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Module Norn.Weighted

Weighted draws.

Weighted draws of a structure 'u are a value of 'u whose every tensor has one leading axis of n draws, and a log weight per draw. The weights need not be normalised, and a draw of log weight -inf has none. Importance sampling, sequential Monte Carlo and nested sampling return them.

#type ('u, 'f, 'd) t = {

#values : 'u;
(*
The draws, on a leading axis of n.
*)
#log_weights : (float, 'f, 'd) Nx.t;
(*
Their log weights, shape [n].
*)

}

The type for weighted draws of 'u.

#val ptree : ('u, 'd) Nx.Ptree.t -> (('u, 'f, 'd) t, 'd) Nx.Ptree.t

ptree u is the structure of weighted draws of u: values, walked as u, and log_weights.

#val ess : ('u, 'f, 'd) t -> (float, 'f, 'd) Nx.t

ess w is Kish's effective sample size (Σ w)² / Σ w², a scalar from 1 to n. It is NaN if no weight is positive.

val resample : 
  ('u, 'd) Nx.Ptree.t ->
  'd Nx.Rng.key ->
  n:int ->
  ('u, 'f, 'd) t ->
  'u

resample u k ~n w is n equal-weight draws of w, by systematic resampling: one uniform v places the points (i + v) / n on the cumulative normalised weights, so a draw of normalised weight w_i is copied floor (n w_i) or ceil (n w_i) times.

Raises Invalid_argument if n < 1.