Dependent¶
Dependent
is an abstract type designed to store values and attributes of model nodes, including parameters to be simulated via MCMC, functions of the parameters, and likelihood specifications on observed data. It extends the base Variate
type with method functions defined for the fields summarized below. Like the type it extends, values are stored in a value
field and can be used with method functions that accept Variate
type objects.
Since parameter values in the Dependent
structure are stored as a scalar or array, objects of this type can be created for model parameters of corresponding dimensions, with the choice between the two being user and applicationspecific. At one end of the spectrum, a model might be formulated in terms of parameters that are all scalars, with a separate instances of Dependent
for each one. At the other end, a formulation might be made in terms of a single parameter array, with one corresponding instance of Dependent
. Whether to formulate parameters as scalars or arrays will depend on the application at hand. Array formulations should be considered for parameters and data that have multivariate distributions, or are to be used as such in numeric operations and functions. In other cases, scalar parametrizations may be preferable. Situations in which parameter arrays are often used include the specification of regression coefficients and random effects.
Declaration¶
abstract Dependent{T} <: Variate{T}
Fields¶
value::T
: a scalar or array ofVariateType
values that represent samples from a target distribution.symbol::Symbol
: an identifying symbol for the node.nlink::Integer
: number of elements returned by thelink
method defined on the type. Generally, this will be the number of unique elements in the node. In most cases,nlink
will be equal tolength(value)
. However, for some structures, like stochastic covariance matrices,nlink
may be smaller.monitor::Vector{Int}
: indices identifying elements of thevalue
field to include in monitored MCMC sampler output.eval::Function
: a function for updating the state of the node.sources::Vector{Symbol}
: symbols of other nodes upon whom the values of this one depends.targets::Vector{Symbol}
: symbols ofDependent
nodes that depend on this one. Elements oftargets
are topologically sorted so that a given node in the vector is conditionally independent of subsequent nodes, given the previous ones.
Methods¶

invlink
(d::Dependent, x, transform::Bool=true)¶ Apply a nodespecific inverselink transformation. In this method, the link transformation is defined to be the identity function. This method may be redefined for subtypes of
Dependent
to implement different link transformations.Arguments
d
: a node on which alink()
transformation method is defined.x
: an object to which to apply the inverselink transformation.transform
: whether to transformx
or assume an identity link.
Value
Returns the inverselinktransformed version ofx
.

link
(d::Dependent, x, transform::Bool=true)¶ Apply a nodespecific link transformation. In this method, the link transformation is defined to be the identity function. This method function may be redefined for subtypes of
Dependent
to implement different link transformations.Arguments
d
: a node on which alink()
transformation method is defined.x
: an object to which to apply the link transformation.transform
: whether to transformx
or assume an identity link.
Value
Returns the linktransformed version ofx
.

logpdf
(d::Dependent, transform::Bool=false)¶ Evaluate the logdensity function for a node. In this method, no density function is assumed for the node, and a constant value of 0 is returned. This method function may be redefined for subtypes of
Dependent
that have distributional specifications.Arguments
d
: a node containing values at which to compute the logdensity.transform
: whether to evaluate the logdensity on the linktransformed scale.
Value
The resulting numeric value of the logdensity.

setmonitor!
(d::Dependent, monitor::Bool)¶ 
setmonitor!
(d::Dependent, monitor::Vector{Int}) Specify node elements to be included in monitored MCMC sampler output.
Arguments
d
: a node whose elements contain sampled MCMC values.monitor
: a boolean indicating whether all elements are monitored, or a vector of elementwise indices of elements to monitor.
Value
Returnsd
with itsmonitor
field updated to reflect the specified monitoring.

show
(d::Dependent)¶ Write a text representation of nodal values and attributes to the current output stream.

showall
(d::Dependent)¶ Write a verbose text representation of nodal values and attributes to the current output stream.
Logical¶
Type Logical
inherits the fields and method functions from the Dependent
type, and adds the constructors and methods listed below. It is designed for nodes that are deterministic functions of model parameters and data. Stored in the field eval
is an anonymous function defined as
function(model::Mamba.Model)
where model
contains all model nodes. The function can contain any valid julia expression or code block written in terms of other nodes and data structures. It should return values with which to update the node in the same type as the value
field of the node.
Declaration¶
type Logical{T} <: Dependent{T}
Fields¶
value::T
: a scalar or array ofVariateType
values that represent samples from a target distribution.symbol::Symbol
: an identifying symbol for the node.nlink::Integer
: number of elements returned by thelink
method defined on the type.monitor::Vector{Int}
: indices identifying elements of thevalue
field to include in monitored MCMC sampler output.eval::Function
: a function for updating values stored invalue
.sources::Vector{Symbol}
: symbols of other nodes upon whom the values of this one depends.targets::Vector{Symbol}
: symbols ofDependent
nodes that depend on this one. Elements oftargets
are topologically sorted so that a given node in the vector is conditionally independent of subsequent nodes, given the previous ones.
Constructors¶

