# Semiparametric Elicitation of a bounded parameter.

### Description

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.

### Details

Package: | SEL |

Type: | Package |

Version: | 1.0-2 |

Date: | 2010-05-21 |

License: | GPL |

### Author(s)

Bjoern Bornkamp

Maintainer: Bjoern Bornkamp <bornkamp@statistik.tu-dortmund.de>

### References

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.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
## 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)
``` |