bayes_inference: Bayesian hypothesis tests and credible intervals
In statsr: Companion Software for the Coursera Statistics with R Specialization

Description Usage Arguments Value Note References Examples

Bayesian hypothesis tests and credible intervals

bayes_inference(
  y,
  x = NULL,
  data,
  type = c("ci", "ht"),
  statistic = c("mean", "proportion"),
  method = c("theoretical", "simulation"),
  success = NULL,
  null = NULL,
  cred_level = 0.95,
  alternative = c("twosided", "less", "greater"),
  hypothesis_prior = c(H1 = 0.5, H2 = 0.5),
  prior_family = "JZS",
  n_0 = 1,
  mu_0 = null,
  s_0 = 0,
  v_0 = -1,
  rscale = 1,
  beta_prior = NULL,
  beta_prior1 = NULL,
  beta_prior2 = NULL,
  nsim = 10000,
  verbose = TRUE,
  show_summ = verbose,
  show_res = verbose,
  show_plot = verbose
)

`y`	Response variable, can be numerical or categorical
`x`	Explanatory variable, categorical (optional)
`data`	Name of data frame that y and x are in
`type`	of inference; "ci" (credible interval) or "ht" (hypothesis test)
`statistic`	population parameter to estimate: mean or proportion
`method`	of inference; "theoretical" (quantile based) or "simulation"
`success`	which level of the categorical variable to call "success", i.e. do inference on
`null`	null value for the hypothesis test
`cred_level`	confidence level, value between 0 and 1
`alternative`	direction of the alternative hypothesis; "less","greater", or "twosided"
`hypothesis_prior`	discrete prior for H1 and H2, default is the uniform prior: c(H1=0.5,H2=0.5)
`prior_family`	character string representing default priors for inference or testing ("JSZ", "JUI","ref"). See notes for details.
`n_0`	n_0 is the prior sample size in the Normal prior for the mean
`mu_0`	the prior mean in one sample mean problems or the prior difference in two sample problems. For hypothesis testing, this is all the null value if null is not supplied.
`s_0`	the prior standard deviation of the data for the conjugate Gamma prior on 1/sigma^2
`v_0`	prior degrees of freedom for conjugate Gamma prior on 1/sigma^2
`rscale`	is the scaling parameter in the Cauchy prior: 1/n_0 ~ Gamma(1/2, rscale^2/2) leads to mu_0 having a Cauchy(0, rscale^2*sigma^2) prior distribution for prior_family="JZS".
`beta_prior, beta_prior1, beta_prior2`	beta priors for p (or p_1 and p_2) for one or two proportion inference
`nsim`	number of Monte Carlo draws; default is 10,000
`verbose`	whether output should be verbose or not, default is TRUE
`show_summ`	print summary stats, set to verbose by default
`show_res`	print results, set to verbose by default
`show_plot`	print inference plot, set to verbose by default

Results of inference task performed.

For inference and testing for normal means several default options are available. "JZS" corresponds to using the Jeffreys reference prior on sigma^2, p(sigma^2) = 1/sigma^2, and the Zellner-Siow Cauchy prior on the standardized effect size mu/sigma or ( mu_1 - mu_2)/sigma with a location of mu_0 and scale rscale. The "JUI" option also uses the Jeffreys reference prior on sigma^2, but the Unit Information prior on the standardized effect, N(mu_0, 1). The option "ref" uses the improper uniform prior on the standardized effect and the Jeffreys reference prior on sigma^2. The latter cannot be used for hypothesis testing due to the ill-determination of Bayes factors. Finally "NG" corresponds to the conjugate Normal-Gamma prior.

https://statswithr.github.io/book/

# inference for the mean from a single normal population using
# Jeffreys Reference prior, p(mu, sigma^2) = 1/sigma^2

library(BayesFactor)
data(tapwater)

# Calculate 95% CI using quantiles from Student t derived from ref prior
bayes_inference(tthm, data=tapwater,
                statistic="mean", 
                type="ci", prior_family="ref",
                method="theoretical")
 
# Calculate 95% CI using simulation from Student t using an informative mean and ref
# prior for sigma^2

bayes_inference(tthm, data=tapwater,
                statistic="mean", mu_0=9.8,
                type="ci",  prior_family="JUI",
                method="theo")

# Calculate 95% CI using simulation  with the 
# Cauchy prior on mu and reference prior on sigma^2


bayes_inference(tthm, data=tapwater,
                statistic="mean", mu_0 = 9.8, rscale=sqrt(2)/2,
                type="ci", prior_family="JZS",
                method="simulation")

                
# Bayesian t-test mu = 0 with ZJS prior  
bayes_inference(tthm, data=tapwater,
                statistic="mean",
                type="ht", alternative="twosided", null=80,
                prior_family="JZS",
                method="sim")
                
               
# Bayesian t-test for two means 

data(chickwts)
chickwts = chickwts[chickwts$feed %in% c("horsebean","linseed"),]
# Drop unused factor levels
chickwts$feed = factor(chickwts$feed)                
bayes_inference(y=weight, x=feed, data=chickwts,
                statistic="mean", mu_0 = 0, alt="twosided",
                type="ht", prior_family="JZS",
                method="simulation")