Logical
(expr::Expr, monitor::Union(Bool, Vector{Int})=true)¶ 
Logical
(d::Integer, expr::Expr, monitor::Union(Bool, Vector{Int})=true) Construct a
Logical
object that defines a logical model node.Arguments
d
: number of dimensions for array nodes.expr
: a quoted expression or codeblock defining the body of the function stored in theeval
field.monitor
: a boolean indicating whether all elements are monitored, or a vector of elementwise indices of elements to monitor.
Value
Returns aLogical{Array{VariateType,d}}
if the dimension argumentd
is specified, and aLogical{VariateType}
if not.Example
See the Model Specification section of the tutorial.
Methods¶

setinits!
(l::Logical, m::Model, ::Any=nothing)¶ Set initial values for a logical node.
Arguments
l
: a logical node to which to assign initial values.m
: a model that contains the node.
Value
Returns the result of a call toupdate!(l, m)
.

update!
(l::Logical, m::Model)¶ Update the values of a logical node according to its relationship with others in a model.
Arguments
l
: a logical node to update.m
: a model that contains the node.
Value
Returns the node with its values updated.
Stochastic¶
Type Stochastic
inherits the fields and method functions from the Dependent
type, and adds the additional ones listed below. It is designed for model parameters or data that have distributional or likelihood specifications, respectively. Its stochastic relationship to other nodes and data structures is represented by the Distributions
structure stored in field distr
. Stored in the field eval
is an anonymous function defined as
function(model::Mamba.Model)
where model
contains all model nodes. The function can contain any valid julia expression or codeblock. It should return a single Distributions object for all node elements or a structure of the same type as the node with elementspecific Distributions objects.
Declaration¶
type Stochastic{T} <: Dependent{T}
Fields¶
value::T
: a scalar or array ofVariateType
values that represent samples from a target distribution.symbol::Symbol
: an identifying symbol for the node.nlink::Integer
: number of elements returned by thelink
method defined on the type.monitor::Vector{Int}
: indices identifying elements of thevalue
field to include in monitored MCMC sampler output.eval::Function
: a function for updating thedistr
field for the node.sources::Vector{Symbol}
: symbols of other nodes upon whom the distributional specification for this one depends.targets::Vector{Symbol}
: symbols ofDependent
nodes that depend on this one. Elements oftargets
are topologically sorted so that a given node in the vector is conditionally independent of subsequent nodes, given the previous ones.distr::DistributionStruct
: the distributional specification for the node.
Aliases¶
typealias DistributionStruct Union(Distribution, Array{Distribution})
Constructors¶

Stochastic
(expr::Expr, monitor::Union(Bool, Vector{Int})=true)¶ 
Stochastic
(d::Integer, expr::Expr, monitor::Union(Bool, Vector{Int})=true) Construct a
Stochastic
object that defines a stochastic model node.Arguments
d
: number of dimensions for array nodes.expr
: a quoted expression or codeblock defining the body of the function stored in theeval
field.monitor
: a boolean indicating whether all elements are monitored, or a vector of elementwise indices of elements to monitor.
Value
Returns aStochastic{Array{VariateType,d}}
if the dimension argumentd
is specified, and aStochastic{VariateType}
if not.Example
See the Model Specification section of the tutorial.
Methods¶

insupport
(s::Stochastic)¶ Check whether stochastic node values are within the support of its distribution.
Arguments
s
: a stochastic node on which to perform the check.
Value
Returnstrue
if all values are within the support, andfalse
otherwise.

invlink
(s::Stochastic, x, transform::Bool=true) Apply an inverselink transformation to map transformed values back to the original distributional scale of a stochastic node.
Arguments
s
: a stochastic node on which alink()
transformation method is defined.x
: an object to which to apply the inverselink transformation.transform
: whether to transformx
or assume an identity link.
Value
Returns the inverselinktransformed version ofx
.

link
(s::Stochastic, x, transform::Bool=true) Apply a link transformation to map values in a constrained distributional support to an unconstrained space. Supports for continuous, univariate distributions and positivedefinite matrix distributions (Wishart or inverseWishart) are transformed as follows:
 Lower and upper bounded: scaled and shifted to the unit interval and logittransformed.
 Lower bounded: shifted to zero and logtransformed.
 Upper bounded: scaled by 1, shifted to zero, and logtransformed.
 Positivedefinite matrix: compute the (uppertriangular) Cholesky decomposition, and return its logtransformed diagonal elements prepended to the remaining uppertriangular part as a vector of length , where is the matrix dimension.
Arguments
s
: a stochastic node on which alink()
transformation method is defined.x
: an object to which to apply the link transformation.transform
: whether to transformx
or assume an identity link.
Value
Returns the linktransformed version ofx
.

logpdf
(s::MCMStochastic, transform::Bool=false) Evaluate the logdensity function for a stochastic node.
Arguments
s
: a stochastic node containing values at which to compute the logdensity.transform
: whether to evaluate the logdensity on the linktransformed scale.
Value
The resulting numeric value of the logdensity.

setinits!
(s::Stochastic, m::Model, x=nothing) Set initial values for a stochastic node.
Arguments
s
: a stochastic node to which to assign initial values.m
: a model that contains the node.x
: values to assign to the node.
Value
Returns the node with its assigned initial values.

update!
(s::Stochastic, m::Model) Update the values of a stochastic node according to its relationship with others in a model.
Arguments
s
: a stochastic node to update.m
: a model that contains the node.
Value
Returns the node with its values updated.