This document describes the process by which
ergm and related packages selects the MCMC proposal for a particular analysis. Note that it is not intended to be a tutorial as much as a description of what inputs and outputs different parts of the system expect. Nor does it cover the C API.
There is a number of factors that can affect MCMC sampling, some of them historical and some of them new:
: functions and other structures defined in an accessible namespace
* `ergm_proposal_table()` a function that if called with no arguments returns a table of registered proposals and updates it otherwise. See `? ergm_proposal_table` for documentation and the meaning of its columns. Of particular interest is its `Constraints` column, which encodes which constraints the proposal **does** (always) enforce and which it **can** enforce. * `InitErgmReference.<REFERENCE>` a family of initializers for the reference distribution. For the purposes of the proposal selection, among its outputs should be `$name` specifying the name of the reference distribution. * `InitErgmConstraint.<CONSTRAINT>` a family of initializers for constraints, weightings, and other high-level specifiers of the proposal distribution. Hard constraints, probabilistic weights, and hints all use this API. For the purposes of the proposal selection, its outputs include * `$constrain` (defaulting to `<CONSTRAINT>`) a character vector specifying which constraints are enforced, and can include several semantically nested elements; * `$dependence` (defaulting to `TRUE`) specifying whether the constraint is dyad-dependent; * `$priority` (defaulting to `Inf`) specifying how important it is that the constraint is met (with `Inf` meaning that it *must* be met); and * `$implies`/`$impliedby` specifying which other constraints this constraint enforces or is enforced by, and this can include itself for constraints, such as `edges` that can only be applied once.
: arguments and settings passed to the call or as control parameters.
* constraints= argument (top-level): A one-sided formula containing a +- or --separated list of constraints. + terms add additional constraints to the model whereas - constraints relax them. - constraints are primarily used internally observational process estimation and are not described in detail, except to note that 1) they must be dyad-independent and 2) they necessitate falling back to the RLEBDM sampling API. * reference= argument (top-level): A one-sided formula specifying the ERGM reference distribution, usually as a name with parameters if appropriate. * control$MCMC.prop= control parameter: A formula whose RHS containing +-separated "hints" to the sampler; an optional LHS may contain the proposal name directly. * control$MCMC.prop.weights= control parameter: A string selecting proposal weighting (probably deprecated) * control$MCMC.prop.args= control parameter: A list specifying information to be passed to the proposal
Most of this is implemented in the
InitErgmReference.<REFERENCE>is called with arguments of
reference='s LHS, obtaining the name of the reference.
InitErgmConstraint.<CONSTRAINT>function is called and their outputs are stored in a list of initialized constraints (an
.dyadspseudo-constraint is added to dyad-independent constraints (not to hints with
$priority < Inf).
ergm_proposal_table()are filtered by
Proposal(if the LHS of
priority=Inf, it is discarded.
priority<Infand that the proposal doesn't and can't enforce, its (innate, specified in the column of the
Priorityvalue is penalised by the
priorityof that constraint.
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