Final pre-Christmas post re this - Mark Brewer pointed out that in
WinBUGS 1.4.3 using the 'round' function produces almost exactly correct
results, at least in this simple example - see below (also shows that
using 'trunc' does not...)
David
[log in to unmask]
Immpact Project
University of Aberdeen
################# #######################
Simple eg of problem poisson code -
{
MuTrunc~dunif(0,100)
MuRound~dunif(0,100)
MuEqual~dunif(0,100)
MuCheck~dunif(0,100)
Trunc~dpois(MuTrunc)
Round~dpois(MuRound)
Equal~dpois(MuEqual)
Check~dpois(MuCheck)
Trunc2 <- trunc(Trunc)
Round2 <- round(Round)
Equal2 <- Equal
ChF1<-equals(Check, 1)
RoF1<-equals(Round2, 1)
TrF1<-equals(Trunc2, 1)
ChF2<-equals(Check, 2)
RoF2<-equals(Round2, 2)
TrF2<-equals(Trunc2, 2)
ChF3<-equals(Check, 3)
RoF3<-equals(Round2, 3)
TrF3<-equals(Trunc2, 3)
ObsTrunc~dbin(0.7,Trunc2)
ObsRound~dbin(0.7,Round2)
ObsEqual~dbin(0.7,Equal2)
ObsCheck~dbin(0.7,Check)
}
Data list( ObsCheck=1 , ObsEqual=1 , ObsRound=1 , ObsTrunc=1 )
Inits list( MuRound=2 , MuCheck=2 , MuEqual=2 , MuTrunc=2 ,
Trunc=3 , Round=3 , Equal=3, Check=3 )
WinBUGS 1.4.3 output
node mean sd MC error 2.5% 5.0%
10.0% 25.0% median 75.0% 90.0% 95.0% 97.5%
start
Check 1.863 1.112 0.003662 1.0
1.0 1.0 1.0 2.0 2.0
3.0 4.0 5.0 23001 178000
Equal 2.208 1.086 0.004199 1.038
1.077 1.155 1.407 1.908 2.695 3.658
4.36 5.05 23001 178000
Equal2 2.208 1.086 0.004199 1.038
1.077 1.155 1.407 1.908 2.695 3.658
4.36 5.05 23001
Round 1.856 1.141 0.004516 0.5505
0.6013 0.7052 1.01 1.538 2.385 3.375
4.12 4.762 23001
Round2 1.857 1.105 0.004434 1.0
1.0 1.0 1.0 2.0 2.0
3.0 4.0 5.0 23001 178000
Trunc 2.352 1.133 0.004155 1.052
1.104 1.205 1.509 2.033 2.878 3.866
4.623 5.251 23001
Trunc2 1.852 1.095 0.004025 1.0
1.0 1.0 1.0 2.0 2.0
3.0 4.0 5.0 23001 178000
MuCheck 2.864 2.024 0.006693 0.3463
0.5092 0.7644 1.373 2.401 3.863 5.564
6.788 8.014 23001
MuEqual 3.201 2.089 0.006871 0.4908
0.6885 0.984 1.668 2.764 4.254 5.985
7.217 8.391 23001
MuRound 2.858 2.036 0.007194 0.323
0.4821 0.7339 1.357 2.4 3.866 5.583
6.818 7.987 23001
MuTrunc 3.353 2.151 0.006642 0.5226
0.7343 1.048 1.769 2.913 4.461 6.231
7.489 8.69 23001
ChF1 0.4884 0.4999 0.001504
ChF2 0.2938 0.4555 0.001123
ChF3 0.133 0.3396 8.901E-4
RoF1 0.4888 0.4999 0.001767
RoF2 0.2952 0.4561 0.001329
RoF3 0.133 0.3396 0.001035
TrF1 0.4898 0.4999 0.001693
TrF2 0.2959 0.4564 0.001371
TrF3 0.1319 0.3383 9.848E-4
################# #######################
-----Original Message-----
From: Braunholtz, David A.
Sent: 19 December 2007 17:57
To: [log in to unmask]
Subject: RE: non integer poisson variates ?
Following earlier Q re this, it was suggested I try Openbugs - see
results below! I think I'll stick to Winbugs for the moment...(for
this at least)
It was also suggested I try JAGS - & and some output sent looked
promising, but I haven't yet worked out how to get JAGS scripts to
run... (in Windows) if anyone can give a hint...
David
################# #######################
Even Simpler eg of problem-with-poisson code
In WinBUGS 1.4 produces non-integer D and Db, contrary to expectations
(low auto-correlations) but fairly close to correct
In OpenBUGS 3.03 produces integer D & Db (but distribution is just
slightly wrong!!) ( & huge auto-correlations)
{
MuProblem~dunif(0,100)
MuCheck~dunif(0,100)
Problem~dpois(MuProblem)
Check~dpois(MuCheck)
Prob2 <- Problem
ObsP~dbin(0.7,Prob2)
ObsCheck~dbin(0.7,Check)
}
Data list( ObsCheck=1 , ObsP=1 )
Inits list( MuProblem=2 , MuCheck=2 , Problem=3 , Check=3 )
Results:
OpenBugs 3.03
mean sd MC_error val2.5pc median val97.5pc
Check 1.863 1.106 0.007267 1.0 2.0 5.0
MuCheck 2.865 2.022 0.01484 0.3502 2.412 8.004
MuProblem 17.74 12.0 0.1325 2.38 15.11 47.66
Prob2 16.74 11.26 0.1284 2.0 14.0 45.0
Problem 16.74 11.26 0.1284 2.0 14.0 45.0
WinBUGS 1.4
node mean sd MC error 2.5% median 97.5%
Check 1.855 1.111 0.005552 1.0 2.0 5.0
MuCheck 2.851 2.032 0.01117 0.3545 2.392 7.968
MuProblem 3.202 2.099 0.01078 0.4907 2.761 8.473
Prob2 2.202 1.089 0.008205 1.038 1.894 5.055
Problem 2.202 1.083 0.005855 1.039 1.903 4.998
################# #######################
-----Original Message-----
From: Braunholtz, David A.
Sent: 17 December 2007 22:26
To: [log in to unmask]
Subject: non integer poisson variates ?
Dear Bugsers,
I have noticed that code like the below results in non integer D (& Db).
Is this is intentional ? Is there a way of forcing the poisson to
produce integral D ? It seems unlikely, but is the distribution for MU
correct despite this ?
Incidentally, while looking into this, I noticed that i was able (in the
simplest possible program) to use the same poisson N for the order of
two binomials - without producing the error message mentioned in 'tips &
troubleshooting
/ restrictions ... / e) ?
Thanks for any help ...
[log in to unmask]
Immpact Project
University of Aberdeen
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