R help - Nov 2008 - sampling from Laplace-Normal

Hi,
I have to draw samples from an asymmetric-Laplace-Normal distribution:
f(u|y, x, beta, phi, sigma, tau) \propto exp( - sum( ( abs(lo) +
(2*tau-1)*lo )/(2*sigma) ) - 0.5/phi*u^2), where lo = (y - x*beta) and
y=(y_1, ..., y_n), x=(x_1, ..., x_n)
-- sorry for this huge formula --
A WinBUGS Gibbs sampler and the HI package arms sampler were used with the
same initial data for all parameters. I compared the mean from both the
Gibbs sample and the arms sample for several y and x. Surprisingly, both
means always differed by the same constant.
Shouldn't the sample means be equal? What could be the reason for the
constant difference? (burnin and sample size variation didn't change this)

Thanks in advance
Armin

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Hi,
I have to draw samples from an asymmetric-Laplace-Normal distribution:
f(u|y, x, beta, phi, sigma, tau) \propto exp( - sum( ( abs(lo) +
(2*tau-1)*lo )/(2*sigma) ) - 0.5/phi*u^2), where lo = (y - x*beta) and
y=(y_1, ..., y_n), x=(x_1, ..., x_n)
-- sorry for this huge formula --
A WinBUGS Gibbs sampler and the HI package arms sampler were used with
the same initial data for all parameters. I compared the mean from
both the Gibbs sample and the arms sample for several y and x.
Surprisingly, both means always differed by the same constant.
Shouldn't the sample means be equal? What could be the reason for the
constant difference? (burnin and sample size variation didn't change
this)

Thanks in advance
Armin

Hi Armin,

Laplace-Normal random variables may be generated as the sum of a Normal 
rv and the difference of two exponential rvs. See

Reed, W.J. and Jorgensen, M.A. (2004) The Double Pareto-Lognormal 
distribution ? A new parametric model for size distributions. 
Communications in Statistics B: Theory and Methods, 33(8), 1733-1753.

Perhaps you can get around your problem using this representation or 
alternatively reproduce the problem with one of the component rvs.

Cheers,

Murray Jorgensen
> Hi,
> I have to draw samples from an asymmetric-Laplace-Normal distribution:
> f(u|y, x, beta, phi, sigma, tau) \propto exp( - sum( ( abs(lo) +
> (2*tau-1)*lo )/(2*sigma) ) - 0.5/phi*u^2), where lo = (y - x*beta) and
> y=(y_1, ..., y_n), x=(x_1, ..., x_n)
> -- sorry for this huge formula --
> A WinBUGS Gibbs sampler and the HI package arms sampler were used with the
> same initial data for all parameters. I compared the mean from both the
> Gibbs sample and the arms sample for several y and x. Surprisingly, both
> means always differed by the same constant.
> Shouldn't the sample means be equal? What could be the reason for the
> constant difference? (burnin and sample size variation didn't change
this)
> 
> Thanks in advance
> Armin
-- 
Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz                                Fax 7 838 4155
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