pmp.bma {BMS}R Documentation

Posterior Model Probabilities


Returns the posterior model probabilites for the best models encountered by a 'bma' object


pmp.bma(bmao, oldstyle = FALSE)



A bma object (see argument nmodel in bms), alternatively an object of class topmod


For normal use, leave this at FALSE. It is an argument for compatibility with older BMS versions - see section 'Notes'


A call to bms with an MCMC sampler (e.g. bms(datafls,mcmc="bd",nmodel=100) uses a Metropolis-Hastings algorithm to sample through the model space - and the frequency of how often models are drawn converges to the distribution of their posterior marginal likelihoods. While sampling, each 'bma' object stores the best models encountered by its sampling chain with their marginal likelihood and their MCMC frequencies.

pmp.bma then allows for comparing the posterior model probabilities (PMPs) for the two different methods, similar to plotConv. It calculates the PMPs based on marginal likelihoods (first column) and the PMPs based on MCMC frequencies (second column) for the best x models stored in the bma object.

The correlation of the two columns is an indicator of how well the MCMC sampler has converged to the actual PMP distribution - it is therefore also given in the output of summary.bma.

The second column is slightly different in case the bms argument mcmc was set to mcmc="enumeration": In this case, the second column is also based on marginal likelihoods. The correlation between the two columns is therefore one.


the result is a matrix, its row names describe the model binaries
There are two columns in the matrix:

PMP (Exact)

posterior model probabilities based on the posterior likelihoods of the best models in bmao


posterior model probabilities of the best models in bmao based on their MCMC frequencies, relative to all models encountered by bmao - see 'Details'


The second column thus shows the PMPs of the best models relative to all models the call to bms has sampled through (therefore typically the second column adds up to less than one). The first column relates to the likelihoods of the best models, therefore it would add up to 1. In order estimate for their marginal likelihoods with respect to the othe rmodels (the ones not retained in the best models), these PMP aadding up to one are multplied with the sum of PMP of the best models accroding to MCMC frequencies. Therefore, the two columns have the same column sum.

CAUTION: In package versions up to BMS 0.2.5, the first column was indeed set always equal to one. This behaviour can still be mimicked by setting oldstyle=TRUE.


Martin Feldkircher and Stefan Zeugner

See Also

plotConv for plotting pmp.bma, pmpmodel to obtain the PMP for any individual model, bms for sampling bma objects

Check for additional help.


## sample BMA for growth dataset, MCMC sampler
mm=bms(datafls[,1:10],nmodel=20, mcmc="bd")

## mmodel likelihoods and MCMC frequencies of best 20 models

#first column: posterior model prob based on model likelihoods,
#  relative to best models in 'mm'
#second column: posterior model prob based MCMC frequencies,
#  relative to all models encountered by 'mm'

#consequently, first column adds up to one
#second column shows how much of the sampled model space is
# contained in the best models

#correlation betwwen the two shows how well the sampler converged

#is the same as given in summary.bma
summary(mm)["Corr PMP"]

#plot the two model probabilites

#equivalent to the following chart
plot(pmp.bma(mm)[,2], type="s")

#moreover, note how the first column is constructed
pmp.bma(mm)[,1] #these two are equivalent

#the example above does not converge well,
#too few iterations and best models
# this is already better, but also not good

# in case the sampler has been 'enumeration' instead of MCMC,
# then both matrix columns are of course equivalent

[Package BMS version 0.3.1 Index]