srbeta_optimize: Optimizing Beta Distribution proposal

Description

The srbeta_optimize() function generates an optimized proposal for a targeted Beta distribution. The proposal can be customized and adjusted based on various options provided by the user.

Usage

srbeta_optimize(
  shape1 = 2,
  shape2 = 2,
  xl = 0,
  xr = 1,
  steps = NULL,
  proposal_range = NULL,
  theta = 0.1,
  target_sample_size = 1000,
  verbose = FALSE
)

Value

A list containing the optimized proposal and related parameters for the specified Beta distribution. The proposal is also cached for internal use.

data: Detailed information about the proposal steps, including x, s_upper, p_a, and s_upper_lower.
areas: The areas under the left tail, steps, and right tail of the proposal distribution.
steps_number: The number of steps in the proposal.
f_params: The parameters (shape1 and shape2) of the Beta distribution.

Arguments

shape1: (optional) Numeric. The first shape parameter (\(\alpha\)) of the Beta distribution. Defaults to 1.
shape2: (optional) Numeric. The second shape parameter (\(\beta\)) of the Beta distribution. Defaults to 1.
xl: Numeric. Left truncation bound for the target distribution. Defaults to 0, as the Beta distribution is defined only on the interval [0, 1].
xr: Numeric. Right truncation bound for the target distribution. Defaults to 1, as the Beta distribution is defined only on the interval [0, 1].
steps: (optional) Integer. Desired number of steps in the proposal. Defaults to 4091.
proposal_range: (optional) Numeric vector. Specifies the range for optimizing the steps part of the proposal. Defaults to NULL, indicating automatic range selection.
theta: Numeric. A parameter for proposal optimization. Defaults to 0.1.
target_sample_size: (optional) Integer. Target sample size for proposal optimization. Defaults to 1000.
verbose: Boolean. If TRUE, detailed optimization information, including areas and steps, will be displayed. Defaults to FALSE.

Details

When srbeta_optimize() is explicitly called:

A proposal is created and cached. If no parameters are provided, a standard proposal is created with shape1 = 1 and shape2 = 1.
Providing shape1 and shape2 creates a custom proposal, which is cached for use with srbeta_custom().
The optimization process can be controlled via parameters such as steps, proposal_range, or theta. If no parameters are provided, the proposal is optimized via brute force based on the target_sample_size.

Examples

Run this code

# Generate a standard proposal with shape1 = 1 and shape2 = 1
standard_proposal <- srbeta_optimize()

# Generate a custom proposal with shape1 = 2 and shape2 = 3
custom_proposal <- srbeta_optimize(shape1 = 2, shape2 = 3)