Recent content by estebanox

The vector μ and the matrix Σ refer to the parameters of the joint distribution of (X,Y,Z). The simulation is fixing all of these parameters, and tracing the probability for different values of "a".

Oh, yes, typo! I'll fix it. Thanks.

Each of X, Y and Z are random variables. I refer to random vector when talking about (X,Y,Z)

Problem: I'm interested in studying the probability of an event involving a random vector. Specifically, I'm interested in (∂/∂a)Pr[X>( (Y-a)/Z )] Where "a" is a non-random parameter and the random vector {X,Y,Z} is distributed Normal( µ, Σ) for µ={0,0,0} and Σ= {{1, 0.5, 0.5}, {0.5, 1, 0}...

Do you mean "if testing is very costly"? In my application it is costly (not cash, but that's besides the point). In other words, I am willing to trade statistic confidence for number of tests. Regarding your last question, the acceptance criterion in my application is not necessarily 0.5, but...

@micromass, thanks a lot for the suggestion of using a Bayesian approach– and for spelling it out. I'll try to implement in computationally.

@micromass: I have continued working on a related problem – I have posted a new thread here. Would be great to hear your thoughts!

Problem: Suppose I have a production process that yields output in batches of n items. For each batch, I can test whether they are of good or bad quality. Let q_i ∈ {1,0} be the quality of tested item i. If more than half of the items are ‘bad’, the batch should be discarded. In other words...

Thanks for this @micromass – very helpful!

Thanks @andrewkirk. Indeed, saying "guarantee" in my question was poor use of language – as a matter of fact I also say "In other words, what is the point after which we can be confident that increasing the sample size...". So your proposal to reformulate the problem is indeed helpful. It'd be...

@andrewkirk and @mfb : I see... but given that I don't know the true value of ##p##, solving the problem assuming the upper bound seems an extreme assumption. My point is that it seems rather wasteful to assume the worst-case scenario to solve for ##k## ex-ante, rather than using information...

@mfb: I think I left relevant information when trying to explain my question. Here is a new attempt -------- Consider a set of random variables ##(X_1,X_2,X_3,...X_k)## that are i.i.d. ##Bernoulli(p)## While I do not know ##p## I can estimate it using $$ Y(k)=\frac{1}{k}\sum_{i=1}^k X_i $$...

Consider a sample consisting of {y1,y2,...,yk} realisations of a random variable Y, and let S(k) denote the variance of the sample as a function of its size; that is S(k)=1/k( ∑ki=1(yi−y¯)2) for y¯=1/k( ∑ki=1 yi) I do not know the distribution of Y, but I do know that S(k) tends to zero as k...

Your answer makes me wonder if applying the cut on both K and T would change things. For instance, for some other cut b, can we know what E[Min[ T | T>t , K<b]] is?

That's quite clear and helpful. Thanks!