Type:	Package
Title:	The Bayes Factor Playground
Version:	0.9.3
Description:	A lightweight modelling syntax for defining likelihoods and priors and for computing Bayes factors for simple one parameter models. It includes functionality for computing and plotting priors, likelihoods, and model predictions. Additional functionality is included for computing and plotting posteriors.
License:	MIT + file LICENSE
Encoding:	UTF-8
Suggests:	testthat, covr, knitr, rmarkdown, markdown, vdiffr, ggplot2, patrick
VignetteBuilder:	knitr
RoxygenNote:	7.2.3
Imports:	methods, gginnards, stats
URL:	https://github.com/bayesplay/bayesplay
BugReports:	https://github.com/bayesplay/bayesplay/issues
NeedsCompilation:	no
Packaged:	2023-04-13 11:23:38 UTC; lc663
Author:	Lincoln John Colling [aut, cre]
Maintainer:	Lincoln John Colling <lincoln@colling.net.nz>
Repository:	CRAN
Date/Publication:	2023-04-13 12:10:02 UTC

bayesplay: The Bayes Factor Playground

Description

A lightweight modelling syntax for defining likelihoods and priors and for computing Bayes factors for simple one parameter models. It includes functionality for computing and plotting priors, likelihoods, and model predictions. Additional functionality is included for computing and plotting posteriors.

Author(s)

Maintainer: Lincoln J Colling lincoln@colling.net.nz (ORCID)

See Also

Useful links:

• https://github.com/bayesplay/bayesplay

• Report bugs at https://github.com/bayesplay/bayesplay/issues

Get fields from data slot

Description

Get fields from data slot

Usage

## S4 method for signature 'bayesplay'
x$name

Arguments

Value

content of the named field from the data slot

Get fields from data slot

Description

Get fields from data slot

Usage

## S4 method for signature 'bayesplay'
x[[i]]

Arguments

Value

content of the specified field from the data slot

Extract the posterior

Description

Extract the posterior object from a product object

Usage

extract_posterior(x)

Arguments

Value

a posterior object

Extract predictions

Description

Extract the marginal predictions over the prior

Usage

extract_predictions(x)

Arguments

Value

a prediction object

Compute integral

Description

Computes the definite integral of a product object over the range of the parameter

Usage

integral(obj)

Arguments

Value

A numeric of the marginal likelihood

Examples

# define a likelihood
data_model <- likelihood(family = "normal", mean = 5.5, sd = 32.35)

# define a prior
prior_model <- prior(family = "normal", mean = 5.5, sd = 13.3)

# multiply the likelihood by the prior
model <- data_model * prior_model

# take the integral
integral(model)

Specify a likelihood

Description

Define likelihoods using different different distribution families

Usage

likelihood(family, ...)

Arguments

Details

Available distribution families

The following distribution families can be used for the likelihood

• normal a normal distribution

• student_t a scaled and shifted t-distribution

• noncentral_t a noncentral t (for t statistic)

• noncentral_d a noncentral t (for one sample d)

• noncentral_d2 a noncentral t (for independent samples d)

• binomial a binomial distribution

The parameters that need to be specified will be dependent on the family

normal distribution

When family is set to normal then the following parameters must be set

• mean mean of the normal likelihood

• sd standard deviation of the normal likelihood

student_t distribution

When family is set to student_t then the following parameters may be set

• mean mean of the scaled and shifted t likelihood

• sd standard deviation of the scaled and shifted t likelihood

• df degrees of freedom

noncentral_t distribution

When family is set to noncentral_t then the following parameters may be set

• t the t value of the data

• df degrees of freedom

noncentral_d distribution

When family is set to noncentral_d then the following parameters may be set

• d the d (mean / sd) value of the data

• n the sample size

noncentral_d2 distribution

When family is set to noncentral_d2 then the following parameters may be set

• d the d (mean / s_pooled) value of the data

• n1 the sample size of group 1

• n2 the sample size of group 2

s_{\mathrm{pooled}} is set as below:

s_{\mathrm{pooled}} = \sqrt{\frac{(n_1 - 1)s^2_1 + (n_2 - 1)s^2_2 } {n_1 + n_2 - 2}}

binomial distribution

When the family is set to binomial then the following parameters may be set

• successes the number of successes

• trials the number of trials

Value

an object of class likelihood

Examples

# specify a normal likelihood
likelihood(family = "normal", mean = 5.5, sd = 32.35)

# specify a scaled and shifted t likelihood
likelihood(family = "student_t", mean = 5.5, sd = 32.35, df = 10)

# specify non-central t likelihood (t scaled)
likelihood(family = "noncentral_t", t = 10, df = 10)

# specify non-central t likelihood (d scaled)
likelihood(family = "noncentral_d", d = 10, n = 10)

# specify non-central t likelihood (independent samples d scaled)
likelihood(family = "noncentral_d2", d = 10, n1 = 10, n2 = 12)

