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::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


# 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)