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The probability that gross domestic product (GDP)

The probability that gross domestic product (GDP) decreases is 20%. The probability that unemployment increases is 10%. The probability that unemployment increases given that GDP has decreased is 40%. What is the probability that GDP decreases given that unemployment has increased? 2. An analyst develops a model for forecasting bond defaults. The model is 90% accurate. In other words, of the bonds that actually default, the model identifies Exhibit 6.8 Covariance Matrices Network 1 Network 2 E S1 S2 E S1 S2 E 24% 12% 5% E 24% 12% 2% S1 12% 25% 2% S1 12% 25% 4% S2 5% 2% 25% S2 2% 4% 24% c06.indd 132 11/11/13 6:56 PM Bayesian Analysis 133 90% of them; likewise, of the bonds that do not default, the model correctly predicts that 90% will not default. You have a portfolio of bonds, each with a 5% probability of defaulting. Given that the model predicts that a bond will default, what is the probability that it actually defaults?

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