# specify a binomial likelihood
likelihood(family = "binomial", successes = 2, trials = 10)

Get names from data slot

Description

Get names from data slot

Usage

## S4 method for signature 'bayesplay'
names(x)

Arguments

Value

the field names from the data slot

Plot a bayesplay object

Description

Plots an object created by bayesplay

Usage

## S3 method for class 'prior'
plot(x, ...)

## S3 method for class 'posterior'
plot(x, add_prior = FALSE, ...)

## S3 method for class 'likelihood'
plot(x, ...)

## S3 method for class 'product'
plot(x, ...)

## S3 method for class 'prediction'
plot(x, model_name = "model", ...)

Arguments

Value

a ggplot2 object

Specify a prior

Description

Define priors using different different distribution families

Usage

prior(family, ...)

Arguments

Details

Available distribution families

The following distributions families can be used for the prior

• normal a normal distribution

• student_t a scaled and shifted t-distribution

• cauchy a Cauchy distribution

• uniform a uniform distribution

• point a point

• beta a beta distribution The parameters that need to be specified will be dependent on the family

Normal distribution

When family is set to normal then the following parameters may be be set

• mean mean of the normal prior

• sd standard deviation of the normal prior

• range (optional) a vector specifying the parameter range

Student t distribution

When family is set to student_t then the following parameters may be set

• mean mean of the scaled and shifted t prior

• sd standard deviation of the scaled and shifted t prior

• df degrees of freedom of the scaled and shifted t prior

• range (optional) a vector specifying the parameter range

Cauchy distribution

When family is set to cauchy then the following parameters may be set

• location the centre of the Cauchy distribution (default: 0)

• scale the scale of the Cauchy distribution

• range (optional) a vector specifying the parameter range

Uniform distribution

When family is set to uniform then the following parameters must be set

• min the lower bound

• max the upper bound

Point

When family is set to point then the following parameters may be set

• point the location of the point prior (default: 0)

Beta

When family is set to beta then the following parameters may be set

• alpha the first shape parameter

• beta the second shape parameter

Value

an object of class prior

Examples

# specify a normal prior
prior(family = "normal", mean = 0, sd = 13.3)

# specify a half-normal (range 0 to Infinity) prior
prior(family = "normal", mean = 0, sd = 13.3, range = c(0, Inf))

# specify a student t prior
prior(family = "student_t", mean = 0, sd = 13.3, df = 79)

# specify a truncated t prior
prior(family = "student_t", mean = 0, sd = 13.3, df = 79, range = c(-40, 40))

# specify a cauchy prior
prior(family = "cauchy", location = 0, scale = .707)

# specify a half cauchy prior
prior(family = "cauchy", location = 0, scale = 1, range = c(-Inf, 0))

# specify a uniform prior
prior(family = "uniform", min = 0, max = 20)

# specify a point prior
prior(family = "point", point = 0)

# specify a beta prior
prior(family = "beta", alpha = 2.5, beta = 3.8)

Compute the Savage-Dickey density ratio

Description

Computes the Saveage-Dickey density ratio from a posterior object at a specified point

Usage

sd_ratio(x, point)

Arguments

Value

A numeric of the Savage-Dickey density ratio

Examples

# define a likelihood
data_model <- likelihood(family = "normal", mean = 5.5, sd = 32.35)

# define a prior
prior_model <- prior(family = "normal", mean = 5.5, sd = 13.3)

model <- extract_posterior(data_model * prior_model)

# compute the Savage-Dickey density ratio at 0
sd_ratio(model, 0)

Summarise a Bayes factor

Description

Provide a verbal summary of a Bayes factor and the level of evidence

Usage

## S4 method for signature 'bf'
summary(object)

Arguments

Value

No return, called for side effects

Visually compare two models

Description

Visually compare two models

Usage

visual_compare(model1, model2, ratio = FALSE)

Arguments

Value

A ggplot2 object

Examples

# define two models
data_model <- likelihood(family = "normal", .5, 1)
h0_mod <- prior(family = "point", point = 0)
h1_mod <- prior(family = "normal", mean = 0, sd = 10)
m0 <- extract_predictions(data_model * h0_mod)
m1 <- extract_predictions(data_model * h1_mod)

# visually compare the model
visual_compare(m0, m1)
# plot the ratio of the two model predictions
visual_compare(m0, m1, ratio = TRUE)