Second and higher-order probabilities

In summary, the conversation discusses the concept of "second-order probabilities" and how they differ from joint and conditional probabilities. The idea is that these probabilities are the likelihood that the probability of an event is a certain value, and they can be affected by random and inaccurate data. However, higher-order probabilities, defined as the CDF of a random variable, are not considered useful as they are uniformly distributed over [0,1]. Some decision theories do incorporate second-order probabilities, but they are not universally accepted.
  • #1
lolgarithms
120
0
Why do I never hear of "second-order probabilities" (probability that the probability of an event is x. for example, you pick a box at random out of 3 boxes, and each box can have either 1, 3 or 5 red marbles out of six marbles)? can measurement or calculation of probability not be affected by random and inaccurate data?
 
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  • #2
How is your concept different from joint probability? How is it different from conditional probability?

Alternatively, you can define higher-order probability as follows. Let P = Prob{X < x} = CDF(x). Since X is a random variable, so is P (because it is a function of a random variable, with CDF of X as the link function). As a random variable, P is distributed uniformly over [0,1]. Defined this way, higher-order probabilities are not interesting: they are all distributed uniformly over [0,1].
 
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  • #3
Decision theory does sometimes use second-order probabilities, although they are distrusted by some.

google has the answers.
 

Related to Second and higher-order probabilities

What are second and higher-order probabilities?

Second and higher-order probabilities refer to the likelihood of an event occurring based on previous probabilities or events. These probabilities take into consideration multiple factors and can be more complex than first-order probabilities.

How are second and higher-order probabilities calculated?

Second and higher-order probabilities are typically calculated using mathematical formulas or statistical methods. These calculations often involve taking into account multiple variables and their respective probabilities.

Why are second and higher-order probabilities important?

Second and higher-order probabilities are important because they provide a more accurate representation of the likelihood of an event occurring. They take into account more information and can better predict outcomes.

What is the difference between first-order and higher-order probabilities?

The main difference between first-order and higher-order probabilities is the level of complexity. First-order probabilities only consider one variable, while higher-order probabilities take into account multiple variables and their respective probabilities.

Can second and higher-order probabilities change?

Yes, second and higher-order probabilities can change as new information or events occur. As more data is gathered, the probabilities can be updated to reflect the most current and accurate prediction of an event.

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