Perfect simulation of conditionally specified models, by J. Moller
J. R. Statist. Soc. B, vol. 61 (1999)

As explained in the paper (see (ii), Section 3.3) two C-programmes 
are available for making perfect simulations of an auto-gamma model 
with conditional distributions

\[
\mathcal{D}(X_0|X_1,\ldots,X_{10})=Gamma(\alpha_0,\beta_0\sum_{i=1}^{10}X_i)
,\]
\[\mathcal{D}(X_i|X_0)=Gamma(\alpha_i,\beta_iX_0),\ i=1,\ldots,
10,
\]


where $X_1,\ldots,X_{10}$ are conditionally independent given $X_0$.
Here $\alpha_i$ and $\beta_i$ are positive parameters as given by 
the posterior distribution for a particular dataset on pump relia-
bility (the values are defined in the computer codes).

Description of C-programmes:

PerfectGammaBackwards.c
The CFTP-algorithm in Section 3.1 for generating a perfect 
simulation when doubling $n$. If the algorithm terminated within 
the maximal allowed time "tmax" --- see the beginning of the programme 
code --- you get the following output: 
start = the value of the coalescence time 
$2^{-N(\epsilon)}$,\\
coal = 1, \\
epsilon = the value of the "accuracy" (set to $0$ at the beginning 
of the programme code, but you may want to define another value of 
epsilon at this place in the code before running the programme),
\\
$L[i]\ =\ U[i]\ =$ the common values of the lower and upper chains 
at time 0 when coalescence has happened.

PerfectGammaForwards.c
For forward runs ONLY (recall that coalescence times using the CFTP-
algorithm follow the same distribution as those obtained by running 
a single pair of upper and lower chains forwards in time; see the 
remarks above Theorem 2). Output:
mean = the average of 10000 i.i.d.\ coalecence times,
std = the corresponding standard deviation, 
epsilon = the value of the "accuracy" (set to $0$ at the beginning 
of the programme code, so you may want to define another value of 
epsilon).

To run e.g. the latter programme type
gcc -g PerfectGammaForwards.c -lm ./a.out

Date: 8 June 1998.
Jesper Moller, 
Department of Mathematics, Aalborg University
Email: jm@math.auc.dk