C-NORTA: A rejection procedure for sampling from the tail of bivariate NORTA distributions. Ghosh, S. & Pasupathy, R. *INFORMS Journal on Computing*, 24(2):295–310, 2012.

Paper doi abstract bibtex

Paper doi abstract bibtex

We propose C-NORTA, an exact algorithm to generate random variates from the tail of a bivariate NORTA random vector. (A NORTA random vector is specified by a pair of marginals and a rank or product?moment correlation, and it is sampled using the popular NORmal-To-Anything procedure.) We first demonstrate that a rejection-based adaptation of NORTA on such constrained random vector generation problems may often be fundamentally intractable. We then develop the C-NORTA algorithm, relying on strategic conditioning of the NORTA vector, followed by efficient approximation and acceptance/rejection steps. We show that, in a certain precise asymptotic sense, the sampling efficiency of C-NORTA is exponentially larger than what is achievable through a naïve application of NORTA. Furthermore, for at least a certain class of problems, we show that the acceptance probability within C-NORTA decays only linearly with respect to a defined rarity parameter. The corresponding decay rate achievable through a naïve adaptation of NORTA is exponential. We provide directives for efficient implementation.

@article{2012ghopas, author = {S. Ghosh and R. Pasupathy}, title = {{C-NORTA}: A rejection procedure for sampling from the tail of bivariate {NORTA} distributions}, journal = {INFORMS Journal on Computing}, year = {2012}, volume = {24}, number = {2}, pages = {295--310}, doi = {10.1287/ijoc.1100.0447}, url = {http://web.ics.purdue.edu/~pasupath/PAPERS/2012ghopas.pdf}, keywords = {random variate generation}, abstract = {We propose C-NORTA, an exact algorithm to generate random variates from the tail of a bivariate NORTA random vector. (A NORTA random vector is specified by a pair of marginals and a rank or product?moment correlation, and it is sampled using the popular NORmal-To-Anything procedure.) We first demonstrate that a rejection-based adaptation of NORTA on such constrained random vector generation problems may often be fundamentally intractable. We then develop the C-NORTA algorithm, relying on strategic conditioning of the NORTA vector, followed by efficient approximation and acceptance/rejection steps. We show that, in a certain precise asymptotic sense, the sampling efficiency of C-NORTA is exponentially larger than what is achievable through a naïve application of NORTA. Furthermore, for at least a certain class of problems, we show that the acceptance probability within C-NORTA decays only linearly with respect to a defined rarity parameter. The corresponding decay rate achievable through a naïve adaptation of NORTA is exponential. We provide directives for efficient implementation.}}

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S.","Pasupathy, R."],"bibbaseid":"ghosh-pasupathy-cnortaarejectionprocedureforsamplingfromthetailofbivariatenortadistributions-2012","bibdata":{"bibtype":"article","type":"article","author":[{"firstnames":["S."],"propositions":[],"lastnames":["Ghosh"],"suffixes":[]},{"firstnames":["R."],"propositions":[],"lastnames":["Pasupathy"],"suffixes":[]}],"title":"C-NORTA: A rejection procedure for sampling from the tail of bivariate NORTA distributions","journal":"INFORMS Journal on Computing","year":"2012","volume":"24","number":"2","pages":"295–310","doi":"10.1287/ijoc.1100.0447","url":"http://web.ics.purdue.edu/~pasupath/PAPERS/2012ghopas.pdf","keywords":"random variate generation","abstract":"We propose C-NORTA, an exact algorithm to generate random variates from the tail of a bivariate NORTA random vector. (A NORTA random vector is specified by a pair of marginals and a rank or product?moment correlation, and it is sampled using the popular NORmal-To-Anything procedure.) We first demonstrate that a rejection-based adaptation of NORTA on such constrained random vector generation problems may often be fundamentally intractable. We then develop the C-NORTA algorithm, relying on strategic conditioning of the NORTA vector, followed by efficient approximation and acceptance/rejection steps. We show that, in a certain precise asymptotic sense, the sampling efficiency of C-NORTA is exponentially larger than what is achievable through a naïve application of NORTA. Furthermore, for at least a certain class of problems, we show that the acceptance probability within C-NORTA decays only linearly with respect to a defined rarity parameter. The corresponding decay rate achievable through a naïve adaptation of NORTA is exponential. We provide directives for efficient implementation.","bibtex":"@article{2012ghopas,\n\tauthor = {S. Ghosh and R. Pasupathy},\n\ttitle = {{C-NORTA}: A rejection procedure for sampling from the tail of bivariate {NORTA} distributions},\n\tjournal = {INFORMS Journal on Computing},\n\tyear = {2012},\n\tvolume = {24},\n\tnumber = {2},\n\tpages = {295--310},\n\tdoi = {10.1287/ijoc.1100.0447},\n\turl = {http://web.ics.purdue.edu/~pasupath/PAPERS/2012ghopas.pdf},\n\tkeywords = {random variate generation},\n\tabstract = {We propose C-NORTA, an exact algorithm to generate random variates from the tail of a bivariate NORTA random vector. (A NORTA random vector is specified by a pair of marginals and a rank or product?moment correlation, and it is sampled using the popular NORmal-To-Anything procedure.) We first demonstrate that a rejection-based adaptation of NORTA on such constrained random vector generation problems may often be fundamentally intractable. We then develop the C-NORTA algorithm, relying on strategic conditioning of the NORTA vector, followed by efficient approximation and acceptance/rejection steps. We show that, in a certain precise asymptotic sense, the sampling efficiency of C-NORTA is exponentially larger than what is achievable through a naïve application of NORTA. Furthermore, for at least a certain class of problems, we show that the acceptance probability within C-NORTA decays only linearly with respect to a defined rarity parameter. The corresponding decay rate achievable through a naïve adaptation of NORTA is exponential. We provide directives for efficient implementation.}}\n\n","author_short":["Ghosh, S.","Pasupathy, R."],"key":"2012ghopas","id":"2012ghopas","bibbaseid":"ghosh-pasupathy-cnortaarejectionprocedureforsamplingfromthetailofbivariatenortadistributions-2012","role":"author","urls":{"Paper":"http://web.ics.purdue.edu/~pasupath/PAPERS/2012ghopas.pdf"},"keyword":["random variate generation"],"metadata":{"authorlinks":{"pasupathy, r":"https://bibbase.org/show?bib=http://web.ics.purdue.edu/~pasupath/rpVitapublist.bib"}},"html":""},"bibtype":"article","biburl":"http://web.ics.purdue.edu/~pasupath/rpVitapublist.bib","downloads":19,"keywords":["random variate generation"],"search_terms":["norta","rejection","procedure","sampling","tail","bivariate","norta","distributions","ghosh","pasupathy"],"title":"C-NORTA: A rejection procedure for sampling from the tail of bivariate NORTA distributions","year":2012,"dataSources":["qnbhPCpdghcXAQgXA"]}