Decision Theory and Bayesian Inference

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Please see the attached document with a Decision Theory and Bayesian Inference assignment. 

I dont know how to do this assignment so please include notes so I understand how it is done - so I can learn

 

 

An organizaton uses a spam flTering soFware To block email messages ThaT may poTentally be spammessages. ±he spam flTer can be seT To one o² Two securiTy modes: High-SecuriTy-Mode (H) or Low-SecuriTy-Mode (L).ExTensive evaluaton using a benchmark corpus consistng exclusively o²spammessages yields The²ollowing per²ormance sTatstcs ²or The spam flTer:96% o² Thespammessages are blocked in The High-SecuriTy-Mode.90% o² Thespammessages are blocked in The Low-SecuriTy-Mode.ExTensive evaluaton using a benchmark corpus consistng exclusively o²non-spam(legitmaTe) messagesyields The ²ollowing per²ormance sTatstcs ²or The spam flTer:10% o² Thenon-spammessages are blocked in The High-SecuriTy-Mode4% o² Thenon-spammessages are blocked in The Low-SecuriTy-Mode±he organizaton estmaTes ThaT 80% o² The messages ThaT iT receives arespammessages.(a) LeTPH(S∨´B)denoTe The conditonal probabiliTy ThaT a message ThaT is noT blocked by The spamflTer operatng in The High-SecuriTy-Mode is acTually a spam message. EstmaTePH(S∨´B).(b) LeTPH(´S∨B)denoTe The conditonal probabiliTy ThaT a message ThaT is blocked by The spamflTer operatng in The High-SecuriTy-Mode is acTually noT a spam message. EstmaTePH(´S∨B).(c) LeTPL(S∨´B)denoTe The conditonal probabiliTy ThaT a message ThaT is noT blocked by The spamflTer operatng in The Low-SecuriTy-Mode is acTually a spam message. EstmaTePL(S∨´B).(d) LeTPL(´S∨B)denoTe The conditonal probabiliTy ThaT a message ThaT is blocked by The spamflTer operatng in The Low-SecuriTy-Mode is acTually noT a spam message. EstmaTePL(´S∨B).(e) I² The cosT o² noT blocking aspammessage is $1 and The cosT o² blocking anon-spammessage is $10,should The organizaton operaTe The spam flTer in The High-SecuriTy-Mode? Why?(²)Recall ThaT The cosT o² noT blocking aspammessage is $1. AT leasT how high should The cosT o²blocking anon-spammessage be ²or a risk-neuTral ratonal decision maker To pre²er operatng Thespam flTer in The Low-SecuriTy-Mode?(g) LeT$ Cbe The amortzed cosT per message o² operatng The spam flTer. WriTe a shorT memo TheCIO o² The organizaton explaining aT mosT how highCcould be ²or The organizaton To use Thespam flTer wiTh The specifed per²ormance?

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• 1494557784-hw2Fall2016.docx