Model¶
The Model
type is designed to store the set of all model nodes, including parameter set as denoted in the Mamba Gibbs sampling scheme. In particular, it stores Dependent
type objects in its nodes
dictionary field. Valid models are ones whose nodes form directed acyclic graphs (DAGs). Sampling functions are saved as Sampler
objects in the vector of field samplers
. Vector elements correspond to sampling blocks
Declaration¶
type Model
Fields¶
nodes::Dict{Symbol, Any}
: all input, logical, and stochastic model nodes.samplers::Vector{Sampler}
: sampling functions for updating blocks of stochastic nodes.states::Vector{ModelState}
: states of chains at the end of an MCMC run in a possible series of runs, whereModelState
has fieldsvalue::Vector{Float64}
andtune::Vector{Any}
to store the last values of sampled nodes and blocksampler tuning parameters, respectively.iter::Int
: current MCMC draw from the target distribution.burnin::Int
: number of initial draws to discard as a burnin sequence to allow for convergence.hasinputs::Bool
: whether values have been assigned to input nodes.hasinits::Bool
: whether initial values have been assigned to stochastic nodes.
Constructor¶

Model
(; iter::Integer=0, burnin::Integer=0, samplers::Vector{Sampler}=Sampler[], nodes...)¶ Construct a
Model
object that defines a model for MCMC simulation.Arguments
iter
: current iteration of the MCMC simulation.burnin
: number of initial draws to be discarded as a burnin sequence to allow for convergence.samplers
: blockspecific sampling functions.nodes...
: arbitrary number of userspecified arguments defining logical and stochastic nodes in the model. Argument values must beLogical
orStochastic
type objects. Their names in the model will be taken from the argument names.
Value
Returns aModel
type object.Example
See the Model Specification section of the tutorial.
MCMC Engine¶

mcmc
(m::Model, inputs::Dict{Symbol}, inits::Vector{Dict{Symbol, Any}}, iters::Integer; burnin::Integer=0, thin::Integer=1, chains::Integer=1, verbose::Bool=true)¶ 
mcmc
(mc::ModelChains, iters::Integer; verbose::Bool=true) Simulate MCMC draws for a specified model.
Arguments
m
: specified model.mc
: chains from a previous call tomcmc
for which to simulate additional draws.inputs
: values for input model nodes. Dictionary keys and values should be given for each input node.inits
: dictionaries that contain initial values for stochastic model nodes. Dictionary keys and values should be given for each stochastic node. Consecutive runs of the simulator will iterate through the vector’s dictionary elements.iters
: number of draws to generate for each simulation run.burnin
: numer of initial draws to discard as a burnin sequence to allow for convergence.thin
: stepsize between draws to output.chains
: number of simulation runs to perform.verbose
: whether to print sampler progress at the console.
Value
AModelChains
type object of simulated draws.Example
See the MCMC Simulation section of the tutorial.
Indexing¶

getindex
(m::Model, nodekey::Symbol)¶ Returns a model node identified by its symbol. The syntax
m[nodekey]
is converted togetindex(m, nodekey)
.Arguments
m
: model containing the node to get.nodekey
: node to get.
Value
The specified node.

keys
(m::Model)¶ 
keys
(m::Model, ntype::Symbol, at...) Extract the symbols (keys) for all existing nodes or for nodes of a specified type.
Arguments
m
: model containing the nodes of interest.ntype
: type of nodes to return. Options are:all
: all input, logical, and stochastic model nodes.:assigned
: nodes that have been assigned values.:block
: stochastic nodes being updated by the sampling block(s)at::Integer=0
(default: all blocks).:dependent
: logical and stochastic (dependent) nodes in topologically sorted order.:independent
or:input
: input (independent) nodes.:logical
: logical nodes.:monitor
: stochastic nodes being monitored in MCMC sampler output.:output
: stochastic nodes upon which no other stochastic nodes depend.:source
: nodes upon which the nodeat::Symbol
or vector of nodesat::Vector{Symbol}
depends.:stochastic
: stochastic nodes.:target
: topologically sorted nodes that depend on the sampling block(s)at::Integer=0
(default: all blocks), nodeat::Symbol
, or vector of nodesat::Vector{Symbol}
.
at...
: additional positional arguments to be passed to thentype
options, as described above.
Value
A vector of node symbols.
Display¶

draw
(m::Model; filename::AbstractString="")¶ Draw a GraphViz DOTformatted graph representation of model nodes and their relationships.
Arguments
m
: model for which to construct a graph.filename
: external file to which to save the resulting graph, or an empty string to draw to standard output (default). If a supplied external file name does not include a dot (.
), the file extension.dot
will be appended automatically.
Value
The model drawn to an external file or standard output. Stochastic, logical, and input nodes will be represented by ellipses, diamonds, and rectangles, respectively. Nodes that are unmonitored in MCMC simulations will be graycolored.Example
See the Directed Acyclic Graphs section of the tutorial.

graph
(m::Model)¶ Construct a graph representation of model nodes and their relationships.
Arguments
m
: model for which to construct a graph.
Value
Returns aGenericGraph
type object as defined in the Graphs package.

graph2dot
(m::Model)¶ Draw a GraphViz DOTformatted graph representation of model nodes and their relationships.
Arguments
m
: model for which to construct a graph.
Value
A character string representation of the graph suitable for inline processing. Stochastic, logical, and input nodes will be represented by ellipses, diamonds, and rectangles, respectively. Nodes that are unmonitored in MCMC simulations will be graycolored.Example
See the Directed Acyclic Graphs section of the tutorial.

