API

logdensityof(object, x)::Real

Compute the logarithmic value of the density object (resp. its associated density) at a given point x.

julia> DensityKind(object)
IsDensity()

julia> logy = logdensityof(object, x); logy isa Real
true

See also DensityKind and densityof.

logdensityof(object)

Return a function that computes the logarithmic value of the density object (resp. its associated density) at a given point.

julia> log_f = logdensityof(object); log_f isa Function
true

julia> log_f(x) == logdensityof(object, x)
true

logdensityof(object) defaults to Base.Fix1(logdensityof, object), but may be specialized. If so, logfuncdensity will typically have to be specialized for the return type of logdensityof as well.

logfuncdensity is the inverse of logdensityof, so logfuncdensity(log_f) must be equivalent to object.

logfuncdensity(log_f)

Return a DensityInterface-compatible density that is defined by a given log-density function log_f:

julia> object = logfuncdensity(log_f);

julia> DensityKind(object)
IsDensity()

julia> logdensityof(object, x) == log_f(x)
true

logfuncdensity(log_f) returns an instance of DensityInterface.LogFuncDensity by default, but may be specialized to return something else depending on the type of log_f). If so, logdensityof will typically have to be specialized for the return type of logfuncdensity as well.

logfuncdensity is the inverse of logdensityof, so the following must hold true:

• d = logfuncdensity(logdensityof(object)) is equivalent to object in respect to logdensityof and densityof. However, d may not be equal to object, especially if DensityKind(object) == HasDensity(): logfuncdensity always creates something that is density, never something that just has a density in some way (like a distribution or a measure in general).
• logdensityof(logfuncdensity(log_f)) is equivalent (typically equal or even identical to) to log_f.

See also DensityKind.

funcdensity(f)

Return a DensityInterface-compatible density that is defined by a given non-log density function f:

julia> object = funcdensity(f);

julia> DensityKind(object)
IsDensity()

julia> densityof(object, x) == f(x)
true

funcdensity(f) returns an instance of DensityInterface.FuncDensity by default, but may be specialized to return something else depending on the type of f). If so, densityof will typically have to be specialized for the return type of funcdensity as well.

funcdensity is the inverse of densityof, so the following must hold true:

• d = funcdensity(densityof(object)) is equivalent to object in respect to logdensityof and densityof. However, d may not be equal to object, especially if DensityKind(object) == HasDensity(): funcdensity always creates something that is density, never something that just has a density in some way (like a distribution or a measure in general).
• densityof(funcdensity(f)) is equivalent (typically equal or even identical to) to f.

See also DensityKind.

densityof(object, x)::Real

Compute the value of the density object (resp. its associated density) at a given point x.

julia> DensityKind(object)
IsDensity()

julia> densityof(object, x) == exp(logdensityof(object, x))
true

densityof(object, x) defaults to exp(logdensityof(object, x)), but may be specialized.

See also DensityKind and densityof.

densityof(object)

Return a function that computes the value of the density object (resp. its associated density) at a given point.

julia> f = densityof(object);

julia> f(x) == densityof(object, x)
true

densityof(object) defaults to Base.Fix1(densityof, object), but may be specialized.

densityof(object)

Return a function that computes the value of the density object (resp. its associated density) at a given point.

julia> f = densityof(object);

julia> f(x) == densityof(object, x)
true

densityof(object) defaults to Base.Fix1(densityof, object), but may be specialized.

struct IsDensity <: DensityKind end

As a return value of DensityKind(object), indicates that object is (represents) a density, like a probability density object.

See DensityKind for details.

struct HasDensity <: DensityKind end

As a return value of DensityKind(object), indicates that object has a density, like a probability distribution has a probability density.

See DensityKind for details.

IsOrHasDensity = Union{IsDensity, HasDensity}

As a return value of DensityKind(object), indicates that object either is or has a density, as understood by DensityInterface.

See DensityKind for details.

struct NoDensity <: DensityKind end

As a return value of DensityKind(object), indicates that object is not and does not have a density, as understood by DensityInterface.

See DensityKind for details.

abstract type DensityKind end

DensityKind(object)

Subtypes of DensityKind indicate if an object is a density or if it has a density, in the sense of the DensityInterface API, or if is not associated with a density (not compatible with DensityInterface).

DensityKind(object) returns either IsDensity(), HasDensity() or NoDensity().

In addition to the subtypes IsDensity, HasDensity or NoDensity, a union IsOrHasDensity = Union{IsDensity, HasDensity} is defined for convenience.

DensityKind(object) isa IsOrHasDensity implies that object is either a density itself or can be said to have an associated density. It also implies that the value of that density at given points can be calculated via logdensityof and densityof.

DensityKind(object) defaults to NoDensity() (object is not and does not have a density). For a type that is (directly represents) a density, like a probability density, define

@inline DensityKind(::MyDensityType) = IsDensity()

For a type that has (is associated with) a density in some way, like a probability distribution has a probability density, define

@inline DensityKind(::MyDensityType) = HasDensity()

struct DensityInterface.LogFuncDensity{F}

Wraps a log-density function log_f to make it compatible with DensityInterface interface. Typically, LogFuncDensity(log_f) should not be called directly, logfuncdensity should be used instead.

struct DensityInterface.FuncDensity{F}

Wraps a non-log density function f to make it compatible with DensityInterface interface. Typically, FuncDensity(f) should not be called directly, funcdensity should be used instead.

DensityInterface.test_density_interface(object, x, ref_logd_at_x; kwargs...)

Test that object is compatible with DensityInterface.

Tests that either DensityKind(object) isa IsOrHasDensity.

Also tests that logdensityof(object, x) equals ref_logd_at_x and that the behavior of logdensityof(object), densityof(object, x) and densityof(object) is consistent.

The results of logdensityof(object, x) and densityof(object, x) are compared to ref_logd_at_x and exp(ref_logd_at_x) using isapprox. kwargs... are forwarded to isapprox.

Also tests that d = logfuncdensity(logdensityof(object)) returns a density (DensityKind(d) == IsDensity()) that is equivalent to object in respect to logdensityof and densityof, and that funcdensity(densityof(object)) behaves the same way.