Uncertainty - what do we mean?

This website is about the use of probability and statistics when dealing with uncertainty, where we use 'uncertainty' in a slightly restricted way. We are only concerned about situations in which individuals or society are uncertain about what is true, which means that we only worry about things that can, at least in principle, be eventually found out to be true or not.

So we are happy to deal with -

• uncertain features of the future, such as how long you will live, the winner of the US Presidential election, mean rise in global temperature by 2100, and so on
• uncertain aspects of the present, such as the average benefit of a drug, what cards have been dealt,
• uncertain events in the past, such as who was Jack the Ripper.

This means that we do not deal with situations such as

• is there a God?
• other more general uses of 'uncertainty', such as being uncertain whether to have rice or noodles.

Even when used in this somewhat restricted sense, we can identify different ways in which uncertainty comes into any attempt to use mathematical and probability models to predict what is going to happen. The modeling process can be thought of as encompassing four main levels of uncertainty:

1. Uncertainty about specific future, present, or past events. This form of uncertainty could be characterized as betting odds or ‘chance’ and has a long history.
2. Uncertainty about the parameters within models: this form of uncertainty dominates biostatistics, where data and judgment may coexist (Bayesian analysis). In areas such as climate modelling, it relates to value uncertainty or ‘likelihood’ (eg about mean temperature increases)
3. Uncertainty about the structure of models: i.e., the degree of confidence in the underlying science. Can a given model be said to have a probability when all models are ‘wrong’?
4. Uncertainty about the relevance to particular problems of the entire modeling process. Are there some possibilities that have not even been considered? (so-called ‘black swan outliers’ like the collapse of the Soviet Union or 9/11 — extreme events that may have been foreseeable but have not been foreseen). Cromwell's Law refers to the principle that no imaginable events should be given zero probability.
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