Anterior Probability

Is there such thing as an anterior probability? I cannot find a definition online…

I’ve never heard of it.

In front of what?

i think this is an invented term by OP. He found Posterior probability - due to Bayes - and thought the opposite is “Anterior”. It just happens to be the original probability before you revise your expectations with Bayes - is called “probability”.

a priori vs a posteriori.

Got it.

"…if an analyst already knows that the firm outperformed and wants to find the probability that the economy did well, the analyst would obtain a

1. posterior probability

2. subjective probability

I feel like the answer would be 2 instead of 1. However, they say the answer is posterior probability, given the fact you are using updated information.

Why wouldn’t it be subjective probability? The words “did well” seem subjective to me…

Subjective probability means a probability based on someone’s opinion or gut feeling, rather than on empirical evidence.

An economy “doing well”, however subjective, is, nonetheless, empirical evidence.

A posterior probability is one that’s been updated based on new evidence. Say . . . evidence that the enonomy’s done well.

“Anterior” probability, as the OP called it, is referred to as an “a priori” (or just the “prior”) probability (as S2000 brought up). Try googling either of those.

What is an example of a subjective probability vs. a posterior probability in a situation like this, where for example we want to find the probability of the economy doing well give the outstanding performance of the company?

I think S2000 had a good explanation, but it’s important to understand that a priori probabilities can be objective (empirical) or subjective.

A subjective probability can be thought of as a degree of belief. Imagine you and your friend go to a hockey game. You may believe (gut feeling or you really like one team), that your team has an 80% chance of winning. The guy behind you hates your team and he believes they have a 10% chance of winning. These are both subjective.

Your friend looked at your team’s winning percentage for the current (or past) season and saw it was 65%, so he believes they have a 65% chance of winning. This is objective.

These are all prior (or a priori) probabilities.

Now, let’s go one step further. Assume your friend, who set the a priori probability to 0.65, incorporated the new information about the current score and periods remaining, but his posterior probability was unchanged and equaled 0.65. This could be interpreted as useless information (since we have the same probability before and after the information).

Hope this helps!

Edit: I totally zoned out on the fact that you wanted something to do with the economy. Hang on.

So you want to find the probability the economy does well, given the current performance.

Subjective: You go by “feel”-- growth has occured above 5% for 3 months, I think there’s an 80% chance it grows by 5% next month because I can “feel” the economy’s direction and the past performance makes me optimistic.

Objective: Your friend looks at historical data and sees that 10 out of 15 months had growth of 5% if they were preceded by 3 months of growth of at least 5%. He says there is a 67% chance next month there is growth of 5%, because the last three months were at least 5% growth.

If you want, you can think of these as a priori probabilities. To get to a posteriori probability, you could incorporate other information, say, a sudden decline in the stock market this month, which might alter the probability you already came up with (44% from the initial 67%, for example).

An analyst determined probabilities that a firm will outperform, do about average or underperform given a great economy, an average economy or a weak economy. If the analyst already knows that the firm outperformed and wants to find the probability that the economy did well, the analyst would obtain

1. posterior probability

2. subjective probability

What I do not get is how would you know in this situation whether the probabilities were derived objective or subjectively. Are we supposed to assume that performance of a firm or economy is based on objective factors?

I see what you’re looking for here. It’s a posterior probability because it takes the prior probability and updates it somehow to give a posterior probability (the updating is the key). I think the point here is that the analyst isn’t just pulling a number out of thin air, but rather, he is doing an analysis and incorporating new information. So for this question, he already has P(performance | economy state), but he wants P(economy state| performance). This should be another clue.

Ok. So since there was a process to determine the probability of the state of the economy given strong performance of the company, it is a posterior probability rather than a subjective probability, which would “guess” the probability for the state of the economy?

For the context of the exam, I think that will get you the answers you need. Just remember that a posterior probability comes from incorporating information to update the prior probability. (The CFA institute seems to think that can only be objective, unless I’m missing something about their point of view.)