Struct BetaNP 

pub struct BetaNP {
    pub alpha: f64,
    pub beta: f64,
}

Beta distribution stored in (α, β) moment parameterisation.

Natural parameters are η = (α − 1, β − 1). Both α and β must be strictly positive and finite for the distribution to be well-defined; the constructor and ExponentialFamily::set_natural reject values outside that open positive quadrant.

Fields

alpha: f64

Shape parameter α > 0.

beta: f64

Shape parameter β > 0.

Implementations

impl BetaNP

pub fn new(alpha: f64, beta: f64) -> Result<Self>

Construct from moment parameters (α, β). Both must be strictly positive and finite.

pub fn from_natural(natural: &[f64]) -> Result<Self>

Reconstruct a Beta from natural parameters η = (α − 1, β − 1).

pub fn expected_x(&self) -> f64

Expected value E[x] = α / (α + β).

pub fn expected_log_x(&self) -> f64

Expected log value E[log x] = ψ(α) − ψ(α + β).

pub fn expected_log_1mx(&self) -> f64

Expected log of the complement E[log(1 − x)] = ψ(β) − ψ(α + β).

pub fn variance(&self) -> f64

Variance Var[x] = α β / ((α + β)² (α + β + 1)).

pub fn multiply_naturals(&self, other: &BetaNP) -> Result<BetaNP>

Sum the natural parameters of self and other. Corresponds to the pointwise product of densities: if both priors are Beta on the same variable, their product is another Beta whose natural parameter is the sum of the two input natural parameters.

Concretely: α_new = α₁ + α₂ − 1 and β_new = β₁ + β₂ − 1.

pub fn kl_to(&self, other: &BetaNP) -> f64

Closed-form KL divergence KL(Beta(α_p, β_p) || Beta(α_q, β_q)).

Standard result:

  KL = ln B(α_q, β_q) − ln B(α_p, β_p)
       + (α_p − α_q) ψ(α_p)
       + (β_p − β_q) ψ(β_p)
       + (α_q − α_p + β_q − β_p) ψ(α_p + β_p)

where ln B(a, b) = ln Γ(a) + ln Γ(b) − ln Γ(a + b).

Trait Implementations

impl Clone for BetaNP

fn clone(&self) -> BetaNP

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for BetaNP

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl ExponentialFamily for BetaNP

fn family_name(&self) -> &'static str

Name of the family (used for error messages, e.g. “Gaussian”).

fn natural_dim(&self) -> usize

Dimensionality of the natural-parameter vector.

fn natural_params(&self) -> Vec<f64>

Return a copy of the current natural parameters.

fn set_natural(&mut self, new_eta: &[f64]) -> Result<()>

Replace the natural parameters with new_eta.

fn sufficient_statistics(&self, value: f64) -> Vec<f64>

Sufficient statistics u(x) evaluated at the scalar or categorical value value.

fn log_partition(&self, natural_params: &[f64]) -> Result<f64>

Log partition function A(η).

fn expected_sufficient_statistics(&self) -> Vec<f64>

Expected sufficient statistics E_q[u(x)] = ∇_η A(η).

fn to_natural(&self) -> Vec<f64>

Read-only view of the natural parameter vector.

fn update_natural(&mut self, delta: &[f64]) -> Result<()>

Additively update the natural parameters: η ← η + δ.

fn entropy(&self) -> Result<f64>

Differential entropy H(q) = A(η) − ηᵀ E_q[u(x)] − E_q[log h(x)].