algebraic.dist (version 0.9.1)

conditional.mixture: Conditional distribution of a mixture.

Description

For a mixture of distributions that support closed-form conditioning (e.g. MVN), uses Bayes' rule to update the mixing weights: $$w_k' \propto w_k f_k(x_{given})$$ where \(f_k\) is the marginal density of component \(k\) at the observed values. The component conditionals are computed via conditional(component_k, given_indices = ..., given_values = ...).

Usage

# S3 method for mixture
conditional(x, P = NULL, ..., given_indices = NULL, given_values = NULL)

Value

A mixture or empirical_dist object.

Arguments

x

A mixture object.

P

Optional predicate function for MC fallback.

...

Additional arguments.

given_indices

Integer vector of observed variable indices.

given_values

Numeric vector of observed values.

Details

Falls back to MC realization if P is provided or if any component does not support given_indices/given_values.

Examples

# Closed-form conditioning on MVN mixture
m <- mixture(
  list(mvn(c(0, 0), diag(2)), mvn(c(3, 3), diag(2))),
  c(0.5, 0.5)
)
# Condition on X2 = 1
mc <- conditional(m, given_indices = 2, given_values = 1)
mean(mc)