Struct rv::dist::Gaussian

pub struct Gaussian { /* fields omitted */ }

Gaussian / Normal distribution, N(μ, σ) over real values.

Examples

Compute the KL Divergence between two Gaussians.

use rv::prelude::*;

let gauss_1 = Gaussian::new(0.1, 2.3).unwrap();
let gauss_2 = Gaussian::standard();

// KL is not symmetric
let kl_12 = gauss_1.kl(&gauss_2);
let kl_21 = gauss_2.kl(&gauss_1);

// ... but kl_sym is because it's the sum of KL(P|Q) and KL(Q|P)
let kl_sym = gauss_1.kl_sym(&gauss_2);
assert!((kl_sym - (kl_12 + kl_21)).abs() < 1E-12);

Implementations

impl Gaussian

pub fn new(mu: f64, sigma: f64) -> Result<Self, GaussianError>

Create a new Gaussian distribution

Aruments

• mu: mean
• sigma: standard deviation

pub fn new_unchecked(mu: f64, sigma: f64) -> Self

Creates a new Gaussian without checking whether the parameters are valid.

pub fn standard() -> Self

Standard normal

Example

let gauss = Gaussian::standard();

assert_eq!(gauss, Gaussian::new(0.0, 1.0).unwrap());

pub fn mu(&self) -> f64

Get mu parameter

Example

let gauss = Gaussian::new(2.0, 1.5).unwrap();

assert_eq!(gauss.mu(), 2.0);

pub fn set_mu(&mut self, mu: f64) -> Result<(), GaussianError>

Set the value of mu

Example

let mut gauss = Gaussian::new(2.0, 1.5).unwrap();
assert_eq!(gauss.mu(), 2.0);

gauss.set_mu(1.3).unwrap();
assert_eq!(gauss.mu(), 1.3);

Will error for invalid values

assert!(gauss.set_mu(1.3).is_ok());
assert!(gauss.set_mu(std::f64::NEG_INFINITY).is_err());
assert!(gauss.set_mu(std::f64::INFINITY).is_err());
assert!(gauss.set_mu(std::f64::NAN).is_err());

pub fn set_mu_unchecked(&mut self, mu: f64)

Set the value of mu without input validation

pub fn sigma(&self) -> f64

Get sigma parameter

Example

let gauss = Gaussian::new(2.0, 1.5).unwrap();

assert_eq!(gauss.sigma(), 1.5);

pub fn set_sigma(&mut self, sigma: f64) -> Result<(), GaussianError>

Set the value of sigma

Example

let mut gauss = Gaussian::standard();
assert_eq!(gauss.sigma(), 1.0);

gauss.set_sigma(2.3).unwrap();
assert_eq!(gauss.sigma(), 2.3);

Will error for invalid values

assert!(gauss.set_sigma(2.3).is_ok());
assert!(gauss.set_sigma(0.0).is_err());
assert!(gauss.set_sigma(-1.0).is_err());
assert!(gauss.set_sigma(std::f64::INFINITY).is_err());
assert!(gauss.set_sigma(std::f64::NEG_INFINITY).is_err());
assert!(gauss.set_sigma(std::f64::NAN).is_err());

pub fn set_sigma_unchecked(&mut self, sigma: f64)

Set the value of sigma

Trait Implementations

impl Cdf<f32> for Gaussian

fn cdf(&self, x: &f32) -> f64

The value of the Cumulative Density Function at x

fn sf(&self, x: &X) -> f64

Survival function, 1 - CDF(x)

impl Cdf<f64> for Gaussian

fn cdf(&self, x: &f64) -> f64

The value of the Cumulative Density Function at x

fn sf(&self, x: &X) -> f64

Survival function, 1 - CDF(x)

impl Clone for Gaussian

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConjugatePrior<f64, Gaussian> for NormalGamma

type Posterior = Self

Type of the posterior distribution

type LnMCache = f64

Type of the ln_m cache

type LnPpCache = (GaussianSuffStat, f64)

Type of the ln_pp cache

fn posterior(&self, x: &DataOrSuffStat<'_, f64, Gaussian>) -> Self

Computes the posterior distribution from the data

fn ln_m_cache(&self) -> Self::LnMCache

Compute the cache for the log marginal likelihood.

