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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 3e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.3 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
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#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.121 seconds (Warm-up)
#> Chain 1:                0.135 seconds (Sampling)
#> Chain 1:                0.256 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 2.5e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.25 seconds.
#> Chain 2: Adjust your expectations accordingly!
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#> Chain 2: 
#> Chain 2:  Elapsed Time: 0.122 seconds (Warm-up)
#> Chain 2:                0.132 seconds (Sampling)
#> Chain 2:                0.254 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 5.8e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.58 seconds.
#> Chain 3: Adjust your expectations accordingly!
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#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.123 seconds (Warm-up)
#> Chain 3:                0.12 seconds (Sampling)
#> Chain 3:                0.243 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 7.2e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.72 seconds.
#> Chain 4: Adjust your expectations accordingly!
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#> Chain 4: 
#> Chain 4:  Elapsed Time: 0.119 seconds (Warm-up)
#> Chain 4:                0.116 seconds (Sampling)
#> Chain 4:                0.235 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     1.75     2.04 1.00     4462     2818
#> zAge          0.11      0.05     0.01     0.22 1.00     4563     3366
#> zBase         0.72      0.05     0.61     0.83 1.00     4614     3142
#> Trt1         -0.19      0.10    -0.39     0.02 1.00     4947     3043
#> 
#> Further Distributional Parameters:
#>       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> shape     2.36      0.32     1.79     3.04 1.00     4858     3302
#> 
#> 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 3.3e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.33 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: 
#> Chain 1:  Elapsed Time: 0.115 seconds (Warm-up)
#> Chain 1:                0.127 seconds (Sampling)
#> Chain 1:                0.242 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 2.6e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.26 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
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#> Chain 2: 
#> Chain 2:  Elapsed Time: 0.116 seconds (Warm-up)
#> Chain 2:                0.112 seconds (Sampling)
#> Chain 2:                0.228 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 2.6e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.26 seconds.
#> Chain 3: Adjust your expectations accordingly!
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#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.113 seconds (Warm-up)
#> Chain 3:                0.124 seconds (Sampling)
#> Chain 3:                0.237 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: 
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#> Chain 4: 
#> Chain 4:  Elapsed Time: 0.115 seconds (Warm-up)
#> Chain 4:                0.108 seconds (Sampling)
#> Chain 4:                0.223 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     4059     3058
#> zAge          0.13      0.05     0.02     0.23 1.00     4590     3303
#> zBase         0.72      0.06     0.62     0.83 1.00     3916     3191
#> 
#> Further Distributional Parameters:
#>       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> shape     2.32      0.31     1.77     3.00 1.00     4130     2849
#> 
#> 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 
#> 0.3510768 0.6489232 

# 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 
#> 0.6831017 0.3168983 
# }