๋ณธ๋ฌธ ๋ฐ”๋กœ๊ฐ€๊ธฐ

Statistics/Bayesian Statistics

์ผค๋ ˆ์‚ฌ์ „๋ถ„ํฌ(Conjugate prior distribution)

์ผค๋ ˆ์‚ฌ์ „๋ถ„ํฌ(Conjugate prior distribution)์— ๋Œ€ํ•ด ์•Œ์•„๋ณผ ๊ฒƒ์ด๋‹ค. ๋‹ค๋ฃฐ ๋‚ด์šฉ์€ ๋‹ค์Œ๊ณผ ๊ฐ™๋‹ค.

 

1. ์ผค๋ ˆ์‚ฌ์ „๋ถ„ํฌ์˜ ์ •์˜

2. ์ผค๋ ˆ์‚ฌ์ „๋ถ„ํฌ์˜ ์˜ˆ์ œ

 

1. ์ผค๋ ˆ์‚ฌ์ „๋ถ„ํฌ์˜ ์ •์˜

 

์ผค๋ ˆ์‚ฌ์ „๋ถ„ํฌ์˜ ์ •์˜๋Š” ๋‹ค์Œ๊ณผ ๊ฐ™๋‹ค.

 

 

โ–ท ์ฆ‰, ์‚ฌ์ „๋ถ„ํฌ(Prior distribution)์™€ ์‚ฌํ›„๋ถ„ํฌ(Posterior distribution)๊ฐ€ ๋™์ผํ•œ ๋ถ„ํฌ์กฑ์— ์†ํ•˜๋ฉด ์‚ฌ์ „๋ถ„ํฌ๋ฅผ ์ผค๋ ˆ์‚ฌ์ „๋ถ„ํฌ๋ผ๊ณ  ํ•œ๋‹ค.

 

โ–ท ์ผค๋ ˆ์‚ฌ์ „๋ถ„ํฌ๋ฅผ ์‚ฌ์šฉํ•˜๋Š” ์ด์œ ๋Š” ์‚ฌํ›„๋ถ„ํฌ์˜ ๊ณ„์‚ฐ์ด ํŽธ๋ฆฌํ•ด์ง€๊ธฐ ๋•Œ๋ฌธ์ด๋‹ค.

 

๋Œ€ํ‘œ์  ์ผค๋ ˆ์‚ฌ์ „๋ถ„ํฌ๋Š” ๋‹ค์Œ๊ณผ ๊ฐ™๋‹ค.

 

 

2. ์ผค๋ ˆ์‚ฌ์ „๋ถ„ํฌ์˜ ์˜ˆ์ œ

 

๋ฌธ์ œ)

 

์‚ฌ์ „๋ถ„ํฌ๊ฐ€ ๋ฒ ํƒ€๋ถ„ํฌ์„ ๋”ฐ๋ฅด๊ณ  ๊ฐ€๋Šฅ๋„ ํ•จ์ˆ˜๊ฐ€ ๋ฒ ๋ฅด๋ˆ„์ด ๋ถ„ํฌ๋ฅผ ๋”ฐ๋ฅผ ๋•Œ, ์ด ์‚ฌ์ „๋ถ„ํฌ๊ฐ€ ์ผค๋ ˆ์‚ฌ์ „๋ถ„ํฌ์ž„์„ ๋ณด์—ฌ๋ผ.

 

ํ’€์ด)

 

โ–ท ์œ„์˜ ๊ฒฐ๊ณผ๋ฅผ ํ†ตํ•ด ์‚ฌ์ „๋ถ„ํฌ์™€ ์‚ฌํ›„๋ถ„ํฌ๊ฐ€ ๋ฒ ํƒ€๋ถ„ํฌ๋ฅผ ๋”ฐ๋ฅด๋Š” ๊ฒƒ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ๋‹ค. ๋”ฐ๋ผ์„œ ์ผค๋ ˆ์‚ฌ์ „๋ถ„ํฌ๋ผ ํ•  ์ˆ˜ ์žˆ๋‹ค.

 

โ–ถ ๊ท ์ผ๋ถ„ํฌ๋Š” ๋ฒ ํƒ€๋ถ„ํฌ์˜ ํŠน์ˆ˜ํ•œ ๊ฒฝ์šฐ๋กœ, ๊ท ์ผ ๋ถ„ํฌ๋ฅผ ์‚ฌ์ „๋ถ„ํฌ๋กœ ์‚ฌ์šฉํ•˜์—ฌ๋„ ์‚ฌํ›„๋ถ„ํฌ๋กœ ๋ฒ ํƒ€๋ถ„ํฌ๊ฐ€ ๋‚˜์˜ค๊ฒŒ ๋œ๋‹ค.

 

โ–ถ ๊ฐ€๋Šฅ๋„ ํ•จ์ˆ˜๊ฐ€ ์ดํ•ญ๋ถ„ํฌ์ผ ๊ฒฝ์šฐ์—๋„ ๋ฒ ํƒ€๋ถ„ํฌ๊ฐ€ ์ผค๋ ˆ์‚ฌ์ „๋ถ„ํฌ์ด๋‹ค. ์ด๋Š” ๋ฒ ๋ฅด๋ˆ„์ด ๋ถ„ํฌ์™€ ์ดํ•ญ๋ถ„ํฌ์˜ ๊ฐ€๋Šฅ๋„ ํ•จ์ˆ˜ ํ˜•ํƒœ๋กœ๋ถ€ํ„ฐ ์ถ”๋ก ํ•  ์ˆ˜ ์žˆ๋‹ค.

 


Reference:

์ •์œค์‹, ใ€Œ๋ฒ ์ด์ง€์•ˆ ํ†ต๊ณ„ํ•™์˜ ์ด๋ก ·๊ณ„์‚ฐ ๋ฐ ์‘์šฉใ€, ์ž์œ ์•„์นด๋ฐ๋ฏธ(2018), p132

"์ผค๋ ˆ์‚ฌ์ „๋ถ„ํฌ Conjugae Prior," ์ƒ์ƒˆ์šฐ์ดˆ๋ฐฅ์ง‘, https://freshrimpsushi.tistory.com/712.

"Bayesian Statistics: From Concept to Data Analysis," Coursera, https://www.coursera.org/learn/bayesian-statistics/.