Imprecise Probabilities
- Represent probability as a range when exact likelihoods are unknown.
- Applied when information is limited or uncertainty is high (e.g., weather, medical diagnosis).
- Useful for decision making by presenting a span of possible probabilities rather than a single value.
Definition
Section titled “Definition”Imprecise probabilities refer to situations where the exact probability of an event occurring is not known, but a range of possible probabilities can be estimated. This type of probability is often used in situations where there is uncertainty or limited information available.
Explanation
Section titled “Explanation”Imprecise probabilities provide a set or interval of possible probability values instead of a single point estimate. They are used when available information does not justify a precise probability. Methods for estimating imprecise probabilities mentioned in the source include subjective probabilities (based on an individual’s beliefs or judgments), objective probabilities (based on objective data and statistical analysis), and interval probabilities (which provide a range based on the minimum and maximum likelihood).
Examples
Section titled “Examples”Weather forecasting
Section titled “Weather forecasting”Meteorologists may not be able to predict the exact probability of precipitation on a given day, but they can provide a range of possible probabilities based on current weather patterns and historical data. For example, they may state that there is a 30-60% chance of rain on a particular day.
Medical diagnosis
Section titled “Medical diagnosis”Doctors may not be able to provide an exact probability of a patient having a certain condition, but they can provide a range of possibilities based on symptoms, test results, and other factors. For example, a doctor may state that there is a 60-80% chance that a patient has a particular illness based on their symptoms and test results.
Use cases
Section titled “Use cases”Imprecise probabilities are often used in decision making because they present a range of possibilities to consider. Examples from the source:
- In weather forecasting, a person may decide to bring an umbrella if the probability of rain is toward the higher end of the stated range.
- In medical diagnosis, a patient may choose to undergo further testing or treatment if the probability of having a condition is toward the higher end of the stated range.
Related terms
Section titled “Related terms”- Subjective probabilities
- Objective probabilities
- Interval probabilities
- Decision making