greta (version 0.2.0)

distributions: probability distributions

Description

These functions can be used to define random variables in a greta model. They return a variable greta array that follows the specified distribution. This variable greta array can be used to represent a parameter with prior distribution, or used with distribution to define a distribution over a data greta array.

Usage

uniform(min, max, dim = NULL)
normal(mean, sd, dim = NULL, truncation = c(-Inf, Inf))
lognormal(meanlog, sdlog, dim = NULL, truncation = c(0, Inf))
bernoulli(prob, dim = NULL)
binomial(size, prob, dim = NULL)
beta_binomial(size, alpha, beta, dim = NULL)
negative_binomial(size, prob, dim = NULL)
hypergeometric(m, n, k, dim = NULL)
poisson(lambda, dim = NULL)
gamma(shape, rate, dim = NULL, truncation = c(0, Inf))
inverse_gamma(alpha, beta, dim = NULL, truncation = c(0, Inf))
weibull(shape, scale, dim = NULL, truncation = c(0, Inf))
exponential(rate, dim = NULL, truncation = c(0, Inf))
pareto(a, b, dim = NULL, truncation = c(0, Inf))
student(df, mu, sigma, dim = NULL, truncation = c(-Inf, Inf))
laplace(mu, sigma, dim = NULL, truncation = c(-Inf, Inf))
beta(shape1, shape2, dim = NULL, truncation = c(0, 1))
cauchy(location, scale, dim = NULL, truncation = c(-Inf, Inf))
chi_squared(df, dim = NULL, truncation = c(0, Inf))
logistic(location, scale, dim = NULL, truncation = c(-Inf, Inf))
f(df1, df2, dim = NULL, truncation = c(0, Inf))
multivariate_normal(mean, Sigma, dim = 1)
wishart(df, Sigma)
lkj_correlation(eta, dim = 2)
multinomial(size, prob, dim = 1)
categorical(prob, dim = 1)
dirichlet(alpha, dim = 1)
dirichlet_multinomial(size, alpha, dim = 1)

Arguments

min, max

scalar values giving optional limits to uniform variables. Like lower and upper, these must be specified as numerics, they cannot be greta arrays (though see details for a workaround). Unlike lower and upper, they must be finite. min must always be less than max.

dim

the dimensions of the greta array to be returned, either a scalar or a vector of positive integers. See details.

mean, meanlog, location, mu

unconstrained parameters

sd, sdlog, sigma, lambda, shape, rate, df, scale, shape1, shape2, alpha, beta, df1, df2, a, b, eta

positive parameters, alpha must be a vector for dirichlet and dirichlet_multinomial.

truncation

a length-two vector giving values between which to truncate the distribution, similarly to the lower and upper arguments to variable

prob

probability parameter (0 < prob < 1), must be a vector for multinomial and categorical

size, m, n, k

positive integer parameter

Sigma

positive definite variance-covariance matrix parameter

Details

The discrete probability distributions (bernoulli, binomial, negative_binomial, poisson, multinomial, categorical, dirichlet_multinomial) can be used when they have fixed values (e.g. defined as a likelihood using distribution, but not as unknown variables.

For univariate distributions dim gives the dimensions of the greta array to create. Each element of the greta array will be (independently) distributed according to the distribution. dim can also be left at its default of NULL, in which case the dimension will be detected from the dimensions of the parameters (provided they are compatible with one another).

For multivariate_normal(), multinomial(), and categorical() dim must be a scalar giving the number of rows in the resulting greta array, each row being (independently) distributed according to the multivariate normal distribution. The number of columns will always be the dimension of the distribution, determined from the parameters specified. wishart() always returns a single square, 2D greta array, with dimension determined from the parameter Sigma.

multinomial() does not check that observed values sum to size, and categorical() does not check that only one of the observed entries is 1. It's the user's responsibility to check their data matches the distribution!

The parameters of uniform must be fixed, not greta arrays. This ensures these values can always be transformed to a continuous scale to run the samplers efficiently. However, a hierarchical uniform parameter can always be created by defining a uniform variable constrained between 0 and 1, and then transforming it to the required scale. See below for an example.

Wherever possible, the parameterisation and argument names of greta distributions matches commonly used R functions for distributions, such as those in the stats or extraDistr packages. The following table states the distribution function to which greta's implementation corresponds:

greta	reference
uniform	stats::dunif
normal	stats::dnorm
lognormal	stats::dlnorm
bernoulli	extraDistr::dbern
binomial	stats::dbinom
beta_binomial	extraDistr::dbbinom
negative_binomial	stats::dnbinom
hypergeometric	stats::dhyper
poisson	stats::dpois
gamma	stats::dgamma
inverse_gamma	extraDistr::dinvgamma
weibull	stats::dweibull
exponential	stats::dexp
pareto	extraDistr::dpareto
student	extraDistr::dnst
laplace	extraDistr::dlaplace
beta	stats::dbeta
cauchy	stats::dcauchy
chi_squared	stats::dchisq
logistic	stats::dlogis
f	stats::df
multivariate_normal	mvtnorm::dmvnorm
multinomial	stats::dmultinom
categorical	stats::dmultinom (size = 1)
dirichlet	extraDistr::ddirichlet
dirichlet_multinomial	extraDistr::ddirmnom
wishart	stats::rWishart
lkj_correlation	rethinking::dlkjcorr

Examples

# NOT RUN {
# a uniform parameter constrained to be between 0 and 1
phi = uniform(min = 0, max = 1)

# a length-three variable, with each element following a standard normal
# distribution
alpha = normal(0, 1, dim = 3)

# a length-three variable of lognormals
sigma = lognormal(0, 3, dim = 3)

# a hierarchical uniform, constrained between alpha and alpha + sigma,
eta = alpha + uniform(0, 1, dim = 3) * sigma

# a hierarchical distribution
mu = normal(0, 1)
sigma = lognormal(0, 1)
theta = normal(mu, sigma)

# a vector of 3 variables drawn from the same hierarchical distribution
thetas = normal(mu, sigma, dim = 3)

# a matrix of 12 variables drawn from the same hierarchical distribution
thetas = normal(mu, sigma, dim = c(3, 4))

# a multivariate normal variable, with correlation between two elements
Sig <- diag(4)
Sig[3, 4] <- Sig[4, 3] <- 0.6
theta = multivariate_normal(rep(mu, 4), Sig)

# 10 independent replicates of that
theta = multivariate_normal(rep(mu, 4), Sig, dim = 10)

# a Wishart variable with the same covariance parameter
theta = wishart(df = 5, Sigma = Sig)
# }