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Conjugate Families

library(bayesrules)

The bayesrules package has a set of functions that support exploring Bayesian models from three conjugate families: Beta-Binomial, Gamma-Poisson, and Normal-Normal. The functions either help with plotting (prior, likelihood, and/or posterior) or summarizing the descriptives (mean, mode, variance, and sd) of the prior and/or posterior.

The Beta-Binomial Model

We use the Beta-Binomial model to show the different set of functions and the arguments.

Prior

plot_beta(alpha = 3, beta = 13, mean = TRUE, mode = TRUE)
#> Warning in geom_segment(aes(x = mean, y = 0, xend = mean, yend = dbeta(mean, : All aesthetics have length 1, but the data has 2 rows.
#> ℹ Please consider using `annotate()` or provide this layer with data containing
#>   a single row.
#> Warning in geom_segment(aes(x = mode, y = 0, xend = mode, yend = stats::dbeta(mode, : All aesthetics have length 1, but the data has 2 rows.
#> ℹ Please consider using `annotate()` or provide this layer with data containing
#>   a single row.

summarize_beta(alpha = 3, beta = 13)
#>     mean      mode         var         sd
#> 1 0.1875 0.1428571 0.008961397 0.09466466

Likelihood

In addition, plot_binomial_likelihood() helps users visualize the Binomial likelihood function and shows the maximum likelihood estimate.

plot_binomial_likelihood(y = 3, n = 15, mle = TRUE)
#> Warning in geom_segment(aes(x = max, xend = max, y = 0, yend = dbinom(success, : All aesthetics have length 1, but the data has 2 rows.
#> ℹ Please consider using `annotate()` or provide this layer with data containing
#>   a single row.

Prior-Likelihood-Posterior

The two other functions plot_beta_binomial() and summarize_beta_binomial() require both the prior parameters and the data for the likelihood.

plot_beta_binomial(alpha = 3, beta = 13, y = 5, n = 10, 
                   prior = TRUE, #the default 
                   likelihood = TRUE,  #the default
                   posterior = TRUE #the default
                   )

summarize_beta_binomial(alpha = 3, beta = 13, y = 5, n = 10)
#>       model alpha beta      mean      mode         var         sd
#> 1     prior     3   13 0.1875000 0.1428571 0.008961397 0.09466466
#> 2 posterior     8   18 0.3076923 0.2916667 0.007889546 0.08882312

Other Conjugate-Families

For Gamma-Poisson and Normal-Normal models, the set of functions are similar but the arguments are different for each model. Arguments of the Gamma-Poisson functions include the shape and rate of the Gamma prior and sum_y and n arguments related to observed data which represent the sum of observed data values and number of observations respectively.

plot_gamma_poisson(
  shape = 3,
  rate = 4,
  sum_y = 3,
  n = 9,
  prior = TRUE,
  likelihood = TRUE,
  posterior = TRUE
)

For the Normal-Normal model functions, the prior Normal model has the mean and sd argument. The observed data has sigma, y_bar, and n which indicate the standard deviation, mean, and sample size of the data respectively.

summarize_normal_normal(mean = 3.8, sd = 1.12, sigma = 5.8, y_bar = 3.35, n = 8)
#>       model     mean     mode      var        sd
#> 1     prior 3.800000 3.800000 1.254400 1.1200000
#> 2 posterior 3.696604 3.696604 0.966178 0.9829435

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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