Timeline for Deciding whether or not an exponentially distributed random variable exists in a set via the use of a "black box" function
Current License: CC BY-SA 3.0
18 events
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| Nov 21, 2012 at 1:41 | answer | added | fedja | timeline score: 1 | |
| Nov 20, 2012 at 17:37 | comment | added | fedja | OK, I guess I figured it out in some decent way :). Now it remains to find some free time to run a couple of computations and to post the solution :(. By the way, get some unique username for God's sake: dealing with "unknowns" is a bit irritating... | |
| Nov 19, 2012 at 4:35 | comment | added | user28187 | I was thinking to use some sort of Bayesian inference scheme, but if there is a simpler method... | |
| Nov 19, 2012 at 4:27 | comment | added | user28187 | @fedja Provided a sufficient number of samplings, is there a known "best" method of deciding whether the element $x_q$ exists in $X$? | |
| Nov 19, 2012 at 4:13 | comment | added | user28187 | @fedja I can probably afford something like ~10^5 samplings, though I'd be interested in what theory has to say regardless of feasibility. | |
| Nov 19, 2012 at 3:58 | comment | added | fedja | Well, the "general theory" says that you will need $C(p)N^2$ observations to achieve the probability of error $p$ or less. I didn't figure out the best possible $C(p)$ yet but if you cannot afford $10000$ samplings, the whole project seems hopeless. What are your actual capabilities? | |
| Nov 19, 2012 at 2:04 | history | edited | user28187 | CC BY-SA 3.0 |
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| Nov 19, 2012 at 2:00 | comment | added | user28187 | @fedja Ah, $R$ is defined earlier as the set of rate parameters associated with the exponentially distributed random variables in $X$. | |
| Nov 19, 2012 at 1:56 | comment | added | user28187 | @fedja I have added some specifications for $N$ and $w$ in Note 2. I can tighten them as needed. $R - \lambda_q$ is meant to be the set $R$ without the element $\lambda_q$ (perhaps this notation is incorrect?) | |
| Nov 19, 2012 at 1:55 | history | edited | user28187 | CC BY-SA 3.0 |
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| Nov 19, 2012 at 1:51 | comment | added | fedja | What are typical values of $N$ and $w$? And what is $R$ in $R-\lambda_q$? | |
| Nov 19, 2012 at 1:34 | history | edited | user28187 | CC BY-SA 3.0 |
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| Nov 18, 2012 at 22:24 | history | edited | user28187 | CC BY-SA 3.0 |
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| Nov 18, 2012 at 7:32 | history | edited | user28187 | CC BY-SA 3.0 |
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| Nov 18, 2012 at 7:20 | comment | added | user28187 | @Anthony Quas Fair point. I am looking for a bound in terms of $N$, and I have changed the question to specify that we know $N$. | |
| Nov 18, 2012 at 7:16 | history | edited | user28187 | CC BY-SA 3.0 |
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| Nov 17, 2012 at 21:16 | comment | added | Anthony Quas | Surely you have to know something about $N$ also in order for this to have any hope? Maybe you want a bound in terms of $N$? | |
| Nov 17, 2012 at 18:47 | history | asked | user28187 | CC BY-SA 3.0 |