getConditionallyIndependentSets {nimble}

Get a list of conditionally independent sets of nodes in a nimble model

Description

A conditionally independent set of nodes is such that the joint probability (density) of nodes in the set will not change even if any non-given node outside the set is changed. Default given nodes are data nodes and parameter nodes (aka "top-level" nodes, i.e. nodes with no parent nodes), but this can be controlled.

Usage

getConditionallyIndependentSets(
  model,
  nodes,
  givenNodes,
  omit = integer(),
  explore = c("both", "down", "up"),
  unknownAsGiven = TRUE,
  returnType = "names",
  returnScalarComponents = FALSE,
  endAsGiven = FALSE
)

Arguments

model

A nimble model object (uncompiled or compiled), such as returned by nimbleModel.

nodes

A vector of stochastic node names (or their graph IDs) to split into conditionally independent sets, conditioned on the givenNodes. If unknownAsGiven=FALSE, the nodes are the starting nodes from which conditionally independent sets of nodes should be found, possibly including additional nodes not included in the nodes argument. If nodes is omitted, the default will be all latent nodes (defined as stochastic nodes that are not data and have at least one stochastic parent node, possibly with determinstic nodes in-between) that are a parent of a givenNode (either provided or default). Note that this will omit latent states that have no hyperparameters. An example is the first latent state in some state-space (time-series) models, which is sometimes declared with known prior.

givenNodes

A vector of node names or their graph IDs that should be considered as fixed (given) and hence can be conditioned on. If omitted, the default will be all data nodes and all parameter nodes, the latter defined as nodes with no stochastic parent nodes (skipping over deterministic parent nodes). See endAsGiven for a variant on defaults.

omit

A vector of node names or their graph IDs that should be omitted and should block further graph exploration.

explore

The method of graph exploration, which may corresond to what the nodes argument represents. For "down", graph exploration starts only down (towards descendants) from nodes. For "up", graph exploration starts only up (towards ancestors) from nodes. For "both" (the default and normal setting), both directions are explored.

unknownAsGiven

Logical for whether a model node not in nodes or givenNodes should be treated as given (default = TRUE). Otherwise (and by default) such a node may be grouped into a conditionally independent set, resulting in more output nodes than input nodes.

returnType

Either "names" for returned nodes to be node names or "ids" for returned nodes to be graph IDs.

returnScalarComponents

If FALSE (default), multivariate nodes are returned as full names (e.g. x[1:3]). If TRUE, they are returned as scalar elements (e.g. x[1], x[2], x[3]).

endAsGiven

If TRUE, end nodes (defined as nodes with stochastic parents but no stochastic children, skipping through deterministic nodes) are included in the default for givenNodes.

Details

This function returns sets of conditionally independent nodes. Multiple input nodes might be in the same set or different sets.

The nodes input and the returned sets include only stochastic nodes because conditional independence is a property of random variables. Deterministic nodes are considered in determining the sets. givenNodes may contain stochastic or deterministic nodes.

Value

List of nodes that are in conditionally independent sets. With each set, nodes are returned in topologically sorted order. The sets themselves are returned in topologically sorted order of their first nodes.

Other nodes (not in nodes) may be included in the output if unknownAsGiven=FALSE.

Author(s)

Perry de Valpine