Function etienne()
is just Etienne's formula 6:
$$P[D|\theta,m,J]=
\frac{J!}{\prod_{i=1}^Sn_i\prod_{j=1}^J{\Phi_j}!}
\frac{\theta^S}{(\theta)_J}\times
\sum_{A=S}^J\left(K(D,A)
\frac{(\theta)_J}{(\theta)_A}
\frac{I^A}{(I)_J}
\right)$$where $K(D,A)$ is given by function logkda
(qv). It might be
useful to know the (trivial) identity for the Pochhammer symbol
documented in theta.prob.Rd
. For convenience, Etienne's
Function optimal.params()
uses optim()
to return the
maximum likelihood estimate for theta and m.
Compare function optimal.theta()
, which is restricted to no
dispersal limitation, ie $m=1$.
Argument log.kda
is optional: this is the $K(D,A)$ as defined
in equation A11 of Etienne 2005; it is computationally expensive to
calculate. If it is supplied,. the functions documented here will not
have to calculate it from scratch: this saves a considerable amount of
time.