Package {abcpp}

Parameter Estimation With Approximate Bayesian Computation (ABC)

Description

Runs Approximate Bayesian Computation (ABC) through the shared C++ backend. The R interface is intentionally small: users provide 'target', 'params', 'sumstats', and an optional nested 'control' list.

Usage

abc(target, params, sumstats, control = list())

Arguments

Details

The algorithmic implementation lives in C++. The R layer only prepares the input matrices, merges the control list with defaults, calls the compiled backend, and attaches the "abcpp" class to the output.

The core ABC procedure calculates the Euclidean distance between the simulated summary statistics and the target summary statistics. Optionally, dimensionality reduction (Principal Component Analysis, PCA, or Partial Least Squares, PLS) can be applied to the summary statistics before calculating distances. A predefined proportion (tol) of the simulations closest to the target are retained. The method parameter in the control list specifies whether the accepted parameters are returned as-is ("rejection") or adjusted using a regression model ("loclinear", "ridge", or "neuralnet") to account for the discrepancy between the simulated and observed summary statistics.

summary() computes statistical summaries from the returned object.

Value

An object of class "abcpp" containing complete algorithm output. This object is a list containing the following components:

• unadj.values: A matrix of unadjusted accepted posterior samples.

• adj.values: A matrix of adjusted posterior samples when a regression method (e.g., "loclinear", "ridge", "neuralnet") is used; otherwise NULL.

• ss: A matrix of accepted summary statistics.

• weights: A numeric vector of regression weights used for adjustments.

• dist: A numeric vector of Euclidean distances between accepted simulated and target summary statistics.

• region: A logical vector indicating which simulations were accepted (unadjusted).

• method: The ABC method used.

• call: The original matched function call.

• names: A list containing parameter.names and statistics.names.

See Also

[control], [summary.abcpp()]

Examples

set.seed(1004)
n <- 200L
params <- cbind(theta = stats::runif(n))
sumstats <- cbind(s = params[, 1] + stats::rnorm(n, sd = 0.05))
fit <- abc(
  target = c(0.5),
  params = params,
  sumstats = sumstats,
  control = list(tol = 0.1)
)
summary(fit)

ABC control options

Description

Documents the nested 'control' list accepted by [abc()]. The control list is merged with defaults, so users may provide only the fields they want to override.

Details

The default control is:

“'r list( method = "rejection", tol = 0.01, kernel = "epanechnikov", hcorr = TRUE, transf = "none", logit.bounds = NULL, subset = NULL, prior.weights = NULL, seed = 1004, reduction = "none", n_comp = 0L, nnet = list( numnet = 10L, sizenet = 5L, lambda = c(0.0001, 0.001, 0.01), maxit = 500L, rang = 0.7, abstol = 1e-4, reltol = 1e-8, verbose = FALSE, skip = FALSE ) ) “'

Control List Fields

method

Character. Selects the ABC method. Supported values are "rejection", "loclinear", "ridge", and "neuralnet".

tol

Numeric. The tolerance proportion in (0, 1]. It determines the proportion of simulations accepted based on distance to the target summary statistics.

kernel

Character. Selects the regression weight kernel. Supported values are "epanechnikov" (default), "rectangular", "gaussian", "triangular", "biweight", and "cosine".

hcorr

Logical. Enables conditional heteroscedastic correction in regression adjustment methods (default is TRUE).

transf

Character vector. Controls parameter transformation before adjustment. Use "none", "log", or "logit". A single value is recycled across all parameters.

logit.bounds

Matrix. Used when transf = "logit" to specify the bounds for each parameter. Each row corresponds to a parameter, with the first column being the lower bound and the second being the upper bound.

subset

Logical vector. An optional mask to apply to simulations, selecting a subset to be considered.

prior.weights

Numeric vector. Optional prior weights for simulated samples. When supplied, its length must match the number of rows in params. For regression adjustment methods, final regression weights are the distance-kernel weights multiplied by these prior weights.

seed

Integer. The seed used by stochastic C++ components (default is 1004L).

reduction

Character. Optionally reduces summary statistics prior to ABC. Supported values are "none", "pca" (Principal Component Analysis), and "pls" (Partial Least Squares).

n_comp

Integer. The number of PCA or PLS components to retain when reduction is active. Use 0L to let the backend decide the default.

nnet

A nested list of settings for the neural network method (method = "neuralnet"):

• numnet: Integer. The number of neural networks to train (default 10L).

• sizenet: Integer. The number of units in the hidden layer (default 5L).

• lambda: Numeric vector. Weight decay parameters sampled uniformly across neural network fits.

• maxit: Integer. The maximum number of BFGS (Broyden-Fletcher-Goldfarb-Shanno) iterations per fit (default 500L).

• rang: Numeric. Initial weights are randomized in [-rang, rang] (default 0.7).

• abstol: Numeric. Absolute convergence tolerance (default 1e-4).

• reltol: Numeric. Relative convergence tolerance (default 1e-8).

• verbose: Logical. If TRUE, requests training progress from the backend.

• skip: Logical. If TRUE, adds direct input-to-output skip-layer connections.

See Also

[abc()]

Examples

target <- c(0.5)
params <- matrix(runif(100), ncol = 1)
sumstats <- matrix(runif(100), ncol = 1)
fit <- abc(
  target = target,
  params = params,
  sumstats = sumstats,
  control = list(tol = 0.1)
)

fit <- abc(
  target = target,
  params = params,
  sumstats = sumstats,
  control = list(
    method = "neuralnet",
    tol = 0.1,
    nnet = list(sizenet = 8, maxit = 1000)
  )
)

Summarize an abcpp Posterior

Description

Summarizes posterior samples returned by [abc()].

Usage

## S3 method for class 'abcpp'
summary(object, unadj = FALSE, intvl = 0.95, ...)

Arguments

Details

The summary extracts the relevant posterior samples and calculates the minimum, lower interval endpoint, median, mean, upper interval endpoint, maximum, and standard deviation for each parameter.

For method = "rejection", or when adjusted values are not available, unadjusted samples are always summarized. When an adjusted method is used (e.g., "loclinear"), the adjusted samples are summarized by default unless unadj = TRUE is specified.

Value

A list of class "summary.abcpp" containing the following components:

• statistics: A matrix of posterior summary statistics for each parameter. The rows include Minimum, Lower endpoint, Median, Mean, Upper endpoint, Maximum, and Standard Deviation.

• unadjusted: A logical value indicating whether the unadjusted samples were summarized.

• interval: The numeric credible interval width specified by the user.

• method: The Approximate Bayesian Computation (ABC) method inherited from the fitted abcpp object.

Examples

set.seed(1004)
n <- 200L
param <- cbind(theta = stats::runif(n))
sumstat <- cbind(s = param[, 1] + stats::rnorm(n, sd = 0.05))
fit <- abc(
  target = c(0.5),
  params = param,
  sumstats = sumstat,
  control = list(tol = 0.1)
)
summary(fit)