FoDAL5_Bayesian Inference

Bayes ' Rule event M. D

PRCMID) = Prc☐fpjPrprtporto.no/Pr(D1M).Pr ( in)to

Pr (MID) = c. Pr ( Dlm) . Pr 1M)

possibly unknown

posterior but fixed constant c.LCM) likelihood prior

up/MID) ✗ f (D) in) . r ( M)org Max avg Maxin ↳ MAP estimate an ↳MLE

Average HeightÉ✗z

..in} = { 113,5, 9,12}

estimate freight M of typical student

prnrrcm)=No÷m?¥¥f¥)T 9mean std -dev

a-66 6--6inches

MLE ( from likelihood of data D)= 5.5 feet

likelihood f (Dlm) = IT gcx) = IT N✗ED

9550mL 0--2 independence✗c-D

"'"( ✗ )

=¥☐(¥,

- expff-c.mx)))#e- b

posterior f-o.o ran)=z¥exp( - %¥)

PCM ID) ✗ f(DIM) . rfiiijooz

h(p(MID)) ✗ h(f(DIM)) + ln(r(M)) + C• €4,> f-£1m-×5))É%u-665 + c

'

☒ -4,9%(14×5) -u-66$ + c"

✗ED

Weighted Average (✗i. wi)-

n values ×, ,-1> , .

. . in weightn weights w, , we , . . Wn Wi 20

É Wi - ✗ i

É=i -w= É w :i - i

ii. wipi =to

e- [oil]E-[ = É pi - ✗ i n

in &:p : -I

n values ✗= { × ,,X> . . ..in)

s ( m) = ET (✗i -MY = É M'- zxim - xi

?

I=\ [=\

= nm?

- ( zÉ✗i)M+Éx ,

?

d- 1 i - i¥s dscm) "

I= 2h M - Z & ✗i =o

i-IM-n-i.I.li

p (MID) ✗exp (h(p(MID)±c))

• compare model S

M, ,Mz PIM .

I D) > pflhz I D)=z

p(MID)• Marginalize over models

§ PCM I D) .HCM) on

M*=azY§caiM£M&ÉD)