“Should convicted murderers be subject to a death penalty”
is a solution looking for a problem
“Why should convicted murderers be put to death?” – explores the reasons
“ Many convicted murderers are being released back into society and murder again. A determination must be made regarding how to prevent convicted murderers from killing again ”
Choices: there are always at least two alternatives (one is “do nothing”)
Uncertainties: situations beyond the direct control of the decision maker; their individual probability of occurrence is only estimable within a certain range
Objectives: methods of establishing the criteria used to measure the value of the outcome
The closer the outcome matches the criteria the more desirable
“ to increase profits” is vague
“ to increase them by 10% over last year” is specific and better
Influence diagram: a simple method of graphing the components of a decision and linking them to show the relationships between them
Decision Objective Uncertainty Decision Uncertainty Decision tree: another diagram that models choices and uncertainties and can be extended to include multiple, sequential decisions
Win £5000 Lose wager Make large profit Lose most of stake Lose/gain nothing 10:1 bet on a horse Invest in stock Do nothing Horse wins Horse loses Significant rise Stocks fall Minor profit/loss Steady change http:// www.psychwww.com/mtsite/dectree.html
The probabilities of all outcomes of an event must add up to the probability of their union
The total probability of a complete set of outcomes must equal 1
But how accurate are our estimates?
16.
Lets look at a Decision Tree again 0.5 Lets keep the maths easy by using p=0.5 for all uncertainties 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 P=0.25 P=0.25 P=0.5 P=0.25 P=0.25 P=0.25 P=0.25 A A1 B1 B2 B ALL uncertainties for events = 1
Direct probability forecasting — an expert is simply asked to estimate the chance that an outcome will occur
Odds forecasting — a series of bets are proposed to determine how strongly the bettor feels an event will occur
Comparison forecasting — similar to odds forecasting except that one game has known probabilities
19.
Calculating Odds in a D/Tree Bet on team A Bet against team A Team A wins Team A loses Team A loses Team A wins £Xx -£X £Y -£Y P(Team A wins)=Y/(X+Y) see text for detail, pg 125/6
Probabilities for complex events may be more easily generated by using conditional probabilities within subsets of the events
For example, it may be easier to forecast sales of a weather-related product by forecasting sales under good weather, then bad weather and then considering the probability of bad weather
A decision maker is said to be well calibrated if his probability forecasts are correct at about the same rate as his confidence in them (9 out of 10 times his 90% confidence intervals should be correct).
Probabilities are a kind of average
Calibration requires years of experience and feedback to develop.
most of us are NOT well calibrated
Better to use confidence intervals
Most of us are too optimistic and our intervals are too tight.
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