setupMargNodes: Organize model nodes for marginalization
In nimble: MCMC, Particle Filtering, and Programmable Hierarchical Modeling

setupMargNodes

R Documentation

Organize model nodes for marginalization

Description

Process model to organize nodes for marginalization (integration over latent nodes or random effects) as by Laplace approximation.

Usage

setupMargNodes(
  model,
  paramNodes,
  randomEffectsNodes,
  calcNodes,
  calcNodesOther,
  split = TRUE,
  check = TRUE
)

Arguments

`model`	A nimble model such as returned by `nimbleModel`.
`paramNodes`	A character vector of names of stochastic nodes that are parameters of nodes to be marginalized over (`randomEffectsNodes`). See details for default.
`randomEffectsNodes`	A character vector of nodes to be marginalized over (or "integrated out"). In the case of calculating the likelihood of a model with continuous random effects, the nodes to be marginalized over are the random effects, hence the name of this argument. However, one can marginalize over any nodes desired as long as they are continuous. See details for default.
`calcNodes`	A character vector of nodes to be calculated as the integrand for marginalization. Typically this will include `randomEffectsNodes` and some data nodes. Se details for default.
`calcNodesOther`	A character vector of nodes to be calculated as part of the log likelihood that are not connected to the `randomEffectNodes` and so are not actually part of the marginalization. These are somewhat extraneous to the purpose of this function, but it is convenient to handle them here because often the purpose of marginalization is to calculate log likelihoods, including from "other" parts of the model.
`split`	A logical indicating whether to split `randomEffectsNodes` into conditionally independent sets that can be marginalized separately (`TRUE`) or to keep them all in one set for a single marginalization calculation.
`check`	A logical indicating whether to try to give reasonable warnings of badly formed inputs that might be missing important nodes or include unnecessary nodes.

Details

This function is used by buildLaplace to organize model nodes into roles needed for setting up the (approximate) marginalization done by Laplace approximation. It is also possible to call this function directly and pass the resulting list (possibly modified for your needs) to buildLaplace.

Any of the input node vectors, when provided, will be processed using nodes <- model$expandNodeNames(nodes), where nodes may be paramNodes, randomEffectsNodes, and so on. This step allows any of the inputs to include node-name-like syntax that might contain multiple nodes. For example, paramNodes = 'beta[1:10]' can be provided if there are actually 10 scalar parameters, 'beta[1]' through 'beta[10]'. The actual node names in the model will be determined by the exapndNodeNames step.

This function does not do any of the marginalization calculations. It only organizes nodes into roles of parameters, random effects, integrand calculations, and other log likelihood calculations.

The checking done if ‘check=TRUE' tries to be reasonable, but it can’t cover all cases perfectly. If it gives an unnecessary warning, simply set 'check=FALSE'.

If paramNodes is not provided, its default depends on what other arguments were provided. If neither randomEffectsNodes nor calcNodes were provided, paramNodes defaults to all top-level, stochastic nodes, excluding any posterior predictive nodes (those with no data anywhere downstream). These are determined by model$getNodeNames(topOnly = TRUE, stochOnly = TRUE, includePredictive = FALSE). If randomEffectsNodes was provided, paramNodes defaults to stochastic parents of randomEffectsNodes. In these cases, any provided calcNodes or calcNodesOther are excluded from default paramNodes. If calcNodes but not randomEffectsNodes was provided, then the default for randomEffectsNodes is determined first, and then paramNodes defaults to stochastic parents of randomEffectsNodes. Finally, any stochastic parents of calcNodes (whether provided or default) that are not in calcNodes are added to the default for paramNodes, but only after paramNodes has been used to determine the defaults for randomEffectsNodes, if necessary.

Note that to obtain sensible defaults, some nodes must have been marked as data, either by the data argument in nimbleModel or by model$setData. Otherwise, all nodes will appear to be posterior predictive nodes, and the default paramNodes may be empty.

For purposes of buildLaplace, paramNodes does not need to (but may) include deterministic nodes between the parameters and any calcNodes. Such deterministic nodes will be included in calculations automatically when needed.

If randomEffectsNodes is missing, the default is a bit complicated: it includes all latent nodes that are descendants (or "downstream") of paramNodes (if provided) and are either (i) ancestors (or "upstream") of data nodes (if calcNodes is missing), or (ii) ancestors or elements of calcNodes (if calcNodes and paramNodes are provided), or (iii) elements of calcNodes (if calcNodes is provided but paramNodes is missing). In all cases, discrete nodes (with warning if check=TRUE), posterior predictive nodes and paramNodes are excluded.

randomEffectsNodes should only include stochastic nodes.

If calcNodes is missing, the default is randomEffectsNodes and their descendants to the next stochastic nodes, excluding posterior predictive nodes. These are determined by model$getDependencies(randomEffectsNodes, includePredictive=FALSE).

If calcNodesOther is missing, the default is all stochastic descendants of paramNodes, excluding posterior predictive nodes (from model$getDependencies(paramNodes, stochOnly=TRUE, self=FALSE, includePosterior=FALSE)) that are not part of calcNodes.

For purposes of buildLaplace, neither calcNodes nor calcNodesOther needs to (but may) contain deterministic nodes between paramNodes and calcNodes or calcNodesOther, respectively. These will be included in calculations automatically when needed.

If split is TRUE, model$getConditionallyIndependentSets is used to determine sets of the randomEffectsNodes that can be independently marginalized. The givenNodes are the paramNodes and calcNodes excluding any randomEffectsNodes and their deterministic descendants. The nodes (to be split into sets) are the randomEffectsNodes.

If split is a numeric vector, randomEffectsNodes will be split by split(randomEffectsNodes, control$split). The last option allows arbitrary control over how randomEffectsNodes are blocked.

If check=TRUE, then defaults for each of the four categories of nodes are created even if the corresponding argument was provided. Then warnings are emitted if there are any extra (potentially unnecessary) nodes provided compared to the default or if there are any nodes in the default that were not provided (potentially necessary). These checks are not perfect and may be simply turned off if you are confident in your inputs.

(If randomEffectsNodes was provided but calcNodes was not provided, the default (for purposes of check=TRUE only) for randomEffectsNodes differs from the above description. It uses stochastic descendants of randomEffectsNodes in place of the "data nodes" when determining ancestors of data nodes. And it uses item (ii) instead of (iii) in the list above.)

Value

A list is returned with elements:

paramNodes: final processed version of paramNodes
randomEffectsNodes: final processed version of randomEffectsNodes
calcNodes: final processed version of calcNodes
calcNodesOther: final processed version of calcNodesOther
givenNodes: Input to model$getConditionallyIndependentSets, if split=TRUE.
randomEffectsSets: Output from model$getConditionallyIndependentSets, if split=TRUE. This will be a list of vectors of node names. The node names in one list element can be marginalized independently from those in other list elements. The union of the list elements should be all of randomEffectsNodes. If split=FALSE, randomEffectsSets will be a list with one element, simply containing randomEffectsNodes. If split is a numeric vector, randomEffectsSets will be the result of split(randomEffectsNodes, control$split).