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Posterior Model Probabilities from Marginal Likelihoods

Source: R/bridgesampling.R
post_prob.brmsfit.Rd

Compute posterior model probabilities from marginal likelihoods. The brmsfit method is just a thin wrapper around the corresponding method for bridge objects.

Usage

# S3 method for class 'brmsfit'
post_prob(x, ..., prior_prob = NULL, model_names = NULL)

Arguments

x

A brmsfit object.

...

More brmsfit objects or further arguments passed to the underlying post-processing functions. In particular, see prepare_predictions for further supported arguments.

prior_prob

Numeric vector with prior model probabilities. If omitted, a uniform prior is used (i.e., all models are equally likely a priori). The default NULL corresponds to equal prior model weights.

model_names

If NULL (the default) will use model names derived from deparsing the call. Otherwise will use the passed values as model names.

Details

Computing the marginal likelihood requires samples of all variables defined in Stan's parameters block to be saved. Otherwise post_prob cannot be computed. Thus, please set save_all_pars = TRUE in the call to brm, if you are planning to apply post_prob to your models.

The computation of model probabilities based on bridge sampling requires a lot more posterior samples than usual. A good conservative rule of thump is perhaps 10-fold more samples (read: the default of 4000 samples may not be enough in many cases). If not enough posterior samples are provided, the bridge sampling algorithm tends to be unstable leading to considerably different results each time it is run. We thus recommend running post_prob multiple times to check the stability of the results.

More details are provided under bridgesampling::post_prob.

See also

bridge_sampler, bayes_factor

Examples

# \dontrun{
# model with the treatment effect
fit1 <- brm(
  count ~ zAge + zBase + Trt,
  data = epilepsy, family = negbinomial(),
  prior = prior(normal(0, 1), class = b),
  save_all_pars = TRUE
)
#> Warning: Argument 'save_all_pars' is deprecated. Please use argument 'all' in function 'save_pars()' instead.
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 2.9e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.29 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
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#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.124 seconds (Warm-up)
#> Chain 1:                0.136 seconds (Sampling)
#> Chain 1:                0.26 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 2.2e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
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#> Chain 2: 
#> Chain 2:  Elapsed Time: 0.122 seconds (Warm-up)
#> Chain 2:                0.134 seconds (Sampling)
#> Chain 2:                0.256 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 2.3e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.23 seconds.
#> Chain 3: Adjust your expectations accordingly!
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#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.121 seconds (Warm-up)
#> Chain 3:                0.128 seconds (Sampling)
#> Chain 3:                0.249 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 2.4e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.24 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4: 
#> Chain 4: 
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#> Chain 4: 
#> Chain 4:  Elapsed Time: 0.127 seconds (Warm-up)
#> Chain 4:                0.143 seconds (Sampling)
#> Chain 4:                0.27 seconds (Total)
#> Chain 4: 
summary(fit1)
#>  Family: negbinomial 
#>   Links: mu = log 
#> Formula: count ~ zAge + zBase + Trt 
#>    Data: epilepsy (Number of observations: 236) 
#>   Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#>          total post-warmup draws = 4000
#> 
#> Regression Coefficients:
#>           Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept     1.89      0.07     1.76     2.04 1.00     4607     3272
#> zAge          0.11      0.05     0.01     0.21 1.00     5072     3299
#> zBase         0.72      0.05     0.61     0.83 1.00     5279     3168
#> Trt1         -0.19      0.10    -0.38     0.01 1.00     4584     2610
#> 
#> Further Distributional Parameters:
#>       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> shape     2.35      0.32     1.80     3.05 1.00     4446     2819
#> 
#> Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
#> and Tail_ESS are effective sample size measures, and Rhat is the potential
#> scale reduction factor on split chains (at convergence, Rhat = 1).

# model without the treatent effect
fit2 <- brm(
  count ~ zAge + zBase,
  data = epilepsy, family = negbinomial(),
  prior = prior(normal(0, 1), class = b),
  save_all_pars = TRUE
)
#> Warning: Argument 'save_all_pars' is deprecated. Please use argument 'all' in function 'save_pars()' instead.
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 2.9e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.29 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 1: Iteration:  200 / 2000 [ 10%]  (Warmup)
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#> Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.117 seconds (Warm-up)
#> Chain 1:                0.103 seconds (Sampling)
#> Chain 1:                0.22 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 2.4e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.24 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
#> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup)
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#> Chain 2: 
#> Chain 2:  Elapsed Time: 0.113 seconds (Warm-up)
#> Chain 2:                0.102 seconds (Sampling)
#> Chain 2:                0.215 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 2.4e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.24 seconds.
#> Chain 3: Adjust your expectations accordingly!
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#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.118 seconds (Warm-up)
#> Chain 3:                0.126 seconds (Sampling)
#> Chain 3:                0.244 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 2.3e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.23 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4: 
#> Chain 4: 
#> Chain 4: Iteration:    1 / 2000 [  0%]  (Warmup)
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#> Chain 4: 
#> Chain 4:  Elapsed Time: 0.112 seconds (Warm-up)
#> Chain 4:                0.114 seconds (Sampling)
#> Chain 4:                0.226 seconds (Total)
#> Chain 4: 
summary(fit2)
#>  Family: negbinomial 
#>   Links: mu = log 
#> Formula: count ~ zAge + zBase 
#>    Data: epilepsy (Number of observations: 236) 
#>   Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#>          total post-warmup draws = 4000
#> 
#> Regression Coefficients:
#>           Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept     1.80      0.05     1.70     1.90 1.00     4395     3220
#> zAge          0.13      0.05     0.03     0.23 1.00     3937     3216
#> zBase         0.72      0.06     0.61     0.84 1.00     3996     2929
#> 
#> Further Distributional Parameters:
#>       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> shape     2.32      0.31     1.77     2.99 1.00     4274     3282
#> 
#> Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
#> and Tail_ESS are effective sample size measures, and Rhat is the potential
#> scale reduction factor on split chains (at convergence, Rhat = 1).

# compute the posterior model probabilities
post_prob(fit1, fit2)
#> Iteration: 1
#> Iteration: 2
#> Iteration: 3
#> Iteration: 4
#> Iteration: 5
#> Iteration: 1
#> Iteration: 2
#> Iteration: 3
#> Iteration: 4
#> Iteration: 5
#>     fit1     fit2 
#> 0.350077 0.649923 

# specify prior model probabilities
post_prob(fit1, fit2, prior_prob = c(0.8, 0.2))
#> Iteration: 1
#> Iteration: 2
#> Iteration: 3
#> Iteration: 4
#> Iteration: 5
#> Iteration: 1
#> Iteration: 2
#> Iteration: 3
#> Iteration: 4
#>      fit1      fit2 
#> 0.6848329 0.3151671 
# }