show
(m::Model)¶ Write a text representation of the model, nodes, and attributes to the current output stream.

showall
(m::Model)¶ Write a verbose text representation of the model, nodes, and attributes to the current output stream.
Initialization¶

setinits!
(m::Model, inits::Dict{Symbol, Any})¶ Set the initial values of stochastic model nodes.
Arguments
m
: model with nodes to be initialized.inits
: initial values for stochastic model nodes. Dictionary keys and values should be given for each stochastic node.
Value
Returns the model with stochastic nodes initialized and theiter
field set equal to 0.Example
See the Development and Testing section of the tutorial.

setinputs!
(m::Model, inputs::Dict{Symbol, Any})¶ Set the values of input model nodes.
Arguments
m
: model with input nodes to be assigned.inputs
: values for input model nodes. Dictionary keys and values should be given for each input node.
Value
Returns the model with values assigned to input nodes.Example
See the Development and Testing section of the tutorial.

setsamplers!
(m::Model, samplers::Vector{T<:Sampler})¶ Set the blocksamplers for stochastic model nodes.
Arguments
m
: model with stochastic nodes to be sampled.samplers
: blockspecific samplers.
Values:
Returns the model updated with the blocksamplers.Example
See the Model Specification and MCMC Simulation sections of the tutorial.
Parameter Block Operations¶

gettune
(m::Model, block::Integer=0)¶ Get blocksampler tuning parameters.
Arguments
m
: model with blocksamplers.block
: block for which to get the tuning parameters (default: all blocks).
Value
AVector{Any}
of all blockspecific tuning parameters ifblock=0
, and turning parameters for the specified block otherwise.

gradlogpdf
(m::Model, block::Integer=0, transform::Bool=false; dtype::Symbol=:forward)¶ 
gradlogpdf
(m::Model, x::AbstractArray{T<:Real}, block::Integer=0, transform::Bool=false; dtype::Symbol=:forward) 
gradlogpdf!
(m::Model, x::AbstractArray{T<:Real}, block::Integer=0, transform::Bool=false; dtype::Symbol=:forward)¶ Compute the gradient of logdensities for stochastic nodes.
Arguments
m
: model containing the stochastic nodes for which to compute the gradient.block
: sampling block of stochastic nodes for which to compute the gradient (default: all stochastic nodes).x
: value (possibly different than the current one) at which to compute the gradient.transform
: whether to compute the gradient of block parameters on the link–transformed scale.dtype
: type of differentiation for gradient calculations. Options are:central
: central differencing.:forward
: forward differencing.
Value
The resulting gradient vector. Methodgradlogpdf!()
additionally updates modelm
with supplied valuesx
.Note
Numerical approximation of derivatives by central and forward differencing is performed with the Calculus package [93].

logpdf
(m::Model, block::Integer=0, transform::Bool=false)¶ 
logpdf
(m::Model, nodekeys::Vector{Symbol}, transform::Bool=false) 
logpdf
(m::Model, x::AbstractArray{T<:Real}, block::Integer=0, transform::Bool=false) 
logpdf!
(m::Model, x::AbstractArray{T<:Real}, block::Integer=0, transform::Bool=false)¶ Compute the sum of logdensities for stochastic nodes.
Arguments
m
: model containing the stochastic nodes for which to evaluate logdensities.block
: sampling block of stochastic nodes over which to sum densities (default: all stochastic nodes).nodekeys
: nodes over which to sum densities.x
: value (possibly different than the current one) at which to evaluate densities.transform
: whether to evaluate evaluate logdensities of block parameters on the link–transformed scale.
Value
The resulting numeric value of summed logdensities. Methodlogpdf!()
additionally updates modelm
with supplied valuesx
.

simulate!
(m::Model, block::Integer=0)¶ Simulate one MCMC draw from a specified model.
Argument:
m
: model specification.block
: block for which to simulate an MCMC draw (default: all blocks).
Value
Returns the model updated with the MCMC draw and, in the case ofblock=0
, theiter
field incremented by 1.Example
See the Development and Testing section of the tutorial.

unlist
(m::Model, block::Integer=0, transform::Bool=false)¶ 
unlist
(m::Model, nodekeys::Vector{Symbol}, transform::Bool=false) 
relist
(m::Model, x::AbstractArray{T<:Real}, block::Integer=0, transform::Bool=false)¶ 
relist
(m::Model, x::AbstractArray{T<:Real}, nodekeys::Vector{Symbol}, transform::Bool=false) 
relist!
(m::Model, x::AbstractArray{T<:Real}, block::Integer=0, transform::Bool=false)¶ 
relist!
(m::Model, x::AbstractArray{T<:Real}, nodekey::Symbol, transform::Bool=false) Convert (unlist) sets of logical and/or stochastic node values to vectors, or reverse (relist) the process.
Arguments
m
: model containing nodes to be unlisted or relisted.block
: sampling block of nodes to be listed (default: all blocks).nodekey/nodekeys
: node(s) to be listed.x
: values to relist.transform
: whether to apply a link transformation in the conversion.
Value
Theunlist
methods return vectors of concatenated node values,relist
return dictionaries of symbol keys and values for the specified nodes, andrelist!
return their model argument with values copied to the nodes.

update!
(m::Model, block::Integer=0)¶ 
update!
(m::Model, nodekeys::Vector{Symbol}) Update values of logical and stochastic model node according to their relationship with others in a model.
Arguments
m
: mode with nodes to be updated.block
: sampling block of nodes to be updated (default: all blocks).nodekeys
: nodes to be updated in the given order.
Value
Returns the model with updated nodes.