Is it possible to give any sensible taxonomy of "probability in the real world"? Here we show some ways in which people have tried to do so.

- 60G42 Martingales with discrete parameter
- 60G44 Martingales with continuous parameter
- 60G45 Martingale theory
- 60G46 Martingales and classical analysis
- 60G48 Generalizations of martingales
- 60G50 Sums of independent random variables; random walks
- 60G51 Processes with independent increments
- 60G52 Stable processes
- 60G55 Point processes
- 60G57 Random measures
- 60G60 Random fields
- 60G70 Extreme value theory; extremal processes

Here is an analogous list from Statistics, where the items represent methodologies.

- 62H12 Estimation
- 62H15 Hypothesis testing
- 62H17 Contingency tables
- 62H20 Measures of association (correlation, canonical correlation, etc.)
- 62H25 Factor analysis and principal components; correspondence analysis
- 62H30 Classification and discrimination; cluster analysis [See also 68T10, 91C20]
- 62H35 Image analysis
- 62H40 Projection pursuit
- 62H86 Multivariate analysis and fuzziness

But returning to the student's question, it's easy to give a list of 10 or 20 very broad areas in which probability is used. For instance (in alphabetical order)

- Bioinformatics
- Cognitive Science
- Finance Theory
- Information (Coding) Theory
- Mathematical Statistics
- Network Theory
- Population genetics
- Queueing Theory
- Reliability Theory
- Risk Theory
- Statistical Physics
- Theory of Algorithms

Creating such a refined list -- and writing the 100 Wikipedia articles! -- would constitute an extremely useful resource. Incidently, the existing Wikipedia article on applied probability is rather similar to what I have written above, but very few existing "topic articles" hit the style I am envisaging.

It's curious that nothing like the desired "list of 100" exists already. Within the research community, one can find lists of the topics of special sessions at academic conferences (a 2009 example) which reflect current research-level activity, but these tend to be methodology-based and relate to some rather narrow portion of an application topic. Occasional panel reports, such as a 2002 report Current and Emerging Research Opportunities in Probability, attempt a bigger picture, but ultimately give short lists of very broad areas like our 1-7 above, or (see e.g. an overview talk associated with report above) revert to talking about intrinsic mathematical structure.

- Classical probability (equally likely outcomes)
- Logical probability (probability as objective degree of belief)
- Frequency interpretations
- Propensity interpretations (probability inherent in the experimental set up)
- Subjective probability

- Windfalls or wind thefts
- Unforeseeable lost or gained opportunities
- Accidents
- Narrow escapes or flukish victimizations
- Coincidences (e.g. "being in the wrong place at the wrong time")
- Consequence-laden mistakes in identification or classification
- Fortuitous encounters
- Welcome or unwelcome anomalies (in generally predictable matters)
- Other people's actions having (un)favorable consequences for you
- Conscious risk-taking that works out well or badly

I collected seventeen ways in which unsought findings have been made.and gives real historical examples of each, in the contexts of science and invention. Interestingly, he interprets seredipity as

- Analogy
- One surprising observation
- Repetition of a surprising observation
- Successful error
- From side-effect to main effect
- From by-product to main product ('spin-off')
- Wrong hypothesis
- No hypothesis
- Inversion
- Testing of a popular 'belief'
- Child, student or outsider
- Disturbance
- Scarcity
- Interruption of work
- Playing
- Joke
- Dream or "forgetting-hypothesis"

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

In the areas above, people don't seem to pay much attention to taxonomies. In contrast, everyone who thinks abstractly about uncertainty and risk seems to devise thier own taxonomy ..... Here are a few examples.

The Intergovernmental Panel on Climate Change (IPCC) issues periodic reports, widely regarded as the most authoritative analysis of scientific understanding of climate change caused by human activity. Future predictions involve uncertainty, and they want their many authors to be consistent in how they write about uncertainty, so provide a technical document Guidance Notes for Lead Authors of the IPCC Fourth Assessment Report on Addressing Uncertainties from which I have extracted the table below, there labelled "A simple typology of uncertainties".

Type | Indicative examples of sources | Typical approaches or considerations |
---|---|---|

Unpredictability | Projections of human behaviour not easily amenable to prediction (e.g. evolution of political systems). Chaotic components of complex systems. | Use of scenarios spanning a plausible range, clearly stating assumptions, limits considered, and subjective judgments. Ranges from ensembles of model runs. |

Structural uncertainty | Inadequate models, incomplete or competing conceptual frameworks, lack of agreement on model structure, ambiguous system boundaries or definitions, significant processes or relationships wrongly specified or not considered. | Specify assumptions and system definitions clearly, compare models with observations for a range of conditions, assess maturity of the underlying science and degree to which understanding is based on fundamental concepts tested in other areas. |

Value uncertainty | Missing, inaccurate or non-representative data, inappropriate spatial or temporal resolution, poorly known or changing model parameters. | Analysis of statistical properties of sets of values (observations, model ensemble results, etc); bootstrap and hierarchical statistical tests; comparison of models with observations. |

Loss event frequency | |

Threat event frequency | Contact |

Action | |

Vulnerability | Control strength |

Threat capability | |

Probable loss magnitude | |

Primary loss factors | Asset loss factors |

Threat loss factors | |

Secondary loss factors | Operational loss factors |

External loss factors |

- Economic
- Geopolitical
- Environmental
- Societal
- Technological.