mixtures of probability distributions

mixture combines other probability distributions into a single mixture distribution, either over a variable, or for fixed data.

mixture(..., weights, dim = NULL)

Arguments

...	variable greta arrays following probability distributions (see distributions()); the component distributions in a mixture distribution.
weights	a column vector or array of mixture weights, which must be positive, but need not sum to one. The first dimension must be the number of distributions, the remaining dimensions must either be 1 or match the distribution dimension.
dim	the dimensions of the greta array to be returned, either a scalar or a vector of positive integers.

Details

The weights are rescaled to sum to one along the first dimension, and are then used as the mixing weights of the distribution. I.e. the probability density is calculated as a weighted sum of the component probability distributions passed in via \dots

The component probability distributions must all be either continuous or discrete, and must have the same dimensions.

Examples

# NOT RUN {
# a scalar variable following a strange bimodal distibution
weights <- uniform(0, 1, dim = 3)
a <- mixture(normal(-3, 0.5),
  normal(3, 0.5),
  normal(0, 3),
  weights = weights
)
m <- model(a)
plot(mcmc(m, n_samples = 500))

# simulate a mixture of poisson random variables and try to recover the
# parameters with a Bayesian model
x <- c(
  rpois(800, 3),
  rpois(200, 10)
)

weights <- uniform(0, 1, dim = 2)
rates <- normal(0, 10, truncation = c(0, Inf), dim = 2)
distribution(x) <- mixture(poisson(rates[1]),
  poisson(rates[2]),
  weights = weights
)
m <- model(rates)
draws_rates <- mcmc(m, n_samples = 500)

# check the mixing probabilities after fitting using calculate()
# (you could also do this within the model)
normalized_weights <- weights / sum(weights)
draws_weights <- calculate(normalized_weights, draws_rates)

# get the posterior means
summary(draws_rates)$statistics[, "Mean"]
summary(draws_weights)$statistics[, "Mean"]

# weights can also be an array, giving different mixing weights
# for each observation (first dimension must be number of components)
dim <- c(5, 4)
weights <- uniform(0, 1, dim = c(2, dim))
b <- mixture(normal(1, 1, dim = dim),
  normal(-1, 1, dim = dim),
  weights = weights
)
# }