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Optimizing Beta Distribution proposal

srbeta_optimize.Rd

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
)

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.

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.

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.

See also

srbeta_custom: Function to sample from a custom proposal generated by srbeta_optimize().

Examples

# 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)