Dear All:
I have an AR(1) example via WinBUGS. Maybe you are interested in.
Many thanks to Professor Farrow.
Best Wishes,
Gary Gau
Math & Stat
Boston University
http://math.bu.edu/people/wgau
----- Original Message -----
>a simulated AR(1) series
>
> y_t = mu + phi*(y_t-1 - mu) + e_t
>
> with mu=10, phi=0.8 and var(e)=1.
>
> The other file contains a (classic) BUGS program which works with this
model and
> these data. The initial observation y_0 is taken as fixed, y_0=13. I took
a
> sample of 10000 phi values and, curiously, there was a little hump at the
upper
> end of the posterior distribution. Otherwise everything seems perfectly
OK.
>
----------------------------------------------------------------------------
----
> 13.0826
> 12.0263
> 13.2564
> 12.1181
> 11.3720
> 12.4619
> 11.2712
> 10.3401
> 10.2225
> 9.4269
> 10.8509
> 9.2491
> 8.1869
> 7.9515
> 7.9624
> 9.5700
> 11.4676
> 9.9282
> 10.0481
> 9.0173
> 9.2939
> 8.4095
> 8.0112
> 8.0132
> 9.1525
> 10.0040
> 8.9083
> 9.1437
> 9.6536
> 10.5645
> 11.2686
> 9.5324
> 10.0392
> 9.3548
> 8.5384
> 9.5017
> 10.3454
> 9.1905
> 8.9498
> 9.1033
> 8.2317
> 6.8483
> 8.05571
> 7.50762
> 5.86687
> 6.94436
> 9.50971
> 9.27238
> 9.46818
> 9.20724
> 7.54402
> 7.41957
> 7.38182
> 8.41263
> 8.31616
> 9.12996
> 9.86440
> 8.57547
> 9.81590
> 9.00445
> 9.43477
> 9.13524
> 9.06310
> 8.1533
> 8.2119
> 8.4364
> 8.4518
> 8.6679
> 9.0107
> 9.3537
> 9.8223
> 10.6041
> 8.8178
> 11.1377
> 11.3183
> 11.9031
> 11.1018
> 9.4257
> 8.8812
> 8.9565
> 8.0170
> 8.5344
> 9.1885
> 8.9057
> 10.1016
> 10.5212
> 10.6441
> 10.1745
> 8.4729
> 9.5725
> 8.7555
> 9.6180
> 8.4995
> 8.5272
> 8.1157
> 9.3125
> 10.0596
> 11.3611
> 10.3386
> 10.2119
----------------------------------------------------------------------------
----
> model ar1a;
>
> const N=100, y0=13;
>
> var y[N], ymean[N], mu, phi, tau;
>
> data y in "ar1.dat";
>
> {
> ymean[1]<-mu + phi*(y0-mu);
> y[1]~dnorm(ymean[1],tau);
>
> for (i in 2:100) {
> ymean[i]<-mu + phi*(y[i-1]-mu);
> y[i]~dnorm(ymean[i],tau);
> }
>
> mu~dnorm(0,0.1);
> tau~dgamma(1,0.1);
> phi~dunif(-1,1);
>
> }
