srexp_optimize: Optimizing Exponential Distribution proposal
In stors: Step Optimised Rejection Sampling

srexp_optimize

R Documentation

Optimizing Exponential Distribution proposal

Description

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

Usage

srexp_optimize(
  rate = NULL,
  xl = NULL,
  xr = NULL,
  steps = 4091,
  proposal_range = NULL,
  theta = 0.1,
  target_sample_size = 1000,
  verbose = FALSE
)

Arguments

`rate`	(optional) Numeric. rate parameter of the Exponential Distribution. Defaults to `NULL`, which implies a scalable proposal with `rate = 1`.
`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 srexp_optimize() is explicitly called:

A proposal is created and cached. If no parameters are provided, a standard proposal is created with rate = 1.
Providing rate creates a custom proposal, which is cached for use with srexp_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.

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.

rate: the rate of the target distribution.

is_symmetric

A logical value indicating whether the proposal is symmetric.

proposal_type

A string indicating the type of the generated proposal:

"scaled": The proposal is "scalable" and standardized with rate = 1. This is used when parameter rate is either NULL or not provided. Scalable proposals are compatible with srexp.
"custom": The proposal is "custom" when rate is provided. Custom proposals are compatible with srexp_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.

Examples

# Generate scalable proposal that with rate = 1, that has 4096 steps
scalable_proposal <- srexp_optimize(steps = 4096)

# Generate custom proposal that with rate = 4
scalable_proposal <- srexp_optimize(rate = 4)

stors documentation built on April 3, 2025, 6:16 p.m.