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, combined into a mixture distribution using mixture, or used with distribution to define a distribution over a data greta array.

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, n_realisations = NULL,
dimension = NULL)

wishart(df, Sigma)

lkj_correlation(eta, dimension = 2)

multinomial(size, prob, n_realisations = NULL, dimension = NULL)

categorical(prob, n_realisations = NULL, dimension = NULL)

dirichlet(alpha, n_realisations = NULL, dimension = NULL)

dirichlet_multinomial(size, alpha, n_realisations = NULL,
dimension = NULL)

## 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. the dimensions of the greta array to be returned, either a scalar or a vector of positive integers. See details. unconstrained parameters positive parameters, alpha must be a vector for dirichlet and dirichlet_multinomial. a length-two vector giving values between which to truncate the distribution, similarly to the lower and upper arguments to variable probability parameter (0 < prob < 1), must be a vector for multinomial and categorical positive integer parameter positive definite variance-covariance matrix parameter the number of independent realisation of a multivariate distribution the dimension of a multivariate distribution

## 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 distributions (multivariate_normal(), multinomial(), categorical(), dirichlet(), and dirichlet_multinomial()) each row of the output and parameters corresponds to an independent realisation. If a single realisation or parameter value is specified, it must therefore be a row vector (see example). n_realisations gives the number of rows/realisations, and dimension gives the dimension of the distribution. I.e. a bivariate normal distribution would be produced with multivariate_normal(..., dimension = 2). The dimension can usually be detected from the parameters.

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 parameterisations and argument names of greta distributions match 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::dlst 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
# note that the parameter must be a row vector
Sig <- diag(4)
Sig[3, 4] <- Sig[4, 3] <- 0.6
theta <- multivariate_normal(t(rep(mu, 4)), Sig)

# 10 independent replicates of that
theta <- multivariate_normal(t(rep(mu, 4)), Sig, n_realisations = 10)

# 10 multivariate normal replicates, each with a different mean vector,
# but the same covariance matrix
means <- matrix(rnorm(40), 10, 4)
theta <- multivariate_normal(means, Sig, n_realisations = 10)
dim(theta)

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

# }