Implement the algorithm from aghq::marginal_laplace(), but making use of
TMB's automatic Laplace approximation. This function takes a function
list from TMB::MakeADFun() with a non-empty set of random parameters,
in which the fn and gr are the unnormalized marginal Laplace
approximation and its gradient. It then calls aghq::aghq() and formats
the resulting object so that its contents and class match the output of
aghq::marginal_laplace() and are hence suitable for post-processing
with summary, aghq::sample_marginal(), and so on.
marginal_laplace_tmb(
ff,
k,
startingvalue,
transformation = default_transformation(),
optresults = NULL,
basegrid = NULL,
control = default_control_tmb(),
...
)If k > 1, an object of class marginallaplace
(and inheriting from class aghq) of the same
structure as that returned by aghq::marginal_laplace(), with plot
and summary methods, and suitable for input into aghq::sample_marginal()
for drawing posterior samples.
The output of calling TMB::MakeADFun() with random set
to a non-empty subset of the parameters. VERY IMPORTANT: TMB's
automatic Laplace approximation requires you to write your template implementing
the negated log-posterior. Therefore, this list that you input here
will contain components fn, gr and he that implement the
negated log-posterior and its derivatives. This is opposite
to every other comparable function in the aghq package, and is done
here to emphasize compatibility with TMB.
Integer, the number of quadrature points to use. I suggest at least 3. k = 1 corresponds to a Laplace approximation.
Value to start the optimization. ff$fn(startingvalue),
ff$gr(startingvalue), and ff$he(startingvalue) must all return
appropriate values without error.
Optional. Do the quadrature for parameter theta, but
return summaries and plots for parameter g(theta). This applies to the theta
parameters only, not the W parameters.
transformation is either: a) an aghqtrans object returned by aghq::make_transformation,
or b) a list that will be passed to that function internally. See ?aghq::make_transformation for details.
Optional. A list of the results of the optimization of the log
posterior, formatted according to the output of aghq::optimize_theta. The
aghq::aghq function handles the optimization for you; passing this list
overrides this, and is useful for when you know your optimization is too difficult to be
handled by general-purpose software. See the software paper for several examples of this.
If you're unsure whether this option is needed for your problem then it probably is not.
Optional. Provide an object of class NIGrid from the mvQuad
package, representing the base quadrature rule that will be adapted. This is only
for users who want more complete control over the quadrature, and is not necessary
if you are fine with the default option which basically corresponds to
mvQuad::createNIGrid(length(theta),'GHe',k,'product'). Note: the mvQuad
functions used within aghq operate on grids in memory, so your basegrid
object will be changed after you run aghq.
A list of control parameters. See ?default_control for details. Valid options are:
method: optimization method to use for the theta optimization:
'sparse_trust' (default): trustOptim::trust.optim
'sparse': trust::trust
'BFGS': optim(...,method = "BFGS")
inner_method: optimization method to use for the W optimization; same
options as for method. Default inner_method is 'sparse_trust' and default method is 'BFGS'.
negate: default TRUE. See ?default_control_tmb. Assumes that your TMB function
template computes the negated log-posterior, which it must if you're using TMB's automatic
Laplace approximation, which you must be if you're using this function!
.
Additional arguments to be passed to ff$fn, ff$gr, and ff$he.
Because TMB does not yet have the Hessian of the log marginal Laplace
approximation implemented, a numerically-differentiated jacobian of the gradient
is used via numDeriv::jacobian(). You can turn this off (using ff$he() instead,
which you'll have to modify yourself) using default_control_tmb(numhessian = FALSE).
Other quadrature:
aghq(),
get_hessian(),
get_log_normconst(),
get_mode(),
get_nodesandweights(),
get_numquadpoints(),
get_opt_results(),
get_param_dim(),
laplace_approximation(),
marginal_laplace(),
nested_quadrature(),
normalize_logpost(),
optimize_theta(),
plot.aghq(),
print.aghqsummary(),
print.aghq(),
print.laplacesummary(),
print.laplace(),
print.marginallaplacesummary(),
summary.aghq(),
summary.laplace(),
summary.marginallaplace()