[R-sig-ME] pMCMC and HPD in MCMCglmm

[Jarrod Hadfield]

Hi,

pMCMC is the two times the smaller of the two quantities: MCMC  
estimates of i) the probability that a<0 or ii) the probability that  
a>0, where a is the parameter value. Its not a p-value as such, and  
better ways of obtaining Bayesian p-values exist.

HPDinterval finds the closest points (c and d) for which Fa(d)-Fa(c) =  
0.95 (If prob=0.95 in HPDinterval) and Fa is the empirical cumulative  
distribution of a.

Cheers,

Jarrod





On 24 Aug 2011, at 16:14, m.fenati at libero.it wrote:

> Hi Jarrod,
> thanks for your answer, but I have again a lot of confusion. If  
> possible,
> could you explain to me the definition of pMCMC?
> Maybe, knowing  the right definition of pMCMC I will be able to  
> understand
> completely your answer.
>
> Thank a lot!
>
> Massimo
>
> -----------------------
> Massimo Fenati
> DVM
> Padova - Italy
>
>
>
>> ----Messaggio originale----
>> Da: j.hadfield at ed.ac.uk
>> Data: 24/08/2011 13.24
>> A: "m.fenati at libero.it"<m.fenati at libero.it>
>> Cc: <ndjido at gmail.com>, <r-sig-mixed-models at r-project.org>
>> Ogg: Re: [R-sig-ME] pMCMC and HPD in MCMCglmm
>>
>> Hi Massimo,
>>
>> They only need to be slightly skewed (even up to Monte Carlo error
>> probably) - conclusions drawn from HPDinterval and pMCMC are in
>> reality almost identical in your example, it is the consequences  of
>> the (arbitrary) distinction between <0.05 and >0.05  that makes them
>> "feel" different.  Lets say we used the cutoff <0.06 and >0.06.  Does
>> HPDinterval(m1$Sol[,3], prob=0.94) overlap zero? If not then
>> HPDinterval and pMCMC "agree" with respect to which side of the  
>> cutoff
>> the probability lies ? It may make us happier, but it shouldn't.
>>
>> Jarrod
>>
>>
>>
>>
>> On 24 Aug 2011, at 11:45, m.fenati at libero.it wrote:
>>
>>> The posterior distribution seem to be only slightly skewed.
>>> However the question remains: what is the sense of the discrepancy
>>> between HPD
>>> and pMCMC?
>>>
>>> Thanks
>>>
>>> Massimo
>>>
>>>
>>>
>>> ----Messaggio originale----
>>> Da: ndjido at gmail.com
>>> Data: 24/08/2011 11.43
>>> A: "m.fenati at libero.it"<m.fenati at libero.it>
>>> Cc: <r-sig-mixed-models at r-project.org>
>>> Ogg: Re: [R-sig-ME] pMCMC and HPD in MCMCglmm
>>>
>>> Check your posterior distributions, the one corresponding to GENDER
>>> seems to
>>> be skewed.
>>> Ardo.
>>> On Wed, Aug 24, 2011 at 11:33 AM, m.fenati at libero.it <m.fenati at libero.it
>>>>
>>> wrote:
>>> As suggested by Ben Bolker, I re-post the following question in this
>>> list.
>>> Thanks
>>>
>>>> Dear R users,
>>>> I’d like to pose aquestion about pMCMC and HDP.
>>>> I have performed a mixed logistic regression by MCMCglmm (a very  
>>>> good
>>> package)
>>>> obtaining the following results:
>>>>
>>>> Iterations = 250001:799901
>>>> Thinning interval = 100
>>>> Sample size = 5500
>>>>
>>>> DIC: 10.17416
>>>>
>>>> G-structure: ~ID_an
>>>>
>>>> post.mean l-95% CI u-95% CIeff.samp
>>>> ID_an 0.7023 0.0001367 3.678 2126
>>>>
>>>> R-structure: ~units
>>>>
>>>> post.mean l-95% CIu-95% CI eff.samp
>>>> units 1 1 1 0
>>>>
>>>> Location effects: febbreq~ as.factor(sex)
>>>>
>>>> post.mean l-95% CIu-95% CI eff.samp pMCMC
>>>> (Intercept) -3.6332 -5.6136 -1.7719 3045 <2e-04 ***
>>>> as.factor(sex)M -2.9959 -6.0690 0.1969 2628 0.0455 *
>>>> ---
>>>> Signif. codes: 0 ‘***’0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>>>>
>>>>
>>>> As you can see, pMCMC for gender is just less than 5%, but the
>>>> credible
>>>> interval (HPD) is wide and includes the 0 value.
>>>> How can I interpret these different results?
>>>>
>>>> Thank you in advance
>>>>
>>>> Massimo
>>>>
>>>> -----------------------
>>>> Massimo Fenati
>>>> DVM
>>>> Padova - Italy
>>>
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>>
>>
>> -- 
>> The University of Edinburgh is a charitable body, registered in
>> Scotland, with registration number SC005336.
>>
>>
>
>
>


-- 
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.