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NeroTulip


Total Posts: 1034
Joined: May 2004
 
Posted: 2019-10-06 20:57
I am trying to find a good practical example of Bayes' theorem use in finance. I have a great example in medicine with cancer screening, but I struggle to find something cool in finance. Should be simple enough for undergraduate students, does anyone have any ideas?


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nikol


Total Posts: 794
Joined: Jun 2005
 
Posted: 2019-10-06 22:21
Risk management problem:

P(account of client-A is in limit breach)*P(history of limit breaches|clients defaulted)=>P(client-A is in default)

Trading problem:

P(see uptick)*P(history of upticks | uptrends)=>P(beginning of uptrend)

PS: My mistake. Above should be modified from 'beginning updtrend' to 'uptrend'.
Correct is this:
P(see uptick)*P(history of upticks | start of uptrends)=>P(we are at beginning of uptrend)

goldorak


Total Posts: 1062
Joined: Nov 2004
 
Posted: 2019-10-07 11:02
We are in 2019 and finance folks are still relying on frequentist statistics. That tells a lot about this industry.



Once you actually reverse the way we have been (wrongly) trained to look at things in finance, and consider the probability of the hypothesis you make given the data you observe rather than the probability of the data given the hypothesis you make, the use of Baye's theorem is pretty straightforward.



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bullero


Total Posts: 57
Joined: Feb 2018
 
Posted: 2019-10-07 11:13
Parameter estimation?

Edit: For example in stat arb you could sample the posterior joint distribution for a set of interesting parameters that describe the stochastic behavior of a spread you are trading. Then, given the joint density you compute the expected pnl.

AB12358


Total Posts: 63
Joined: Apr 2014
 
Posted: 2019-10-08 00:26
Monty Hall? :D

NeroTulip


Total Posts: 1034
Joined: May 2004
 
Posted: 2019-10-10 08:32
@goldorak, we have:

P(H|D)=P(D|H)*P(H)/P(D)

So in order to get the probability of the hypothesis (H) given the data (D), we need unconditional probabilities of the data and hypothesis... How do we go about those?

I know you are super clever, please explain like I am 12 years old.

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Maggette


Total Posts: 1156
Joined: Jun 2007
 
Posted: 2019-10-10 11:38
Sorry, I guess I am missing something here. I don't get the question. You are aware of the classical Bayesian inference stuff (start with a prior for the parameters ...posterion = prior * likelihood..etc)?

In general you don't do that in a closed form pen and paper way....

Edit: I get know that I misunderstood the question. I guess you are looking for a more direct application of the theorem, other than general bayesian statistics

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nikol


Total Posts: 794
Joined: Jun 2005
 
Posted: 2019-10-10 15:10
@NeroTulip

>> P(H|D)=P(D|H)*P(H)/P(D)

Usually P(D) = 1.

>> I know you are super clever, please explain like I am 12 years old.

Hm... Assume that you already explained the concept of probability.

Imagine walking in the museum and seeing Kandinsky's Composition no.XI
https://www.wassily-kandinsky.org/Yellow-Red-Blue.jsp

Data is painting
H is everything what tells imagination about the picture. P(H) is a probability that particular H (let say face) will appear among anything else. P(D|H) is a number (EDIT: better fraction=P(D|H)/P(D)) of paintings with faces on it. Portraits included.

Then P(H|D) is a probability that what I see is face indeed.
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