Risk Assessment and Decision Analysis with Bayesian Networks

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3

Measuring Uncertainty: The

Inevitability of Subjectivity

3.1 Introduction

Probability is the term used to quantify our uncertainty about some

unknown entity—be it a future event, a thing whose properties we are

unsure of, or even a past event about which we are unsure. We made

numerous references to probability in Chapters 1 and 2 without actually

dening it or explaining how to compute it in particular instances. What

should be clear from Chapter 1 is that probability reasoning can be

extremely confusing and difcult even for highly trained professionals.

Moreover, many professional statisticians use a different notion of prob-

ability (called frequentist) to the one (called subjective) that plays a cen-

tral role in our approach to risk assessment. So, it is clear that we need to

get the basic rules of probability right. To prepare for that (which we do

in Chapter 4) this chapter lays the necessary groundwork by discussing

the different approaches to measuring uncertainty.

Because we are interested in risk, the kinds of uncertain events we have

to deal with are very diverse. At one extreme we have events where we

apparently have good understanding of the uncertainty, like:

◾ The next toss on a coin will be a head.

◾ The next roll of a die will be a 6.

At the other extreme are events where we apparently have a poor under-

standing of the uncertainty like:

◾ England will win the next World Cup.

◾ My bank will suffer a loss (such as a fraud or lost transaction)

tomorrow.

◾ A hurricane will destroy the White House within the next

5years.

Or even an “unknown” event like

◾ My bank will be forced out of business in the next two years as

a result of a threat that we do not yet know about.

Visit www.bayesianrisk.com for your free Bayesian network software and models in

this chapter