> For the complete documentation index, see [llms.txt](https://ykkim.gitbook.io/wiki/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://ykkim.gitbook.io/wiki/machine-learning/probability-and-statistics-for-machine-learning/frequentist-methods.md).
# Frequenist Methods
#### Frequentist school of statistics
**Introduction**
* 베이지안 통계 다음으로 등장한 통계학파
* 20세기에 지배적인 학파였음
* confidence intervals, p-values, t-test, x^2-test가 이에 해당됨
* 컴퓨터의 등장 이후로는 bayesian method가 가장 보편적인 방법이 됨
**The fork in the road**
* Bayesian inference: 지금까지 공부했던 방법
* H가 hypothesis, D가 data
* prior를 확실히 안다면 정확하게 작동함: 그러나 실제로 완벽한 prior는 없음
**-> Bayesian은 prior, Frequentist는 likelyhood func.을 사용함**
**What is probability?**
* Frequentist
* 고정 값을 가진 파라미터의 확률 분포를 무의미하다고 생각함, 가설에 대한 신뢰도를 정량화하기 위해 확률 사용을 거부함
* ex) 동전을 던졌을 때 앞면이 나올 확률 1/2 -> 동전을 던지는 횟수가 무한대로 갈수록 1/2에 가까워짐
* 가설이 주어진 데이터에 확률 분포(랜덤, 반복 가능, 실험적)를 적용함
* Bayesian
* 고정된 파라미터에 대해 불완전한 지식을 설명하기 위해 확률을 사용함
* 모든 것(가설, 데이터)에 확률 분포를 적용함
***
#### Null Hypothesis Significance Testing 1
**Introduction**
* Neyman-Pearson 패러다임을 주로 사용함
* ex) 동전을 10번 던졌을 때 앞면이 나오는 횟수
**Types of error**
**Composite hypothesis**
ex) 동전을 던졌을 때 나올 수 있는 앞면의 개수의 평균
**Null distribution:**
**High and low power test**
* both standard normal
* High power: 높은 검정력
* Low power: 낮은 검정력
**Designing a hypothesis test**
* Pick the null hypothesis H0.
* Decide if HA is one-sided or two-sided
* Pick the test statistic.
* ex) z-test, t-test, x^2-test
* Pick a significance level and determine the rejection region
* ex) 0.1, 0.05, 0.001
* Determine the power
**Critical values**
ex) critical value = 0.05
**p-values**
* reject region의 면적
ex) IQ의 normal distribution = N(100, 15^2)
9명의 학생들의 평균 IQ가 112일 때 신뢰수준 0.05로 H0을 reject할 수 있는가?
reject H0
+예시
---
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