srchisq_optimize: Optimizing Chi-squared Distribution proposal

Description

The srchisq_optimize() function generates an optimized proposal for a targeted Chi-squared Distribution. The proposal can be customized and adjusted based on various options provided by the user.

Usage

srchisq_optimize(
  df = 2,
  xl = NULL,
  xr = NULL,
  steps = 4091,
  proposal_range = NULL,
  theta = 0.1,
  target_sample_size = 1000,
  verbose = FALSE
)

Value

The user does not need to store the returned value, because the package internally cashes the proposal. However, we explain here the full returned proposal for advanced users.

A list containing the optimized proposal and related parameters for the specified built-in distribution:

data

A data frame with detailed information about the proposal steps, including:

x: The start point of each step on the x-axis.
s_upper: The height of each step on the y-axis.
p_a: Pre-acceptance probability for each step.
s_upper_lower: A vector used to scale the uniform random number when the sample is accepted.

areas

A numeric vector containing the areas under:

left_tail: The left tail bound.

steps

The middle steps.

right_tail

The right tail bound.

steps_number

An integer specifying the number of steps in the proposal.

sampling_probabilities

A numeric vector with:

left_tail: The probability of sampling from the left tail.

left_and_middle

The combined probability of sampling from the left tail and middle steps.

unif_scaler

A numeric scalar, the inverse probability of sampling from the steps part of the proposal (\(\frac{1}{p(lower < x < upper)}\)). Used for scaling uniform random values.

lt_properties

A numeric vector of 5 values required for Adaptive Rejection Sampling (ARS) in the left tail.

rt_properties

A numeric vector of 6 values required for ARS in the right tail.

alpha

A numeric scalar representing the uniform step area.

tails_method

A string, either "ARS" (Adaptive Rejection Sampling) or "IT" (Inverse Transform), indicating the sampling method for the tails.

proposal_bounds

A numeric vector specifying the left and right bounds of the target density.

cnum

An integer representing the cache number of the created proposal in memory.

symmetric

A numeric scalar indicating the symmetry point of the proposal, or NULL if not symmetric.

f_params

A list of parameters for the target density that the proposal is designed for.

is_symmetric

A logical value indicating whether the proposal is symmetric.

proposal_type

A string indicating the type of the genedfd proposal:

"custom": The proposal is "custom" when df is provided. Custom proposals are compatible with srchisq_custom.

target_function_area

A numeric scalar estimating the area of the target distribution.

dens_func

A string containing the hardcoded density function.

density_name

A string specifying the name of the target density distribution.

lock

An identifier used for saving and loading the proposal from disk.

Arguments

df: (optional) Numeric. degrees of freedom parameter of the Chi-squared Distribution. Defaults to NULL, which implies proposal with df = 2.
xl: Numeric. Left truncation bound for the target distribution. Defaults to -Inf, representing no left truncation.
xr: Numeric. Right truncation bound for the target distribution. Defaults to Inf, representing no right truncation.
steps: (optional) Integer. Desired number of steps in the proposal. Defaults to NULL, which means the number of steps is determined automatically during optimization.
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 srchisq_optimize() is explicitly called:

A proposal is created and cached. If no parameters are provided, a standard proposal is created with df = 2.
Providing df creates a custom proposal, which is cached for use with srchisq_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

# Genedf custom proposal that with df = 2, that has 4096 steps
scalable_proposal <- srchisq_optimize(steps = 4096)

# Genedf custom proposal that with df = 4
scalable_proposal <- srchisq_optimize(df = 4)