fn ln_m_with_cache(
    &self,
    cache: &Self::LnMCache,
    x: &DataOrSuffStat<'_, f64, Gaussian>
) -> f64

Log marginal likelihood with supplied cache.

fn ln_pp_cache(&self, x: &DataOrSuffStat<'_, f64, Gaussian>) -> Self::LnPpCache

Compute the cache for the Log posterior predictive of y given x.

fn ln_pp_with_cache(&self, cache: &Self::LnPpCache, y: &f64) -> f64

Log posterior predictive of y given x with supplied ln(norm)

fn ln_m(&self, x: &DataOrSuffStat<'_, X, Fx>) -> f64

The log marginal likelihood

fn ln_pp(&self, y: &X, x: &DataOrSuffStat<'_, X, Fx>) -> f64

Log posterior predictive of y given x

fn m(&self, x: &DataOrSuffStat<'_, X, Fx>) -> f64

Marginal likelihood of x

fn pp(&self, y: &X, x: &DataOrSuffStat<'_, X, Fx>) -> f64

Posterior Predictive distribution

impl ConjugatePrior<f64, Gaussian> for NormalInvChiSquared

type Posterior = Self

Type of the posterior distribution

type LnMCache = f64

Type of the ln_m cache

type LnPpCache = (GaussianSuffStat, f64)

Type of the ln_pp cache

fn posterior(&self, x: &DataOrSuffStat<'_, f64, Gaussian>) -> Self

Computes the posterior distribution from the data

fn ln_m_cache(&self) -> Self::LnMCache

Compute the cache for the log marginal likelihood.

fn ln_m_with_cache(
    &self,
    cache: &Self::LnMCache,
    x: &DataOrSuffStat<'_, f64, Gaussian>
) -> f64

Log marginal likelihood with supplied cache.

fn ln_pp_cache(&self, x: &DataOrSuffStat<'_, f64, Gaussian>) -> Self::LnPpCache

Compute the cache for the Log posterior predictive of y given x.

fn ln_pp_with_cache(&self, cache: &Self::LnPpCache, y: &f64) -> f64

Log posterior predictive of y given x with supplied ln(norm)

fn ln_m(&self, x: &DataOrSuffStat<'_, X, Fx>) -> f64

The log marginal likelihood

fn ln_pp(&self, y: &X, x: &DataOrSuffStat<'_, X, Fx>) -> f64

Log posterior predictive of y given x

fn m(&self, x: &DataOrSuffStat<'_, X, Fx>) -> f64

Marginal likelihood of x

fn pp(&self, y: &X, x: &DataOrSuffStat<'_, X, Fx>) -> f64

Posterior Predictive distribution

impl ConjugatePrior<f64, Gaussian> for NormalInvGamma

type Posterior = Self

Type of the posterior distribution

type LnMCache = f64

Type of the ln_m cache

type LnPpCache = (GaussianSuffStat, f64)

Type of the ln_pp cache

fn posterior(&self, x: &DataOrSuffStat<'_, f64, Gaussian>) -> Self

Computes the posterior distribution from the data

fn ln_m_cache(&self) -> Self::LnMCache

Compute the cache for the log marginal likelihood.

fn ln_m_with_cache(
    &self,
    cache: &Self::LnMCache,
    x: &DataOrSuffStat<'_, f64, Gaussian>
) -> f64

Log marginal likelihood with supplied cache.

fn ln_pp_cache(&self, x: &DataOrSuffStat<'_, f64, Gaussian>) -> Self::LnPpCache

Compute the cache for the Log posterior predictive of y given x.

