What is Subjective (Bayesian) Probability?

http://www.criticalthinkeracademy.com

This is a sample video from my tutorial course titled "What is Probability?". Click the link above to see the full table of contents on CriticalThinkerAcademy.com.

Probability concepts are important in everyday reasoning about chance and uncertainty, in the formal methods of inductive logic and scientific reasoning, and in philosophical arguments of many different kinds.

This course focuses on the MEANING of probability, how to understand the different things that people mean, or what scientists or mathematicians mean, when they use expressions like "the odds of getting a 2 on a dice roll is 1/6", or "the probability of precipitation is 60%", or "the probability of the atom decaying in one hour is 50%".

There are, in fact, several different views of how such language should be interpreted. Becoming familiar with these views will help you to think more clearly and critically about situations where probability concepts arise.

Table of Contents:

Part 1: Introduction
1.1 Probability: Why Learn This Stuff?
1.2 What is Inductive Logic?
1.3 Probability as a Mathematical Object vs. What That Object Represents

Part 2: Interpretations of The Concept of Probability
2.1 Classical Probability
2.2 Logical Probability
2.3 Frequency Interpretations
2.4 Subjective Probability
2.5 Propensity Interpretations

Category:

Education

Tags:

• subjective probability
• Bayesian probability
• probability
• von Mises
• Frank Ramsey
• Bayesianism
• Bayesian

[MrFairObserver]

At the end you mentioned Glymour's argument about the "problem of old evidence" as an objection to Bayesian probability.

Yet, the "problem of old evidence" is bogus, and no one outside of philosophy take it seriously. Glymour in his paper used sloppy notation and conditioned on the wrong events, and thus reached a nonsensical result.

I suggest you read the presentation "Bayesians Can Learn From Old Data", at omega.albany.edu:8008/ME07dir/­WilliamJefferys/slides.pdf

[PhilosophyFreak]

@MrFairObserver That's a great link, thanks for that. I'm not an expert on interpretations of probability theory so I can't judge the adequacy of Jaynes' approach to these issues, but I do agree that he's under-read among philosophers who write on probability theory.

[gjsterp]

I don't see how "probability" can be said to be 'true'.

It is only a chance that it will be true.

But the 'truth' of the probability is only known after the fact.

After the coin is tossed.

The 'truth' will change after each toss.

[PhilosophyFreak]

@gjsterp Any interpretation of probability needs to make sense of statements like "It's true that the probability of a fair coin landing heads is 0.5". They'll differ on what makes such a claim true. Sounds like you're thinking of "relative frequency" interpretations of probability? Check out the "video response" on frequency interpretations of probability.

[menonfire12]

Do you have complete courses on decision theory and on game theory on the critical thinking academy ??

[PhilosophyFreak]

@menonfire12 Not yet, but these are planned. First up I'm finishing a course on the basic rules for reasoning with probabilities. Then I'm doing a course on fallacies of probabilistic reasoning. I do have plans for a course on elementary decision theory and game theory, because this helps to set up a whole other set of fallacies and cognitive biases that we can talk about. If you go to my site you can sign up for an email newsletter and I can let you know when new courses become available.

[powerdriller10]

@ChadSmith1452

How is "Dutch Book" worded in Holland ? Can you imagined calling "nigger idea" to an idea that makes no sense? It would create a lot of fuss and even a few murders, and rightly so. (Let´s hope that nobody pays attention to expressions like "black list" or "dark side of the Force".)

Netherlanders should protest and ask for compensation against the Book Printers that are publishing Bayesian books. And Germans should also do, because they call themselves Dutchs.

[CPLains]

Good video! Funny point about the "very reliable test" that i learned somewhere: If the test is 95% accurate, and we give the test to 20 people, then if one of them tests positive, then it's equally likely that it is a false positive as it is that that person is positive positive. ;)

[Spadie1]

Thanks for the great lecture. Very well produced, very good content.

[ChadSmith1452]

@PhilosophyFreak Oops. I meant to reply to you, not menonfire12.

[ChadSmith1452]

@menonfire12 I would surmise that the term "Dutch Book" is in keeping with the the tradition of affixing "Dutch" as a modifier to connote ersatz inauthenticity (eg, Dutch oven, Dutch courage). This has its origins in the seventeenth century rivalry between the Dutch and the English (rather like Italians referring to syphilis as the "French disease", and vice versa).