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  "Title": "Consider Ambiguity in Probabilistic Descriptions Using Density\nRatio Classes",
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  "Authors@R": "c(person(given = \"Peter\",\nfamily = \"Reichert\",\nrole = c(\"aut\", \"cre\"),\nemail = \"peter.reichert@emeriti.eawag.ch\"),\nperson(given = \"Ambuj\",\nfamily = \"Sriwastava\",\nrole = \"aut\"))",
  "Description": "Consider ambiguity in probabilistic descriptions by\nreplacing a parametric probabilistic description of uncertainty\nby a non-parametric set of probability distributions in the\nform of a Density Ratio Class. This is of particular interest\nin Bayesian inference. The Density Ratio Class is particularly\nsuited for this purpose as it is invariant under Bayesian\ninference, marginalization, and propagation through a\ndeterministic model. Here, invariant means that the result of\nthe operation applied to a Density Ratio Class is again a\nDensity Ratio Class. In particular the invariance under\nBayesian inference thus enables iterative learning within the\nsame framework of Density Ratio Classes. The use of imprecise\nprobabilities in general, and Density Ratio Classes in\nparticular, lead to intervals of characteristics of probability\ndistributions, such as cumulative distribution functions,\nquantiles, and means. The package is based on a sample of the\ndistribution proportional to the upper bound of the class.\nTypically this will be a sample from the posterior in Bayesian\ninference. Based on such a sample, the package provides\nfunctions to calculate lower and upper class boundaries and\nlower and upper bounds of cumulative distribution functions,\nand quantiles. Rinderknecht, S.L., Albert, C., Borsuk, M.E.,\nSchuwirth, N., Kuensch, H.R. and Reichert, P. (2014) \"The\neffect of ambiguous prior knowledge on Bayesian model parameter\ninference and prediction.\" Environmental Modelling & Software.\n62, 300-315, 2014. <doi:10.1016/j.envsoft.2014.08.020>.\nSriwastava, A. and Reichert, P. \"Robust Bayesian Estimation of\nValue Function Parameters using Imprecise Priors.\" Submitted.\n<https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4973574>.",
  "License": "GPL-3",
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  "Author": "Peter Reichert [aut, cre], Ambuj Sriwastava [aut]",
  "Maintainer": "Peter Reichert <peter.reichert@emeriti.eawag.ch>",
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      "title": "Consider Ambiguity in Probabilistic Descriptions Using Density Ratio Classes",
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        "DRclass-package"
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    },
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      "page": "DRclass_k_Cdf",
      "title": "Calculate lower and upper bounds of the cumulative density function for the marginals of a Density Ratio Class for which the lower and upper bounding functions are proportional.",
      "topics": [
        "DRclass_k_Cdf"
      ]
    },
    {
      "page": "DRclass_k_Pdf",
      "title": "Calculate marginal class bounding functions for a special Density Ratio Class for which the lower and upper bounding functions are proportional.",
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    },
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      "page": "DRclass_k_Quantile",
      "title": "Calculate lower and upper bounds of quantiles of marginals of a Density Ratio Class for which the lower and upper bounding functions are proportional.",
      "topics": [
        "DRclass_k_Quantile"
      ]
    },
    {
      "page": "DRclass_lu_Cdf",
      "title": "Calculate lower and upper bounds of the cumulative density function for the marginals of a general Density Ratio Class. The cumulative density functions for the marginals of a distributions proportional to the lower and upper bounding functions are also provided. See the function 'DRclass_k_Cdf' for the case in which the upper and lower bounding functions of the class are proportional.",
      "topics": [
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      "page": "DRclass_lu_Pdf",
      "title": "Calculate marginal class bounding functions for the general case of a Density Ratio Class.",
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      ]
    },
    {
      "page": "DRclass_lu_Quantile",
      "title": "Calculate lower and upper bounds of quantiles of marginals of a Density Ratio Class. Quantiles of the marginals of distributions proportional to the lower and upper bounding functions are also provided. See the function 'DRclass_k_Quantile' for the case in which the upper and lower bounding functions of the class are proportional.",
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