Initial Values

JuliaBUGS draws initial values from each parameter's prior when it constructs a model. This is often sufficient, but explicit initial values are useful when reproducing an existing BUGS analysis, comparing chains from known starting points, or working with priors that can generate poor starting values.

Initialize while constructing a model

Pass a NamedTuple of initial values as the second argument when calling an @bugs model definition:

using JuliaBUGS

model_def = @bugs begin
    a ~ dnorm(0, 1)
    b ~ dnorm(a, 1)
    y ~ dnorm(b, 1)
end

data = (; y=3.0)
inits = (; a=1.0, b=2.0)
model = model_def(data, inits)
params = JuliaBUGS.getparams(Dict, model)
(; a=params[@varname(a)], b=params[@varname(b)])

(a = 1.0, b = 2.0)

The names in inits correspond to unobserved stochastic variables in the model. Named values are given in the variables' original, constrained space. getparams(Dict, model) returns the current parameter values keyed by VarName; because a and b are unconstrained, their transformed and original values are identical here.

Initial values can be partial. JuliaBUGS draws omitted parameters from their priors and then recomputes deterministic variables:

model = model_def(data, (; a=1.0))
params = JuliaBUGS.getparams(Dict, model)
params[@varname(a)]

1.0

The output confirms that a kept its supplied value. The omitted b is still drawn from its prior, so its value is intentionally not shown.

Array-valued parameters are initialized under their model name with an array of the corresponding shape. For example, a model containing theta[i] ~ dnorm(0, 1) for i in 1:3 accepts (; theta=[1.0, 2.0, 3.0]).

Reinitialize an existing model

Use initialize! to replace the initial state after constructing a model:

model = model_def(data)
model = initialize!(model, inits)
params = JuliaBUGS.getparams(Dict, model)
(; a=params[@varname(a)], b=params[@varname(b)])

(a = 1.0, b = 2.0)

As during construction, a NamedTuple contains values in the original space and may omit parameters that should be drawn from their priors.

initialize! also accepts a flat parameter vector. Its order must match the model's parameter order, and its values use transformed coordinates when the model is in transformed mode. A safe way to obtain a compatible vector is to start from the model's current parameters:

initial_θ = JuliaBUGS.getparams(model)
model = initialize!(model, initial_θ)

Initial values passed to a sampler

Samplers using the AbstractMCMC interface accept a flat parameter vector through init_params:

initial_θ = JuliaBUGS.getparams(model)
chain = AbstractMCMC.sample(
    model, sampler, n_samples;
    init_params=initial_θ,
    # other sampler options...
)

For multiple chains, provide one initial vector per chain. See Parallel and Distributed Sampling for the multi-chain forms.

The classic examples bundled with JuliaBUGS include published initial values. For example, JuliaBUGS.BUGSExamples.VOLUME_1.seeds.inits is a NamedTuple that can be passed while constructing or reinitializing the Seeds model.