Semiparametric Elicitation of a bounded parameter.
This package implements a novel method for fitting a bounded probability distribution to quantiles stated for example by an expert (see Bornkamp and Ickstadt (2009)). For this purpose B-splines are used, and the density is obtained by penalized least squares based on a Brier entropy penalty. The package provides methods for fitting the distribution as well as methods for evaluating the underlying density and cdf. In addition methods for plotting the distribution, drawing random numbers and calculating quantiles of the obtained distribution are provided.
Maintainer: Bjoern Bornkamp <firstname.lastname@example.org>
Bornkamp, B. and Ickstadt, K. (2009). A Note on B-Splines for Semiparametric Elicitation. The American Statistician, 63, 373–377
O'Hagan A., Buck C. E., Daneshkhah, A., Eiser, R., Garthwaite, P., Jenkinson, D., Oakley, J. and Rakow, T. (2006), Uncertain Judgements: Eliciting Expert Probabilities, John Wiley and Sons Inc.
Garthwaite, P., Kadane, J. O'Hagan, A. (2005), Statistical Methods for Eliciting Probability Distributions, Journal of the American Statistical Association, 100, 680–701
Dierckx, P. (1993), Curve and Surface Fitting with Splines, Clarendon Press.
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## example from O'Hagan et al. (2006) x <- c(177.5, 183.75, 190, 205, 220) y <- c(0.175, 0.33, 0.5, 0.75, 0.95) default <- SEL(x, y, Delta = 0.05, bounds = c(165, 250)) bernst <- SEL(x, y, d = 10, N = 0, Delta = 0.05, bounds = c(165, 250)) unifknots <- SEL(x, y, d = 3, N = 5, Delta = 0.05, bounds = c(165, 250)) lin <- SEL(x, y, d = 1, inknts = x, Delta = 0.05, bounds = c(165, 250)) comparePlot(default, bernst, unifknots, lin, type = "cdf") comparePlot(default, bernst, unifknots, lin, type = "density") ## compare summaries summary(default) summary(bernst) summary(unifknots) summary(lin) ## sample from SEL object and evaluate density xxx <- rvSEL(50000, bernst) hist(xxx, breaks=100, freq=FALSE) curve(predict(bernst, newdata=x), add=TRUE)