I would like to know the difference between uncertainty and randomness in mathematical fashion. I tried to find it but I get confused , as some people said they are the same? But can any one provide me logical reasoning behind it. If they are not same then please explain it why?
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Try asking this in http://math.stackexchange.com/. randomness is about entropy and uncertainty is about probability, you are comparing apples and pears – dmaij Apr 01 '15 at 21:46
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1@dmaij As per my understanding I am not comparing apple and pears. I saw many pages where people have opinions about this. – mangleshwar srivastava Apr 01 '15 at 23:29
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Don't get too hung up on it. People use different words in different situations. It's not so much that they have different meanings, as that their meanings are situation-dependent.
Randomness is just a fuzzy general term meaning something is random.
In statistics, uncertainty is used to mean that some property of a distribution, such as its mean, is itself unknown but can be given a distribution.
For example, suppose you want to know the average weight of all people. You could find it out exactly if you could go around to all people, get their weight, add it all up, and divide by the number of people.
But that's too hard to do, so suppose you just pick 10 people at random and get their average weight, and pretend it's the same as the average of everybody. That's called the sample mean, but you know it isn't accurate. It has what is called a standard error, meaning it has uncertainty.
In fact, if you were to do that experiment many times over with different people, you would get a different sample mean every time, and those sample means would themselves form a bell-shaped distribution, the standard deviation of which would be called the standard error, representing its uncertainty.
In general, if you increased the number of people you look at by a factor of 100, you can reduce the standard error, the uncertainty, by a factor of 10.
I bet you can tell that people who take polls for a living care about this stuff very much.
EDIT for the downvoter: In case the downvote is because this doesn't look like a stackoverflow question or answer, I've made a point of advocating the random pausing method of profiling. Profiling in large part is perceived to be about measuring (statistically) the time that programming constructs are responsible for. Often people are inhibited from using that method because they are afraid the results have too much uncertainty.
This post gets very specific about what that uncertainty actually is. It shows that the bogey-man fear of uncertainty has the effect of preventing people from finding really substantial speedups in their code. So naivete' about statistics is definitely a serious programming problem.
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Mike Dunlavey
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So does that mean we can only determine the "Uncertainty" when we know the probability distribution? – mangleshwar srivastava Apr 01 '15 at 23:26
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@mangleshwarsrivastava: It means when you get really technical about the statistics, the term "uncertainty" is used with a specific meaning. If you want to learn more about it, you can visit [*this stackexchange site*](http://stats.stackexchange.com/), where people are both sophisticated and helpful. – Mike Dunlavey Apr 02 '15 at 02:19
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Careful, the terms "accuracy" and "precision" have very specific meaning with regard to estimators such as the sample mean. Accuracy refers to bias in the estimator, precision refers to the magnitude of any variability. A scale which gives weights that are always exactly 1 kilo below a calibrating reference weight is precise but inaccurate. A scale which is +/-10 kilos but with enough weighings averages towards the reference weight is accurate but imprecise. – pjs Apr 02 '15 at 04:51
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My view looks at a scenario using three different coloured balls:
I love some of the answers given here. My own view, based on my current research, is that these are two distinct terms. Uncertainty refers to not knowing in advance which ball could be selected when a person, for instance, is given a chance to select one ball from three different coloured balls.
This remains true when each ball has an equal chance of being selected i.e. equal probabilities. However, things soon get complex when each ball has it's own distinct probability. Chances are that the one with the highest probability will be selected. This seems especially true in algorithm development which would almost always select the highest probability compromising the meaning of randomness.
Having said all of this - I believe these concepts remain confusing which has just made me realise the time I need to dedicate on clearly distinguishing between the two to make sure my current research is not confusing. My own predicament is that I need to work on stochastic vs deterministic views. Based on the current view stochastic would be more uncertain than random whereas deterministic would be more probability based i.e. knowing for certain that the highest probability would be chosen; but this seems very far from the truth.
It seems as if uncertainty holds until just before a ball is selected/touched and soon looses its meaning as soon as the ball is picked which should result to its probability being revised. I personally think the terms have theoretical differences which perhaps allows them to be used interchangeably.
Mthandeni Langa
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Uncertainty in math and science typically means there are a lack of facts, or the facts are unobtainable. Weather forecasting is a great example of uncertainty.
Randomness has many definitions. Commonly it's used in probability / statistics as a measure or quantification of uncertainty. So in my weather example, a 30% chance of rain is a measure of uncertainty. The more general definition (which also applies to math / science) is unpredictable, or lack of order.
There is definitely a fuzzy distinction between the two.
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According to the Bayesian interpretation of probability, uncertainty and randomness are just two names for the same thing.
Robert Dodier
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If an experiment is random, then it is uncertain to you. If something is uncertain to you, then it has the randomness property.
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