Contents
How to generate random samples from a Gaussian variable?
Partly based on the ECE662 Spring 2014 lecture material of Prof. Mireille Boutin. 1 1. Introduction 2 2. Inverse transform sampling 3 3. Box Muller Transform 4 4. Marsaglia polar method 5 5. Generate a Gaussian random variable using a normal distributed random variable. 6 6.
How are independent random samples selected in a sample?
Independent random samples are selected by randomization of each sampling element. An independent random sample is a sequence of observations which are not dependent on any other sample or data. 1. Each member of the population must have an equal chance of selection. 2. The members are selected randomly instead of voluntarily selecting themselves.
Can you generate a Gaussian sample from thin air?
Of course, we can’t generate Gaussian samples from thin air. Instead, we start with a random number generator that exists in almost all programming languages: the uniform random number generator. It generates a random number that could take any value between 0 and 1.
How to transform a uniform sample to a Gaussian sample?
This method works by applying the inverse function of the Gaussian CDF (cumulative distribution function) to transform a uniform sample to a Gaussian sample. To make sure that the Gaussian samples for the x- and y-coordinates are independent, we can use two different uniform samples, one for x (U₁), and one for y (U₂).
What can you do with Gaussian distributed numbers?
It can be used to dramatically improve some aspect of your game, such as procedural terrain generation, enemy health and attack power, etc. Despite being so ubiquitous, very few gaming frameworks offer functions to generate numbers which follow such distribution. Unity developers, for instance, heavily rely on
How is Gaussian sampling used in data science?
Gaussian sampling — that is, generating samples from a Gaussian distribution — plays an important role in many cutting-edge fields of data science, such as Gaussian process, variational autoencoder, or generative adversarial network. As a result, you often see functions like tf.random.normal in their tutorials.