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}
: a dictionary containing all input, logical, and stochastic model nodes.dependents::Vector{Symbol}
: symbols of allDependent
nodes in topologically sorted order so that a given node in the vector is conditionally independent of subsequent nodes, given the previous ones.samplers::Vector{Sampler}
: sampling functions for updating blocks of stochastic nodes.states::Vector{Vector{VariateType}}
: states of chains at the end of a possible series of MCMC runs.iter::Integer
: current MCMC draw from the target distribution.burnin::Integer
: number of initial draws to discard as a burnin sequence to allow for convergence.chain::Integer
: current run of an MCMC simulator in a possible series of runs.hasinputs::Bool
: whether values have been assigned to the input nodes.hasinits::Bool
: whether initial values have been assigned to stochastic nodes.
Constructor¶

Model
(; iter::Integer=0, burnin::Integer=0, chain::Integer=1, samplers::Vector{Sampler}=Array(Sampler, 0), 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.chain
: current run of the MCMC simulator in a possible sequence of runs.samplers
: a vector of blockspecific sampling functions.nodes...
: an 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.
Methods¶

draw
(m::Model; filename::String="")¶ Draw a GraphViz DOTformatted graph representation of model nodes and their relationships.
Arguments
m
: a model for which to construct a graph.filename
: an 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.

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

gradlogpdf
(m::Model, block::Integer=0, transform::Bool=false; dtype::Symbol=:forward)¶ 
gradlogpdf
(m::Model, x::Vector{T<:Real}, block::Integer=0, transform::Bool=false; dtype::Symbol=:forward) 
gradlogpdf!
(m::Model, x::Vector{T<:Real}, block::Integer=0, transform::Bool=false; dtype::Symbol=:forward)¶ Compute the gradient of logdensities for stochastic nodes.
Arguments
m
: a model containing the stochastic nodes for which to compute the gradient.x
: a value (possibly different than the current one) at which to compute the gradient.block
: the sampling block of stochastic nodes for which to compute the gradient, if specified; otherwise, all sampling blocks are included.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 [76].

graph
(m::Model)¶ Construct a graph representation of model nodes and their relationships.
Arguments
m
: a 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
: a 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.

keys
(m::Model, ntype::Symbol=:assigned, block::Integer=0)¶ Return the symbols of nodes of a specified type.
Arguments
m
: a model containing the nodes of interest.ntype
: the 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 blocksampled.:dependent
: logical or stochastic (dependent) nodes.: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.:stochastic
: stochastic nodes.
block
: the block for which to return nodes ifntype = :block
, or all blocks ifblock = 0
(default).
Value
A vector of node symbols.

logpdf
(m::Model, block::Integer=0, transform::Bool=false)¶ 
logpdf
(m::Model, x::Vector{T<:Real}, block::Integer=0, transform::Bool=false) 
logpdf!
(m::Model, x::Vector{T<:Real}, block::Integer=0, transform::Bool=false)¶ Compute the sum of logdensities for stochastic nodes.
Arguments
m
: a model containing the stochastic nodes for which to evaluate logdensities.x
: a value (possibly different than the current one) at which to evaluate densities.block
: the sampling block of stochastic nodes over which to sum densities, if specified; otherwise, all stochastic nodes are included.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
.

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
(c::Chains, iters::Integer; verbose::Bool=true) Simulate MCMC draws for a specified model.
Arguments
m
: a specified mode.c
: chains from a previous call tomcmc
for which to simulate additional draws.inputs
: a dictionary of values for input model nodes. Dictionary keys and values should be given for each input node.inits
: a vector of 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
AChains
type object of simulated draws.Example
See the MCMC Simulation section of the tutorial.

relist
(m::Model, values::Vector{T<:Real}, block::Integer=0, transform::Bool=false)¶ 
relist
(m::Model, values::Vector{T<:Real}, nkeys::Vector{Symbol}, transform::Bool=false) Convert a vector of values to a set of logical and/or stochastic node values.
Arguments
m
: a model with nodes to serve as the template for conversion.values
: values to convert.block
: the sampling block of nodes to which to convertvalues
. Defaults to all blocks.nkeys
: a vector of symbols identifying the nodes to which to convertvalues
.transform
: whether to apply an inverselink transformation in the conversion.
Value
A dictionary of node symbols and converted values.

relist!
(m::Model, values::Vector{T<:Real}, block::Integer=0, transform::Bool=false)¶ 
relist!
(m::Model, values::Vector{T<:Real}, nkeys::Vector{Symbol}, transform::Bool=false) Copy a vector of values to a set of logical and/or stochastic nodes.
Arguments
m
: a model with nodes to which values will be copied.values
: values to copy.block
: the sampling block of nodes to which to copyvalues
. Defaults to all blocks.nkeys
: a vector of symbols identifying the nodes to which to copyvalues
.transform
: whether to apply an inverselink transformation in the copy.
Value
Returns the model with copied node values.

setinits!
(m::Model, inits::Dict{Symbol, Any})¶ Set the initial values of stochastic model nodes.
Arguments
m
: a model with nodes to be initialized.inits
: a dictionary of 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
: a model with input nodes to be assigned.inputs
: a dictionary of 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{Sampler})¶ Set the blocksamplers for stochastic model nodes.
Arguments
m
: a 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.

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.

simulate!
(m::Model, block::Integer=0)¶ Simulate one MCMC draw from a specified model.
Argument:
m
: a model specification.block
: the block for which to simulate an MCMC draw, if specified; otherwise, simulate draws for all blocks (default).
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.

tune
(m::Model, block::Integer=0)¶ Get blocksampler tuning parameters.
Arguments
m
: a model with blocksamplers.block
: the block for which to return the tuning parameters, if specified; otherwise, the tuning parameters for all blocks.
Value
Ifblock = 0
, a vector of dictionaries containing blockspecific tuning parameters; otherwise, one blockspecific dictionary.

unlist
(m::Model, block::Integer=0, transform::Bool=false)¶ 
unlist
(m::Model, nkeys::Vector{Symbol}, transform::Bool=false) Convert a set of logical and/or stochastic node values to a vector.
Arguments
m
: a model with nodes to be converted.block
: the sampling block of nodes to be converted. Defaults to all blocks.nkeys
: a vector of symbols identifying the nodes to be converted.transform
: whether to apply a link transformation in the conversion.
Value
A vector of concatenated node values.

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