rlcd {LogConcDEAD}

Sample from a log-concave maximum likelihood estimate

Description

Draws samples from a log-concave maximum likelihood estimate. The estimate should be specified in the form of an object of class "LogConcDEAD", the result of a call to mlelcd.

Usage

rlcd(n=1, lcd, method=c("Independent","MH"))

Arguments

n

A scalar integer indicating the number of samples required

lcd

Object of class "LogConcDEAD" (typically output from mlelcd)

method

Indicator of the method used to draw samples, either via independent rejection sampling (default choice) or via Metropolis-Hastings

Details

This function by default uses a simple rejection sampling scheme to draw independent random samples from a log-concave maximum likelihood estimator. One can also use the Metropolis-Hastings option to draw (dependent) samples with a higher acceptance rate.

For examples, see mlelcd.

Value

A numeric matrix with nsample rows, each row corresponding to a point in R^d drawn from the distribution with density defined by lcd.

Note

Details of the rejection sampling can be found in Appendix B.3 of Cule, Samworth and Stewart (2010). Details of the Metropolis-Hastings scheme can be found in Gopal and Casella (2010)

Author(s)

Yining Chen

Madeleine Cule

Robert Gramacy

Richard Samworth

References

Cule, M. L., Samworth, R. J., and Stewart, M. I. (2010) Maximum likelihood estimation of a multi-dimensional log-concave density J. Roy. Statist. Soc., Ser. B. (with discussion), 72, 545-600.

Gopal, V. and Casella, G. (2010) Discussion of Maximum likelihood estimation of a log-concave density by Cule, Samworth and Stewart J. Roy. Statist. Soc., Ser. B., 72, 580-582.

See Also

mlelcd