delay_multinomial_lpmf.stan File Reference

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Functions
real	delay_multinomial_lpmf (array[] int obs, vector log_exp_obs)
real	delay_multinomial_snaps (int start, int end, array[] int obs, vector log_exp_obs, int exp_offset, array[] int total, array[] int obs_lookup, array[] int lsl, array[] int clsl, array[] int nsl, array[] int cnsl)

Function Documentation

delay_multinomial_lpmf()

real delay_multinomial_lpmf	(	array[]int	obs,
		vector	log_exp_obs )

(Truncated) multinomial delay-only likelihood for one snapshot

Conditional log probability of a reference date's observed delay cells given their total. Renormalising the delay intensities over the observed cells gives the plain multinomial when the row is complete and the truncated multinomial when only early delays are observed. The shared log(total) offset cancels, so the total enters only through the cells.

Parameters

obs	Observed cell counts (one per observed delay).
log_exp_obs	Log expected cells, log(total) + log(p_d).

Returns

Log probability mass under the (truncated) multinomial.

Definition at line 14 of file delay_multinomial_lpmf.stan.

delay_multinomial_snaps()

real delay_multinomial_snaps	(	int	start,
		int	end,
		array[]int	obs,
		vector	log_exp_obs,
		int	exp_offset,
		array[]int	total,
		array[]int	obs_lookup,
		array[]int	lsl,
		array[]int	clsl,
		array[]int	nsl,
		array[]int	cnsl )

Delay-only multinomial likelihood over a range of snapshots

Sums a (truncated) multinomial over each snapshot, conditioning on the known total. The delay probabilities are renormalised over every slot up to the observation cutoff (lsl), so interior cells that are unobserved but before the cutoff keep their weight; only right-truncated slots beyond the cutoff are excluded. With an observation indicator the unobserved before-cutoff cells are marginalised into a single residual category whose count is the known total minus the observed counts, leaving the observed cells plus that residual as the multinomial categories.

Parameters

start	First snapshot in the range.
end	Last snapshot in the range.
obs	Flat observed cell counts.
log_exp_obs	Gap-filled log expected cells over the cutoff range.
exp_offset	Flat index of the first cutoff cell of the range.
total	Known integer total by snapshot (the cutoff running total).
obs_lookup	Maps each observed cell to its cutoff-block position.
lsl	Cutoff slots per snapshot (max consecutive observed + 1).
clsl	Cumulative lsl.
nsl	Observed cells per snapshot.
cnsl	Cumulative nsl.

Returns

Summed log probability mass over the snapshots.

Definition at line 44 of file delay_multinomial_lpmf.stan.