What does "Acceptance-Rejection Sampling" mean?

Table of Contents

• How It Works
• Why Use It?

Acceptance-rejection sampling is a method used in statistics to generate samples from a specific distribution. This process works by first creating a sample from an easier distribution and then deciding whether to keep or discard that sample based on a set of rules.

#How It Works

1. Generate a Sample: Start by picking a random sample from a distribution that is easier to work with.
2. Calculate Acceptance Criteria: Use a comparison between the sampled value and a target distribution. This involves using a simple rule to decide if the sample is a good fit.
3. Accept or Reject: If the sample meets the criteria, it is kept; if not, it is discarded. This step may need to be repeated many times to get enough valid samples.

#Why Use It?

This method is helpful because it allows for sampling from complex distributions without needing to calculate all the details of that distribution directly. It provides a way to approximate the desired outcome while reducing the need for complicated calculations.