Math 319 - Outside Readings for Unit I

Introduction, Probability and Bayes' Theorem

 

Both of these books are on reserve in the Library:

  1. Judgment and Decision Making edited by Arkes and Hammond (JADM)
  2. Risk Assessment and Risk Management The Annals of the American Academy of Political and Social Science Vol. 545 May 1996 (RARM)

 

In JADM read Judgment under uncertainty: Heuristics and biases pp.38-55 by Tversky and Kahneman

These authors have done classic work on the difficulty of making subjective estimates of probabilities. We saw a little of their work in the example in class about being a librarian and a feminist. Being aware of the pitfalls in making probability estimates should help you make more accurate estimates.

This article has some tough slogging and you are welcome to read and discuss it in groups.

What is meant by each of the following terms?

  1. Representativeness


    1. Insensitivity to possibility of prior outcomes


    2. Insensitivity to sample size


    3. Misconceptions about chance


    4. Insensitivity to predictability


    5. Illusion of validity


    6. Misconceptions about regression


  2. Availability


    1. Biases due to retreivability of instances


    2. Biases due to effectiveness of a search set


    3. Biases of imagineability


    4. Illusory Correlation


  3. Anchoring and Adjustments (We will talk about this more later)


    1. Insufficient adjustment


    2. Biases in evaluation of conjunctive and disjunctive events


    3. Anchoring in assessment of subjective probability distributions

 

 

 

 

You should also read at least two of the following articles. In reading these articles I want you to pay attention to the general ideas, rather than the details, and to gain an appreciation of some of the practical problems we have in using utility theory, and to gain an appreciation of the wide spread application of risk analysis. You should also ask yourself if the authors have any biases you should beware of.

 

 

i. In JADM A computer-based system for identifying suicide attemptors p. 432-446 by Gustafson, Tianen and Greist.

This article compares a Bayesian and a regression model for predicting who will attempt suicide by first identifying those variables which seem to have most influence (e.g. lives alone, age, etc.), and then using both models. Each of the two models is developed based on data from staff at a mental health center and based on data from psychiatry residents. The models are used to predict both successful and unsuccessful attemptors.

Please note the following about the regression model: In Math 118 you learned how to use one variable, x, to predict another variable, y by fitting data to a line

y = a + b x

 For example, if x is number of cigarettes smoked a day, and y is age at death you might develop an equation such as

 y = 75 - 20 x

 If you have more than one variable to use in prediction then instead of fitting a line to your data you fit a plane. If the variables are x1, x2, etc. then the equation becomes

 

y = a1(x1) + a2(x2) etc.

 

For example, if x1 is number of cigarettes smoked a day and x2 is % overweight then we might find an equation for y = age at death

 y = 76 - 20 x1 - 5 x2

  In RARM How risks are identified and assessed pp15-24 by Graham and Rhomberg. This article discusses public health risks by people in the field.

 

  1. In RARM Valuing risks to the environment pp. 54-63 by Gregory Brown and Knetsch. This article discusses difficulties in setting values (utilities) for different goals when there are many "stakeholders" (people with an interest in the solution of the problem). Again, the authors are in the field.

 

  1. In RARM The role of values in risk management pp 126-134 by Keeney. This article focuses on the differences in individuals' vs. public (governmental) bodies' risk assessment, with examples where the author argues for non-intervention. What do you think of his choice of examples?

 

 

I will also be asking you to read Choices, Values and Frames by Kahneman and Tversky — reading notes and reference to be provided.