"Computational Statistics with Matlab" hard translation

Chapter 1th sampling from random variables

The probability model proposed by the researcher is often more complex for analytical methods, and the researchers rely more and more on computational and numerical methods when dealing with complex probabilistic models, and by using computational methods, researchers do not have to make unrealistic assumptions about some analytical techniques (such as normality and independence).

The key to most approximation techniques is the ability to sample from the distribution. Sampling is needed to predict what a particular model looks like in some scenarios, and to find the appropriate values for the implicit variables (parameters) applied to the model on the experimental data. Most computational sampling methods transform the problem of sampling from complex distributions into sub-problems of simple sampling distributions. In this chapter we will introduce two methods of sampling: Inverse transform and reject sampling. These methods are suitable for most single-variable single-value outputs, and in the next chapter we will discuss the Markov chain Monte Carlo method, which can effectively handle multivariate distributions.

"Computational Statistics with Matlab" hard translation