Inference with observed data

The following functions facilitate the use of a trained neural estimator with observed data.

NeuralEstimators.estimate Function

estimate(estimator::BayesEstimator, Z; batchsize::Integer = 32, use_gpu::Bool = true, kwargs...)

Applies estimator to data Z and returns the resulting estimates.

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NeuralEstimators.bootstrap Function

bootstrap(estimator::PointEstimator, parameters::P, Z; use_gpu = true) where P <: Union{AbstractMatrix, AbstractParameterSet}
bootstrap(estimator::PointEstimator, parameters::P, simulator, m::Integer; B = 400, use_gpu = true) where P <: Union{AbstractMatrix, AbstractParameterSet}
bootstrap(estimator::PointEstimator, Z; B = 400, blocks = nothing, trim = true, use_gpu = true)

Generates B bootstrap estimates using estimator.

Parametric bootstrapping is facilitated by passing a single parameter configuration, parameters, and corresponding simulated data, Z, whose length implicitly defines B. Alternatively, one may provide a simulator and the desired sample size, in which case the data will be simulated using simulator(parameters, m).

Non-parametric bootstrapping is facilitated by passing a single data set, Z. The argument blocks caters for block bootstrapping, and it should be a vector of integers specifying the block for each replicate. For example, with 5 replicates, the first two corresponding to block 1 and the remaining three corresponding to block 2, blocks should be [1, 1, 2, 2, 2]. The resampling algorithm generates resampled data sets by sampling blocks with replacement. If trim = true, the final block is trimmed as needed to ensure that the resampled data set matches the original size of Z.

The return type is a × B matrix, where is the dimension of the parameter vector.

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NeuralEstimators.interval Function

interval(θ::Matrix; probs = [0.05, 0.95], parameter_names = nothing)
interval(estimator::IntervalEstimator, Z; parameter_names = nothing, use_gpu = true)

Computes a confidence/credible interval based either on a × matrix θ of parameters (typically containing bootstrap estimates or posterior draws), where denotes the number of parameters to make inference on, or from an IntervalEstimator and data Z.

When given θ, the intervals are constructed by computing quantiles with probability levels controlled by the keyword argument probs.

The return type is a × 2 matrix, whose first and second columns respectively contain the lower and upper bounds of the interval. The rows of this matrix can be named by passing a vector of strings to the keyword argument parameter_names.

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NeuralEstimators.sampleposterior Function

sampleposterior(estimator::PosteriorEstimator, Z, N::Integer = 1000; kwargs...)
sampleposterior(estimator::RatioEstimator, Z, N::Integer = 1000; θ_grid, logprior::Function = θ -> 0f0, kwargs...)

Samples from the approximate posterior distribution implied by estimator.

The positional argument N controls the size of the posterior sample.

If Z represents a single data set as determined by Flux.numobs(), returns a × N matrix of posterior samples, where is the dimension of the parameter vector. Otherwise, if Z contains multiple data sets, a vector of matrices will be returned.

When using a RatioEstimator, the prior distribution is controlled through the keyword argument logprior (by default, a uniform prior is used). The sampling algorithm is based on a fine-gridding of the parameter space, specified through the keyword argument θ_grid. The approximate posterior density is evaluated over this grid, which is then used to draw samples. This is effective when making inference with a small number of parameters. For models with a large number of parameters, other sampling algorithms (e.g., MCMC) may be needed (please contact the package maintainer).

Keyword arguments are passed onto summarystatistics.

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NeuralEstimators.posteriormean Function

posteriormean(θ::AbstractMatrix)	
posteriormean(estimator, Z, N::Integer = 1000; kwargs...)

Computes the posterior mean based either on a × matrix θ of posterior draws, where denotes the number of parameters to make inference on, or directly from an estimator that allows for posterior sampling via sampleposterior().

See also posteriormedian(), posteriormode().

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NeuralEstimators.posteriormedian Function

posteriormedian(θ::AbstractMatrix)	
posteriormedian(estimator, Z, N::Integer = 1000; kwargs...)

Computes the vector of marginal posterior medians based either on a × matrix θ of posterior draws, where denotes the number of parameters to make inference on, or directly from an estimator that allows for posterior sampling via sampleposterior().

See also posteriormean(), posteriorquantile().

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NeuralEstimators.posteriorquantile Function

posteriorquantile(θ::AbstractMatrix, probs)	
posteriorquantile(estimator, Z, probs, N::Integer = 1000; kwargs...)

Computes the vector of marginal posterior quantiles with (a collection of) probability levels probs, based either on a × matrix θ of posterior draws, where denotes the number of parameters to make inference on, or directly from an estimator that allows for posterior sampling via sampleposterior().

The return value is a × length(probs) matrix.

See also posteriormedian().

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NeuralEstimators.posteriormode Function

posteriormode(estimator::RatioEstimator, Z; θ₀ = nothing, θ_grid = nothing, logprior::Function = θ -> 0f0, use_gpu = true)

Computes the (approximate) posterior mode (maximum a posteriori estimate) given data ,

where    denotes the approximate log-likelihood function implied by estimator, and denotes the prior density function controlled through the keyword argument prior. Note that this estimate can be viewed as an approximate maximum penalised likelihood estimate, with penalty term .

If a vector θ₀ of initial parameter estimates is given, the approximate posterior density is maximised by gradient descent (requires Optim.jl to be loaded). Otherwise, if a matrix of parameters θ_grid is given, the approximate posterior density is maximised by grid search.

See also posteriormedian(), posteriormean().

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NeuralEstimators.logratio Function

logratio(estimator::RatioEstimator, Z, θ_grid)
logratio(estimator::RatioEstimator, Z; θ_grid)

Compute the log likelihood-to-evidence ratios over a grid of parameter values θ_grid for the data Z.

Arguments

• estimator: a RatioEstimator

• Z: observed data

• θ_grid: matrix of parameter values, where each column is a parameter configuration

Returns

A vector of log ratios, one for each column of θ_grid.

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