fn ln_pp_with_cache(&self, cache: &Self::LnPpCache, y: &f64) -> f64

Log posterior predictive of y given x with supplied ln(norm)

fn ln_m(&self, x: &DataOrSuffStat<'_, X, Fx>) -> f64

The log marginal likelihood

fn ln_pp(&self, y: &X, x: &DataOrSuffStat<'_, X, Fx>) -> f64

Log posterior predictive of y given x

fn m(&self, x: &DataOrSuffStat<'_, X, Fx>) -> f64

Marginal likelihood of x

fn pp(&self, y: &X, x: &DataOrSuffStat<'_, X, Fx>) -> f64

Posterior Predictive distribution

impl ContinuousDistr<Gaussian> for NormalGamma

fn pdf(&self, x: &X) -> f64

The value of the Probability Density Function (PDF) at x

fn ln_pdf(&self, x: &X) -> f64

The value of the log Probability Density Function (PDF) at x

impl ContinuousDistr<f32> for Gaussian

fn pdf(&self, x: &X) -> f64

The value of the Probability Density Function (PDF) at x

fn ln_pdf(&self, x: &X) -> f64

The value of the log Probability Density Function (PDF) at x

impl ContinuousDistr<f64> for Gaussian

fn pdf(&self, x: &X) -> f64

The value of the Probability Density Function (PDF) at x

fn ln_pdf(&self, x: &X) -> f64

The value of the log Probability Density Function (PDF) at x

impl Debug for Gaussian

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

Formats the value using the given formatter.

impl Default for Gaussian

fn default() -> Self

Returns the “default value” for a type.

impl Display for Gaussian

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

Formats the value using the given formatter.

impl Entropy for Gaussian

fn entropy(&self) -> f64

The entropy, H(X)

impl GewekeTestable<Gaussian, f64> for NormalGamma

fn prior_draw<R: Rng>(&self, rng: &mut R) -> Gaussian

fn update_params<R: Rng>(&self, data: &Vec<f64>, rng: &mut R) -> Gaussian

fn geweke_stats(&self, fx: &Gaussian, xs: &Vec<f64>) -> BTreeMap<String, f64>

impl GewekeTestable<Gaussian, f64> for NormalInvChiSquared

fn prior_draw<R: Rng>(&self, rng: &mut R) -> Gaussian

fn update_params<R: Rng>(&self, data: &Vec<f64>, rng: &mut R) -> Gaussian

fn geweke_stats(&self, fx: &Gaussian, xs: &Vec<f64>) -> BTreeMap<String, f64>

impl GewekeTestable<Gaussian, f64> for NormalInvGamma

fn prior_draw<R: Rng>(&self, rng: &mut R) -> Gaussian

fn update_params<R: Rng>(&self, data: &Vec<f64>, rng: &mut R) -> Gaussian

fn geweke_stats(&self, fx: &Gaussian, xs: &Vec<f64>) -> BTreeMap<String, f64>

impl HasSuffStat<f32> for Gaussian

type Stat = GaussianSuffStat

fn empty_suffstat(&self) -> Self::Stat

impl HasSuffStat<f64> for Gaussian

type Stat = GaussianSuffStat

fn empty_suffstat(&self) -> Self::Stat

impl InverseCdf<f32> for Gaussian

fn invcdf(&self, p: f64) -> f32

The value of the x at the given probability in the CDF

fn quantile(&self, p: f64) -> X

Alias for invcdf

fn interval(&self, p: f64) -> (X, X)

Interval containing p proportion for the probability

impl InverseCdf<f64> for Gaussian

fn invcdf(&self, p: f64) -> f64

The value of the x at the given probability in the CDF

fn quantile(&self, p: f64) -> X

Alias for invcdf

fn interval(&self, p: f64) -> (X, X)

Interval containing p proportion for the probability

impl KlDivergence for Gaussian

fn kl(&self, other: &Self) -> f64

The KL divergence, KL(P|Q) between this distribution, P, and another, Q

fn kl_sym(&self, other: &Self) -> f64

Symmetrised divergence, KL(P|Q) + KL(Q|P)

impl Kurtosis for Gaussian

fn kurtosis(&self) -> Option<f64>

impl Mean<f32> for Gaussian

fn mean(&self) -> Option<f32>

Returns None if the mean is undefined

impl Mean<f64> for Gaussian

fn mean(&self) -> Option<f64>

Returns None if the mean is undefined

impl Median<f32> for Gaussian

fn median(&self) -> Option<f32>

Returns None if the median is undefined

impl Median<f64> for Gaussian

fn median(&self) -> Option<f64>

Returns None if the median is undefined

impl Mode<f32> for Gaussian

fn mode(&self) -> Option<f32>

Returns None if the mode is undefined or is not a single value

impl Mode<f64> for Gaussian

fn mode(&self) -> Option<f64>

Returns None if the mode is undefined or is not a single value

impl PartialEq<Gaussian> for Gaussian

fn eq(&self, other: &Gaussian) -> bool

This method tests for self and other values to be equal, and is used by ==.

