P&S L2 C1 S5
S5: Model: Useful, NOT correct
It is important to understand that models are NEVER correct. Models exist in an imaginary world of perfection, which abstracts from many, many complications of the real world. By definition of what a model is, they are not TRUE representations of reality. Nonetheless, we often regard the model as BEING the reality, and talk about the probability of a coin flip being heads -- it is too complicated to say that we are talking about the probability in a MODEL of the coin flip as a random event. This mistaken language leads to many confusions. The important questions about models are not whether the assumptions match (they will NEVER do) but whether identifying the model with reality leads to useful insights. Whether or not the model is useful is ALWAYS an empirical matter -- it depends on the real world context, and cannot be decided in advance of the application.
The MOST important use of probability models: To assess the chances of an event --
More than 99%: Very Likely to Happen
More than 95%: Likely to Happen
Between 5% and 95%: Uncertain -- may or may not happen
Less than 5%: Unlikely to happen
Less than 1%: Highly Unlikely
Calculating probabilities allows us to forecast the future, which is extremely useful in many situations. For example, in order to decide whether or not to take an umbrella, we would like to be able to estimate the probability of rain. PROBABILITY MODELS of real world situations allow us to make such forecasts. The reliability of such models is assessed in terms of how well they perform in terms of providing accurate probabilities of future events.
Informal and subjective methods of assessing probabilities of future events can be extremely bad. That is why models are useful to provide a more systematic method of assessing probabilities. NONETHELESS, a model is NO GUARANTEE of a reliable forecast, BAD models can provide VERY BAD forecasts, and also an assurance and confidence that is not justified.
Jean Drapeau: Mayor of Montreal:
The Olympics can no more lose money than a man can have a baby. -
A Wrong Forecast, with important consequences:
Drapeau's mishandling of the construction of the Olympic Games facilities resulted in massive cost overruns and left the city with a debt of over $1 billion that has taken its citizens over thirty years to fully pay off.
