Dear friends,
I search solution of the following problem. I have a probability box as initial data and I need to generate samples from it: no exact distribution is given; all that is known is imprecise probabilities - we have only the domain (probability box) for cumulative distribution function (cdf) F(x), the domain that gives us ranges of possible values of function F for all possible arguments x. (For references on probability boxes, see, for example, publications list on https://en.wikipedia.org/wiki/Probability_box). The research is published how to handle with probability boxes, but I don't know publications how to efficiently generate samples from such boxes.
Are there any ideas or publications how to do this efficiently in computational sense? I suppose that all possible distributions from probability box are equally possible (fiducial distribution of possible cfds is uniform in Fisher's sense).
.
http://rec2012.fce.vutbr.cz/documents/papers/zhang.pdf
and other publications by Hao Zhang tackle this problem and give useful referneces
(also a proposal of importance sampling by the same author
http://www.sciencedirect.com/science/article/pii/S0167473012000124
but behind a paywall)
.
Hello Konstantin! I agree with Lenny that more information is needed so we can understand better what you need. I have been working on simulation studies for which we have generated different type of data but I do not know it is what you are asking for. Thus, in you can provide more information, it will help us understand your research question/problem better. In the meantime, I hope that the following reference is of help. This SAS macro generates response data from provided parameters. This macro generates data for several logistic models, one of which follows a CDF (which you mention in your message). This macro might not be what you need but the documentation is very helpful because it explain how the data are generated based on probabilities distributions. it might help you understand what you would need to do to create your sample data. This is the reference: Whittaker, T. A., Fitzpatrick, S. J., Williams, N. J., and Dodd, B.G. (2003). IRTGEN: A SAS Macro Program to Generate Known Trait Scores and Item Responses from Commonly Used Item Response Theory Models. Applied Psychological Measurement, 27, 299-300. You could request the SAS code and documentation from Dr. Whittaker (her contact information is in the attached document). If it happens that you cannot contact her, I will share the documents with you. I hope this helps. Cheers!
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