kac 3y ago
"Uniform" here indicates that all values have an equal probability of being picked. The distribution is flat.
pvg 3y ago
No, 'uniform' refers to the distribution, which need not be uniform, e.g. https://numpy.org/doc/stable/reference/random/generated/numpy.random.normal.html https://numpy.org/doc/stable/reference/random/generated/nump... Or in god's own words (TAOCP section 3.4): Applications of random numbers often call for other kinds of distributions, however; for example, if we want to make a random choice from among k alternatives, we want a random integer between 1 and k. If some simulation process calls for a random waiting time between occurrences of independent events, a random number with the exponential distribution is desired. Sometimes we don't even want random numbers — we want a random permutation (a random arrangement of n objects) or a random combination (a random choice of k objects from a collection of n). In principle, any of these other random quantities can be obtained from the uniform deviates U0, U1, U2, ...; people have devised a number of important "random tricks" for the efficient transformation of uniform deviates. A study of these techniques also gives us insight into the proper use of random numbers in any Monte Carlo application.
- jerf 3y ago
  "All distributions are uniform" is one of the two cardinal crimes of a school level of statistics understanding, the other being "all probabilities are independent".
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wodenokoto 3y ago
No. I would go so far as to say, if it’s not uniformly random, it isn’t random. My reasoning is, if you are counting cards in a game, you are giving yourself an advantage. But what really happens is that from your point of view cards will be drawn less and less uniformly randomly. Or put in another way, if you know the distribution is normal, you can bet on the the result being near the center and come out on top, but if it’s uniformly random distribution all hopes are out.
- olliej 3y ago
  There are plenty of things that are random, that are not uniformly random. The hardware RNGs that are used for physically based RNG are not uniform, including the great lava lamp wall or geiger counters, etc. The problem is if you are doing something that requires uniform random values, and your random source is not uniform, then things will go wrong.
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- kelseyfrog 3y ago
  By that criteria, wouldn't a discrete distribution with infinite support be even more random? Finite support somehow seems less random because you can still say something interesting about its mean and bounds in the same way you can say something about the mean and variance of a normal distribution.
- zamadatix 3y ago
  Random (in statistics) means you cannot conclude the next value ahead of time. That's different than saying the next value is uniformly likely to be any value and the two concepts are actually orthogonal. E.g. If I had a bag with 99 red balls and 1 blue ball then randomly selected one you may assume there is a high chance there will be a red ball, based on the odds, but you aren't able to actually know which ball will be next until it's drawn.
olliej 3y ago
Nope, uniform is a description of the probabilities of a random distribution. The easiest example most people are aware of in practice is throwing two 6 sided dice vs one 12 sided dice. The outcome of both is random, but people seem to know fairly intuitively that the two dice case produces is more likely to produce middle values than extreme ones, while the single 12 sided dice doesn't have that behavior.
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The article explains this quite early on, as I understand it, it means that every spot has the same chance of being picked.

bqmjjx0kac 3y ago

"Uniform" here indicates that all values have an equal probability of being picked. The distribution is flat.

pvg 3y ago

No, 'uniform' refers to the distribution, which need not be uniform, e.g. https://numpy.org/doc/stable/reference/random/generated/numpy.random.normal.html https://numpy.org/doc/stable/reference/random/generated/nump... Or in god's own words (TAOCP section 3.4): Applications of random numbers often call for other kinds of distributions, however; for example, if we want to make a random choice from among k alternatives, we want a random integer between 1 and k. If some simulation process calls for a random waiting time between occurrences of independent events, a random number with the exponential distribution is desired. Sometimes we don't even want random numbers — we want a random permutation (a random arrangement of n objects) or a random combination (a random choice of k objects from a collection of n). In principle, any of these other random quantities can be obtained from the uniform deviates U0, U1, U2, ...; people have devised a number of important "random tricks" for the efficient transformation of uniform deviates. A study of these techniques also gives us insight into the proper use of random numbers in any Monte Carlo application.

jerf 3y ago
"All distributions are uniform" is one of the two cardinal crimes of a school level of statistics understanding, the other being "all probabilities are independent".
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wodenokoto 3y ago

No. I would go so far as to say, if it’s not uniformly random, it isn’t random. My reasoning is, if you are counting cards in a game, you are giving yourself an advantage. But what really happens is that from your point of view cards will be drawn less and less uniformly randomly. Or put in another way, if you know the distribution is normal, you can bet on the the result being near the center and come out on top, but if it’s uniformly random distribution all hopes are out.

olliej 3y ago
There are plenty of things that are random, that are not uniformly random. The hardware RNGs that are used for physically based RNG are not uniform, including the great lava lamp wall or geiger counters, etc. The problem is if you are doing something that requires uniform random values, and your random source is not uniform, then things will go wrong.
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kelseyfrog 3y ago
By that criteria, wouldn't a discrete distribution with infinite support be even more random? Finite support somehow seems less random because you can still say something interesting about its mean and bounds in the same way you can say something about the mean and variance of a normal distribution.
zamadatix 3y ago
Random (in statistics) means you cannot conclude the next value ahead of time. That's different than saying the next value is uniformly likely to be any value and the two concepts are actually orthogonal. E.g. If I had a bag with 99 red balls and 1 blue ball then randomly selected one you may assume there is a high chance there will be a red ball, based on the odds, but you aren't able to actually know which ball will be next until it's drawn.

olliej 3y ago

Nope, uniform is a description of the probabilities of a random distribution. The easiest example most people are aware of in practice is throwing two 6 sided dice vs one 12 sided dice. The outcome of both is random, but people seem to know fairly intuitively that the two dice case produces is more likely to produce middle values than extreme ones, while the single 12 sided dice doesn't have that behavior.

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