Posterior Model Probabilities from Marginal Likelihoods

Generic function that computes posterior model probabilities from marginal likelihoods.

Usage

post_prob(x, ..., prior_prob = NULL, model_names = NULL)

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

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

# Default S3 method
post_prob(x, ..., prior_prob = NULL, model_names = NULL)

Arguments

x: Object of class "bridge" or "bridge_list" as returned from bridge_sampler. Additionally, the default method assumes that all passed objects are numeric log marginal likelihoods (e.g., from logml) and will throw an error otherwise.
...: further objects of class "bridge" or "bridge_list" as returned from bridge_sampler. Or numeric values for the default method.
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.

Value

For the default method and the method for "bridge" objects, a named numeric vector with posterior model probabilities (i.e., which sum to one).

For the method for "bridge_list" objects, a matrix consisting of posterior model probabilities where each row sums to one and gives the model probabilities for one set of logmls. The (named) columns correspond to the models and the number of rows is given by the "bridge_list" element with the most repetitions. Elements with fewer repetitions will be recycled (with warning).

Note

For realistic examples, see bridge_sampler and the accompanying vignettes:
vignette("bridgesampling_example_jags")
vignette("bridgesampling_example_stan")

Author

Quentin F. Gronau and Henrik Singmann

Examples


H0 <- structure(list(logml = -20.8084543022433, niter = 4, method = "normal"),
                .Names = c("logml", "niter", "method"), class = "bridge")
H1 <- structure(list(logml = -17.9623077558729, niter = 4, method = "normal"),
                .Names = c("logml", "niter", "method"), class = "bridge")
H2 <- structure(list(logml = -19, niter = 4, method = "normal"),
                .Names = c("logml", "niter", "method"), class = "bridge")


post_prob(H0, H1, H2)
#>         H0         H1         H2 
#> 0.04111453 0.70804533 0.25084015 
post_prob(H1, H0)
#>         H1         H0 
#> 0.94511915 0.05488085 

## all produce the same (only names differ):
post_prob(H0, H1, H2)
#>         H0         H1         H2 
#> 0.04111453 0.70804533 0.25084015 
post_prob(H0$logml, H1$logml, H2$logml)
#>   H0$logml   H1$logml   H2$logml 
#> 0.04111453 0.70804533 0.25084015 
post_prob(c(H0$logml, H1$logml, H2$logml))
#>   c(H0$logml, H1$logml, H2$logml) c(H0$logml, H1$logml, H2$logml).1 
#>                        0.04111453                        0.70804533 
#> c(H0$logml, H1$logml, H2$logml).2 
#>                        0.25084015 
post_prob(H0$logml, c(H1$logml, H2$logml))
#>                H0$logml   c(H1$logml, H2$logml) c(H1$logml, H2$logml).1 
#>              0.04111453              0.70804533              0.25084015 
post_prob(H0$logml, c(H1$logml, H2$logml), model_names = c("H0", "H1", "H2"))
#>         H0         H1         H2 
#> 0.04111453 0.70804533 0.25084015 


### with bridge list elements:
H0L <- structure(list(logml = c(-20.8088381186739, -20.8072772698116,
-20.808454454621, -20.8083419072281, -20.8087870541247, -20.8084887398113,
-20.8086023582344, -20.8079083169745, -20.8083048489095, -20.8090050811436
), niter = c(4, 4, 4, 4, 4, 4, 4, 4, 4, 4), method = "normal",
    repetitions = 10), .Names = c("logml", "niter", "method",
"repetitions"), class = "bridge_list")

H1L <- structure(list(logml = c(-17.961665507006, -17.9611290723151,
-17.9607509604499, -17.9608629535992, -17.9602093576442, -17.9600223300432,
-17.9610157118017, -17.9615557696561, -17.9608437034849, -17.9606743200309
), niter = c(4, 4, 4, 4, 4, 4, 4, 4, 3, 4), method = "normal",
    repetitions = 10), .Names = c("logml", "niter", "method",
"repetitions"), class = "bridge_list")

post_prob(H1L, H0L)
#>             H1L        H0L
#>  [1,] 0.9451723 0.05482765
#>  [2,] 0.9451192 0.05488076
#>  [3,] 0.9451999 0.05480015
#>  [4,] 0.9451882 0.05481178
#>  [5,] 0.9452451 0.05475488
#>  [6,] 0.9452394 0.05476064
#>  [7,] 0.9451938 0.05480620
#>  [8,] 0.9451298 0.05487017
#>  [9,] 0.9451873 0.05481270
#> [10,] 0.9452323 0.05476767
post_prob(H1L, H0L, H0) # last element recycled with warning.
#> Warning: Not all objects provide 10 logmls. Some values are recycled.
#>             H1L        H0L         H0
#>  [1,] 0.8960265 0.05197679 0.05199675
#>  [2,] 0.8960037 0.05202875 0.05196754
#>  [3,] 0.8960938 0.05195311 0.05195312
#>  [4,] 0.8960781 0.05196387 0.05195803
#>  [5,] 0.8961597 0.05191153 0.05192881
#>  [6,] 0.8961632 0.05191751 0.05191930
#>  [7,] 0.8960760 0.05195815 0.05196584
#>  [8,] 0.8959934 0.05201751 0.05198912
#>  [9,] 0.8960782 0.05196480 0.05195703
#> [10,] 0.8961265 0.05192243 0.05195104