nikol


Total Posts: 1388 
Joined: Jun 2005 


Question came from (infinite) discussions about usefulness of vaccination, but I extended it to the markets as well:  Suppose specific event (e.g. loss or contagion) occurs at the rate of 1 out 100 (1%).  Specific observer records 100 out of 1000 and naturally deduces 10% rate for the same type of events, which could mean that he might get emotionally involved (vaccine does not work!) or starts dumping his position.
Perhaps it is trivial stuff... but it occurred to me in this form just yesterday. Any comment? 
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) 


Maggette


Total Posts: 1325 
Joined: Jun 2007 


I am not sure that I get the point.
In our toy model world we know that specific event occurs at the rate of 1%? And that is a true fact? And now somebody takes a sample from this distribution and ends up with the unlikely case where he sees the event at a rate of 10% (instead of 1%)? And our actor reacts (by basically rejecting the 1% hypothesis? Was the 1% also his prior?) on the observed frequency (10%)?
I am not sure where the bias is coming in? Could you elaborate a bit on that ?
Thanks

Ich kam hierher und sah dich und deine Leute lächeln,
und sagte mir: Maggette, scheiss auf den small talk,
lass lieber deine Fäuste sprechen...


ronin


Total Posts: 689 
Joined: May 2006 


I feel like we are not getting enough information here.
The error of mean is standard deviation / sqrt(number of samples).
We know the number of samples (n=1000), we know the mean (\mu = 1%)  but we don't know the standard deviation.
So we have no idea if this is "as close to the mean as you would expect for 1000 measurements" or "this is like nine hundred and seventy six standard errors out  clearly something must be wrong".
And we also don't know what the population is. Is this like "1% of the normal population, but 10% of the infectious disease ward in a specialist hospital"?
So, I'd ask for a bit more information before reaching conclusions. 
"There is a SIX am?"  Arthur 


nikol


Total Posts: 1388 
Joined: Jun 2005 


Gentlemen, my apology for incompleteness, however, it is my "formulation struggle" of the sort "proper formulation of question is half an answer".
Mathematically you capture it all correct, if everyone observes 1%, there is no bias.
This "1%" is not "true fact" like physics type of measurement. It is based on the measurements done by experts.
Now, another observer (let say youngster) sees different sample of the same phenomena but with 10% or he just started to learn things, therefore, his view is obfuscated. He sees the difference with 1% (published by expert) and says  "perhaps market turns negative", so he reduces exposure. His perception as reaction to that difference is the bigger, the bigger is the pain, so you get fear bias or loss of confidence. 
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) 

Jim


Total Posts: 167 
Joined: Jun 2004 


I think the issue (as ronin alludes to) is that the iid assumption underpinning standard probability theory doesn't hold with contagions. Clearly, the probability of getting infected is not independent whether the guy next to you is infected or not. Moreover, there is significant nonlinearity in the mortality rate once infected. Simple ratios ignore these complexities and result in wrong inferences from the observations.




nikol


Total Posts: 1388 
Joined: Jun 2005 


My idea was not about structural differences between statistical models, but rather skewed view on data content/interpretation and consecutive bias on the decision.
I do not believe into emotional detach from the market leveraged by algos, because everyday one have to let it run or stop or even start changing the algo.
Covid infections have inspirational impact on this question nothing more. 
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) 
