class8 - 26:010:680 Current Topics in Accounting Research...

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26:010:680 Current Topics in Accounting Research Dr. Peter R. Gillett Associate Professor Department of Accounting and Information Systems Rutgers Business School–Newark and New Brunswick
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Current Topics in Accounting Research March 9, 2011 Dr. Peter R. Gillett 2 OVERVIEW Valuation Networks * Shenoy-Shafer * Possibility Theory * Spohn’s Epistemic Calculus Homework 5 Imprecise Probabilities, Previsions & Gambles Homework 6 Readings for Week 9
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Current Topics in Accounting Research March 9, 2011 Dr. Peter R. Gillett 3 HUGIN The Aalborg architecture has been implemented in Bayesian Network software called HUGIN Download a demonstration version from http://www.hugin.com/productsservices/demo/ hugin-lite/200-hugin-lite-windows Recompute this example using HUGIN Add to the HUGIN model the observation that the student suffers from Insomnia , and examine what happens to the posterior probability of the student being Overworked as a result
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Current Topics in Accounting Research March 9, 2011 Dr. Peter R. Gillett 4 Shenoy-Shafer Architecture Building the Join Tree * Detailed algorithms were provided in the readings for Shenoy-Shafer Join Trees * Later work has proposed a refinement that is more efficient – Binary Join Trees * The Shenoy-Shafer algorithm was designed to work with both probabilities and belief functions * The axioms are fairly general, and the algorithm has been found to apply to many other valuations, such as Possibilities and Spohn’s Epistemic (Dis)beliefs
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Current Topics in Accounting Research March 9, 2011 Dr. Peter R. Gillett 5 Shenoy-Shafer Architecture Rules for propagation * There is no distinction between inward and outward passes Each node waits to send its message to a given neighbor until it has received messages from all its other neighbors When a node is ready to send its message to a particular neighbor, it computes the message by collecting all its messages from other neighbors, multiplying its own potential by these messages, and marginalizing the product to its intersection with the neighbor to which it is sending
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Current Topics in Accounting Research March 9, 2011 Dr. Peter R. Gillett 6 Shenoy-Shafer Architecture Let’s return to our example of cross, tired doctoral students – but, now adding the knowledge that the student suffers from Insomnia
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Current Topics in Accounting Research March 9, 2011 Dr. Peter R. Gillett 7 Shenoy-Shafer Architecture Join Tree { O , I , C } { I } { O } { C } { T } { O , I , T } { O , I }
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Current Topics in Accounting Research March 9, 2011 Dr. Peter R. Gillett 8 { O , I , C } { I } { O } { C } { T } { O , I , T } { O , I } Shenoy-Shafer Architecture Initially   ¬  .2 .8 o o ¬ .01 .99 i i ¬ 1 0 c c ¬ 1 0 t t ¬ 1 0 i i ¬ ¬ ¬¬ ¬ ¬ ¬¬ , , .96 , , .04 , , .90 , , .10 , , .60 , , .40 , , .01 , , .99 oic oi c o ic ¬ ¬ ¬ , , .98 , , .02 , , .80 , , .20 , , .90 , , .10 , , .05 , , .95 oit oi t o it
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Current Topics in Accounting Research March 9, 2011 Dr. Peter R. Gillett 9 { O , I , C } { I } { O } { C } { T } { O , I , T } { O , I } Shenoy-Shafer Architecture Propagation   ¬  .2 .8 o o ¬ .01 .99 i i ¬ 1 0 c c ¬ 1 0 t t ¬ 1 0 i i ¬ ¬ ¬¬ ¬ ¬ ¬¬ , , .96 , , .04 , , .90 , , .10 , , .60 , , .40 , , .01 , , .99 oic oi c o ic ¬ ¬ ¬ , , .98 , , .02
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This note was uploaded on 03/08/2012 for the course ACCT 680 taught by Professor Peterr.gillett during the Spring '11 term at Rutgers.

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class8 - 26:010:680 Current Topics in Accounting Research...

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