7/24/2019 Revising Judgments in the Light of New Information

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FLORENTINA ANDRE

21914312

YP52A

Revising judgments in the light of new infom!tion

Bayes theorem

In "!#es$ theoem !n initi!l %o&!&ilit# estim!te is 'nown !s ! prior probability( Thus the

m!'eting m!n!ge$s !ssessment th!t thee w!s !n)*+ %o&!&ilit# th!t s!les of the ,!l,ul!to

would e!,h &e!'-even levelw!s ! %io %o&!&ilit#( .hen "!#es$ theoem is used to modif#! %io%o&!&ilit# in the light of new infom!tion the esult is 'nown !s ! posterior

probability(

The effect of new information on the revision of probability judgments

It is inteesting to e/%loe the el!tive in0uen,e whi,h %io %o&!&ilities !nd new

infom!tion h!ve on the esulting %osteio %o&!&ilities( 1u%%ose th!t ! geologist is involved

in ! se!,h fo new sou,es of n!tu!l g!s in southen Engl!nd( In one %!ti,ul! lo,!tion he is

!s'ed to estim!te on the &!sis of ! %elimin!# suve# the %o&!&ilit# th!t g!s will &e found

in th!t lo,!tion( 3!ving m!de his estim!te he will e,eive new infom!tion fom ! test

dilling(

pplying Bayes theorem to a decision problem.e will now ,onside the !%%li,!tion of "!#es$ theoem to ! de,ision %o&lem4 ! %o,ess

whi,h is sometimes efeed to !s posterior analysis( This sim%l# involves the use of the

%osteio %o&!&ilities !the th!n the %io %o&!&ilities in the de,ision model( .e ,!n use

"!#es$ theoem to modif# the et!ile$s %io %o&!&ilities in the light of the new infom!tion

ssessing the value of new information

New infom!tion ,!n emove o edu,e the un,et!int# involved in ! de,ision !nd thee

in,e!se the e/%e,ted %!#off 3oweve in m!n# ,i,umst!n,es it m!# &e e/%ensive to o&t!in

infom!tion sin,e it might involve fo e/!m%le the use of s,ienti, tests the eng!gement of

the sevi,es of ! ,onsult!nt o the need to ,!# out ! m!'et ese!,h suve#( If this is the

,!se then the 6uestion !ises !s to whethe it is woth o&t!ining the infom!tion in the st

%l!,e o if thee !e seve!l %otenti!l sou,es of infom!tion whi,h one is to &e %efeed7sometimes the %o,ess of detemining whethe it is woth o&t!ining new infom!tion is

efeed to !spreposterior analysis8(

The e!pected value of perfect information

In m!n# de,ision situ!tions it is not %ossi&le to o&t!in %efe,tl# eli!&le infom!tion &ut

nevetheless the ,on,e%t of the e/%e,ted v!lue of %efe,t infom!tion 7E9PI8 ,!n still &e

useful( Thee is !n !lten!tive w!# of loo'ing !t the v!lue of infom!tion( New infom!tion

,!n &e eg!ded !s &eing of no v!lue if #ou would still m!'e the s!me de,ision eg!dless of

wh!t the infom!tion told #ou( If the f!m m!n!ge wee to go !he!d !nd %l!nt ! ,o% of

%ot!toes wh!teve the test indi,!ted then thee would ,le!l# &e no %oint in &u#ing the test(

Infom!tion h!s v!lue if some of its indi,!tions would ,!use #ou to t!'e ! diffeent de,ision

th!n the one #ou would t!'e without the &enet of the infom!tion("ractical considerations

.e will now outline ! num&e of e/!m%les of the !%%li,!tion of the methods we h!ve just

dis,ussed !nd ,onside some of the %!,ti,!l %o&lems involved( :le!l# it is e!sie to

identif# the e/%e,ted v!lue of %efe,t !s o%%osed to im%efe,t infom!tion !nd we

e,ommend th!t in gene!l ,!l,ul!ting the E9PI should &e the st ste% in !n# infom!tion-

ev!lu!tion e/e,ise( The E9PI ,!n !,t !s ! useful s,een sin,e some sou,es of infom!tion

m!# %ove to &e too e/%ensive even if the# wee to offe %efe,tl# eli!&le d!t! whi,h is

unli'el#(