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Rejection Sampling - Definition, Methods &amp; Examples

# Rejection Sampling - Definition, Methods &amp; Examples

Today, you are here to learn about rejection sampling, so I will not disappoint you. The reason is that today’s article is all about defining this important sampling method

Have you ever done sampling from a distribution? If yes, then you must know about rejection sampling and its types. Ohh, you do not have an idea about it? Okay, no problem. This sampling is a type of sampling used for generating random variates or samples from a distribution. Its working principle is based on the rejection of the values that lie outside the bounds of distribution. However, as it is a probability distribution, students like you do not give much attention to this sampling method.

Today, you are here to learn about rejection sampling, so I will not disappoint you. The reason is that today’s article is all about defining this important sampling method, explaining its method of conduction, and giving examples. At the end of the article, you will also find some advantages and disadvantages of using this method. So, let’s start with the definition.

## What is rejection sampling?

The method of rejection sampling is a method of statistical inference. This method involves drawing random variables from a distribution. The analyst who is doing all these things rejects all the samples that do not meet a certain threshold. The rejected values are either out of the bounds of distribution or do not meet the criteria established by the analyst at the start. So, this is what this sampling type is all about.

## What is an example of rejection sampling?

There are a lot of examples of this sampling method that we see in our daily life. Let’s suppose after high school you are in search of a job. You apply to three different companies, and the companies take your interview. After some time, out of those three companies, only one gives you an offer. This means that the other two companies have rejected you and chosen someone else. The reasons for your rejection might be:

·       Not meeting the job criteria

·       Not having enough skills to work on the project

So, this is how rejection sampling works. The values that are not representative of the distribution are discarded, and new values are added until a certain level is reached. If you are still unable to understand this, you can take help from dissertation writers UK.

## How to conduct rejection sampling?

After reading the information above, you now have a good idea of this sampling method, and the example given above must have strengthened your knowledge further. However, you still do not have an idea about how to do this sampling. What are the steps involved in this sampling method? Now, let’s talk about those steps.

1.       The first step is the common one which is part of almost every kind of sampling method. In the first step, you need to set up the proposal distribution from which you are going to collect samples. The density, q(x), of the distribution must be known.
2. After the selection of the distribution, the next task is to draw a random number x. While drawing this number, it is important to remember that the number must be distributed between 0 and 1.
3. Step no. 3 is the same as step no.2, but with a little difference. In step no. 2, you have drawn a random number x distributed between 0 and 1. In step no. 3, this number is now changed to y.
4. Once you are done drawing x and y from the distribution, the next step is to choose a method for the rejection sampling. You may use the naïve iteration method for this sampling.
5. Lastly, it is time to accept or reject the sample. If y < f(x)/M, where f(x) is the probability density function (PDF) and M is the constant, accept the value as sample. Reject the value straightforward if it does not meet this criterion.

So, this is how you conduct rejection sampling. However, if you still do not get this idea, you can take dissertation help UK.

## What are the advantages of rejection sampling?

This sampling method is particularly used for distributions which are complex and intractable. There are a lot of advantages of this sampling method. Some of the most prominent advantages are as follows:

•         It can be used on any distribution, whether normal or Gaussian.
•         As you are in control, you can easily modify this sampling method for different distributions
•        It is a very powerful sampling method and can generate any number of samples
•        As the analyst, you can reject the samples even if you do not know the probability density function.
•        Lastly, it is an easy-to-implement method which does not require much expertise.

## Conclusion

Conclusively, rejection sampling is a method of sampling based on rejecting values that do not meet the criteria. The way of doing it is very simple, and you can learn it easily by paying close attention to the steps mentioned above. So, read the text given above and enjoy sampling.