#[must_use]

pub fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl QuadBounds for Gaussian

fn quad_bounds(&self) -> (f64, f64)

impl Rv<Gaussian> for NormalGamma

fn ln_f(&self, x: &Gaussian) -> f64

Probability function

fn draw<R: Rng>(&self, rng: &mut R) -> Gaussian

Single draw from the Rv

fn f(&self, x: &X) -> f64

Probability function

fn sample<R: Rng>(&self, n: usize, rng: &mut R) -> Vec<X>

Multiple draws of the Rv

fn sample_stream<'r, R: Rng>(
    &'r self,
    rng: &'r mut R
) -> Box<dyn Iterator<Item = X> + 'r>

Create a never-ending iterator of samples

impl Rv<Gaussian> for NormalInvChiSquared

fn ln_f(&self, x: &Gaussian) -> f64

Probability function

fn draw<R: Rng>(&self, rng: &mut R) -> Gaussian

Single draw from the Rv

fn f(&self, x: &X) -> f64

Probability function

fn sample<R: Rng>(&self, n: usize, rng: &mut R) -> Vec<X>

Multiple draws of the Rv

fn sample_stream<'r, R: Rng>(
    &'r self,
    rng: &'r mut R
) -> Box<dyn Iterator<Item = X> + 'r>

Create a never-ending iterator of samples

impl Rv<Gaussian> for NormalInvGamma

fn ln_f(&self, x: &Gaussian) -> f64

Probability function

fn draw<R: Rng>(&self, rng: &mut R) -> Gaussian

Single draw from the Rv

fn f(&self, x: &X) -> f64

Probability function

fn sample<R: Rng>(&self, n: usize, rng: &mut R) -> Vec<X>

Multiple draws of the Rv

fn sample_stream<'r, R: Rng>(
    &'r self,
    rng: &'r mut R
) -> Box<dyn Iterator<Item = X> + 'r>

Create a never-ending iterator of samples

impl Rv<f32> for Gaussian

fn ln_f(&self, x: &f32) -> f64

Probability function

fn draw<R: Rng>(&self, rng: &mut R) -> f32

Single draw from the Rv

fn sample<R: Rng>(&self, n: usize, rng: &mut R) -> Vec<f32>

Multiple draws of the Rv

fn f(&self, x: &X) -> f64

Probability function

fn sample_stream<'r, R: Rng>(
    &'r self,
    rng: &'r mut R
) -> Box<dyn Iterator<Item = X> + 'r>

Create a never-ending iterator of samples

impl Rv<f64> for Gaussian

fn ln_f(&self, x: &f64) -> f64

Probability function

fn draw<R: Rng>(&self, rng: &mut R) -> f64

Single draw from the Rv

fn sample<R: Rng>(&self, n: usize, rng: &mut R) -> Vec<f64>

Multiple draws of the Rv

fn f(&self, x: &X) -> f64

Probability function

fn sample_stream<'r, R: Rng>(
    &'r self,
    rng: &'r mut R
) -> Box<dyn Iterator<Item = X> + 'r>

Create a never-ending iterator of samples

impl Skewness for Gaussian

fn skewness(&self) -> Option<f64>

impl Support<Gaussian> for NormalGamma

fn supports(&self, x: &Gaussian) -> bool

Returns true if x is in the support of the Rv

impl Support<f32> for Gaussian

fn supports(&self, x: &f32) -> bool

Returns true if x is in the support of the Rv

impl Support<f64> for Gaussian

fn supports(&self, x: &f64) -> bool

Returns true if x is in the support of the Rv

impl Variance<f64> for Gaussian

fn variance(&self) -> Option<f64>

Returns None if the variance is undefined