031-001. meaning of test and parameter estimation @ First assumption of data analysis is "data what you want to analyze is sample which was realized from certain random variable" This means that what we're interested in is not "data" which we have as nothing but realization but "random variable" which generates data Data is nothing but reference materials for finding random variable Random variable has "distribution model" and "parameter" Therefore, finding random variable is to answer about following example questions 1. Corresponding data is generated from specific distribution model like gaussian normal distribution? 1. If so, that gaussian normal distribution has expection $\mu$ and variance $\sigma^{2}$? For example, $\mu=0$ or not? 1. If $\mu \neq 0$, what value does $\mu$ have? @ Answering these questions is called "test" or "parameter estimation" "parameter estimation" can be simply "estimation" @ 1. Corresponding data is generated from specific distribution model like gaussian normal distribution? This question tests if hypothesis about distribution of random variable is right or wrong This question is called "distribution test of random variable" This question uses hypothesis that random variable follows gaussian normal distribution Testing this kind of hypothesis is called "normality test" which is one of most used test in data analysis @ 1. If so, that gaussian normal distribution has expection $\mu$ and variance $\sigma^{2}$? In this question, the fact that random variable follows which distribution model is fixed On this state, we test if coefficient of pdf has specific value We test if coefficient of pdf is greater or smaller than specific value For example, if you want to test if expection parameter \mu equals to 0 or not, you want to prove hypothesis that expection parameter of gaussian normal distribution equals to 0 Testing this kind of hypothesis is called "parameter test" @ 1. If $\mu \neq 0$, what value does $\mu$ have? This question is task of finding highest probability when parameter has certain value This step is called "parameter estimation" or "estimation" There are various ways of "parameter estimation" MSE(Maximum Squred Error) and MLE(Maximum Likelihood Estimation) find one value with highest probability Bayesian Estimation finds all potential value And it also finds all probabilities of those values becoming actual parameter and then, it display distribution of those probabilities