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?
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
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.