Distributions

A distribution must be sampleable and must be associated to a density w.r.t. some base measure (which is kept implicit).

type 'a dist = private {
  1. sample : RNG.t -> 'a;
  2. ll : 'a -> Log_space.t;
}

'a dist is the type of distributions on the type 'a.

type 'a kernel = private {
  1. start : 'a;
  2. sample : 'a -> RNG.t -> 'a;
  3. ll : 'a -> 'a -> Log_space.t;
}

'a kernel is the type of kernels (ie random walks) on the type 'a.

type 'a t = private
  1. | Stateless of 'a dist
  2. | Kernel of 'a kernel

A "distribution" as understood by this library is either a kernel or a plain distribution.

val stateless : (RNG.t -> 'a) -> ('a -> Log_space.t) -> 'a t

Create a distribution from a sampler and a log-density.

val kernel : 'a -> ('a -> RNG.t -> 'a) -> ('a -> 'a -> Log_space.t) -> 'a t

Create a kernel from an initial point, a kernel and its associated log-density.

Helpers for parameterized distributions and kernels.

val dist0 : (RNG.t -> 'a) -> ('a -> Log_space.t) -> 'a t
val dist1 : ('a -> RNG.t -> 'b) -> ('a -> 'b -> Log_space.t) -> 'a -> 'b t
val dist2 : ('a -> 'b -> RNG.t -> 'c) -> ('a -> 'b -> 'c -> Log_space.t) -> 'a -> 'b -> 'c t
val kernel1 : ('a -> 'b -> RNG.t -> 'b) -> ('a -> 'b -> 'b -> Log_space.t) -> 'b -> 'a -> 'b t

Combinators on distributions and kernels.

val iid : int -> 'a t -> 'a array t

iid n dist constructs the n-fold iid distribution where each component is distributed according to dist.

val conv : ('a -> 'b) -> ('b -> 'a) -> 'a t -> 'b t

conv f g dist transports a distribution along a pair of maps f,g. f,g must both be total. They need not be bijections, though not respecting this additional constraint might cause unspecified behaviours for some inference algorithms..