comp_sim.hpp File Reference

Random draws for composition-style observations, used by SIMULATE. More...

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Functions
template<class Type>
vector< Type >	rmultinom_rce (Type N, vector< Type > p)
	Draw multinomial counts by sequential conditional binomials.
template<class Type>
vector< Type >	rdirichlet_rce (vector< Type > alpha)
	Draw Dirichlet proportions as normalized independent gammas.
template<class Type>
vector< Type >	rdirmultinom_rce (Type N, vector< Type > alpha)
	Draw Dirichlet-multinomial counts.

Detailed Description

Random draws for composition-style observations, used by SIMULATE.

Every composition likelihood in the model – age/length comps, conditional age-at-length, and stomach contents – is a multinomial or a Dirichlet-multinomial over a vector of bins, and TMB supplies neither draw: distributions_R.hpp stops at univariate generators (rbinom, rgamma, runif, ...). These are the two multivariate draws built from them, both the standard constructions and exact given N and p, with N rounded to a whole count the only approximation either makes:

• A multinomial is drawn as a sequence of conditional binomials: having placed the first a bins, the count in bin a+1 is binomial in the observations still unplaced, with probability rescaled by the probability still unspent – one rbinom per bin. One categorical variate per observation instead (as WHAM's rmultinom does, src/age_comp_sim.hpp) is equally valid but costs one uniform per observation, which stomach sample sizes make expensive.
• A Dirichlet-multinomial is a multinomial whose probabilities are a Dirichlet draw, itself a vector of independent gammas divided by its own sum.

Both return COUNTS summing to N, as the densities in helper_functions.hpp and comp_osa.hpp read them; the caller converts back to its data object's scale. They run only inside SIMULATE{}, where Type is always double and there is no AD tape, so CppAD::Integer() and the R generators underneath are safe.

Definition in file comp_sim.hpp.

Function Documentation

rdirichlet_rce()

template<class Type>

vector< Type > rdirichlet_rce

(

vector< Type >

alpha

)

Draw Dirichlet proportions as normalized independent gammas.

With a very small concentration every gamma can underflow to zero in double precision, leaving nothing to normalize; onset is around sum(alpha) below 1e-3. The limit of a Dirichlet as alpha -> 0 is degenerate – all the mass in ONE bin, chosen with probability proportional to alpha – so that is what is returned. A flat vector would be the opposite of the near-degenerate composition the parameters describe, turning a concentrated diet into a diffuse one.

Parameters

alpha

Concentration parameters, one per bin, non-negative.

Returns

Proportions summing to 1.

Definition at line 88 of file comp_sim.hpp.

Referenced by rdirmultinom_rce().

rdirmultinom_rce()

template<class Type>

vector< Type > rdirmultinom_rce	(	Type	N,
		vector< Type >	alpha )

Draw Dirichlet-multinomial counts.

Parameters

N	Number of observations to place.
alpha	Concentration parameters, one per bin; here predicted proportion * N * theta. The draw reproduces the MEAN the density predicts but not every moment of it: the density is evaluated on offset data while the draw is on the raw scale.

Returns

Counts, one per bin, summing to the rounded N.

Definition at line 128 of file comp_sim.hpp.

References rdirichlet_rce(), and rmultinom_rce().

rmultinom_rce()

template<class Type>

vector< Type > rmultinom_rce	(	Type	N,
		vector< Type >	p )

Draw multinomial counts by sequential conditional binomials.

Parameters

N	Number of observations to place. Rounded to a whole number, as the binomial size must be an integer; effective sample sizes reaching here are whole counts (stomachs sampled, fish aged) or a weighting of them.
p	Bin probabilities. Rescaled internally, so they need not sum to 1, but must be non-negative.

Returns

Counts, one per bin, summing to the rounded N.

Definition at line 41 of file comp_sim.hpp.

Referenced by rdirmultinom_rce().