I really have a hard time understanding the point of this section.
What difference is there between calculating the posterior given an evidence -- thus updating the future prior -- and questioning the prior "in the first place"? Isn't this the whole point of the process? to examine the prior and question it in case of an extraordinary evidence?
This (the ignoring of cost) seems like a flaw to Bayesian analysis, and makes me think there's probably some extension to it, which is being omitted here for simplicity, but which takes into account something like cost, value, or utility.
For example, the "cost" of a bayesian filter deciding to show a salesman a spam email is far lower than the "cost" of the same filter deciding to prevent them from seeing an email from a million-dollar sales lead.
So, while the calculation of probabilities should not take into account cost, it feels like the making decisions of based on those probabilities should take cost into account.
For example: the chances of our getting wiped out in the near future by a natural disaster. Yet, the potential consequences are dire, and the net costs per person of detection are low, or even negative. Therefore, we have a global near-earth-object detection network, a tsunami and quake detection network, fire watch towers, weather and climate monitors, disease tracking centers, and so on.
If this extension to Bayesian analysis exists, this seem a sensible place to link to it.
We see on the next (log probability) that a plethora of small evidences sums to a very large number of bits.
In the bookcase aliens example, if you went to 312 houses and found that every one of them had a new bookcase, then by this approach, it's time to reexamine the aliens hypothesis.
In practice, it's just simply not. Aliens are still just as unlikely as they were previously. New bookcases are now more likely.
It's time to reexamine your 50:1 in favor of aliens estimate for a new bookcase. It's time to check whether there's a really good door-to-door bookcase salesman offering ridiculous deals in the area. Or whether there are new tax incentives for people with more bookcases. Or a zillion other far more likely things than the false dichotomy of "either each person bought bookcases independently with odds of 50:1 against, or it's bookcase aliens."
The corollary of Doyle's "Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth" is "make damn sure to eliminate all the probable stuff, before gallivanting into the weeds of the infeasible".
"ceteris paribus" is an unusual Latin phrase in English. For clarity, a native English phrase may be better. Could go literal, changing "ceteris paribus be," to ", all other conditions remaining the same," or a bit more idiomaticly ", normally, be,".
I, in general, think things are clearer when real world examples like this are given in the beginning, rather than after the abstract explanation. I think most people find the same thing.
Possible inferential gap given just the pages I saw on my path to this one: the notion of "causally downstream" and the reason why "observed temperatures for the last 200 years" are causally downstream from "simple models of geophysics constructed to explain data about Earth and other planets".
This seems less clear than saying "greater." Am I missing something?
I really have a hard time understanding the point of this section.
What difference is there between calculating the posterior given an evidence -- thus updating the future prior -- and questioning the prior "in the first place"? Isn't this the whole point of the process? to examine the prior and question it in case of an extraordinary evidence?
This (the ignoring of cost) seems like a flaw to Bayesian analysis, and makes me think there's probably some extension to it, which is being omitted here for simplicity, but which takes into account something like cost, value, or utility.
For example, the "cost" of a bayesian filter deciding to show a salesman a spam email is far lower than the "cost" of the same filter deciding to prevent them from seeing an email from a million-dollar sales lead.
So, while the calculation of probabilities should not take into account cost, it feels like the making decisions of based on those probabilities should take cost into account.
For example: the chances of our getting wiped out in the near future by a natural disaster. Yet, the potential consequences are dire, and the net costs per person of detection are low, or even negative. Therefore, we have a global near-earth-object detection network, a tsunami and quake detection network, fire watch towers, weather and climate monitors, disease tracking centers, and so on.
If this extension to Bayesian analysis exists, this seem a sensible place to link to it.
Be wary here.
We see on the next (log probability) that a plethora of small evidences sums to a very large number of bits.
In the bookcase aliens example, if you went to 312 houses and found that every one of them had a new bookcase, then by this approach, it's time to reexamine the aliens hypothesis.
In practice, it's just simply not. Aliens are still just as unlikely as they were previously. New bookcases are now more likely.
It's time to reexamine your 50:1 in favor of aliens estimate for a new bookcase. It's time to check whether there's a really good door-to-door bookcase salesman offering ridiculous deals in the area. Or whether there are new tax incentives for people with more bookcases. Or a zillion other far more likely things than the false dichotomy of "either each person bought bookcases independently with odds of 50:1 against, or it's bookcase aliens."
The corollary of Doyle's "Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth" is "make damn sure to eliminate all the probable stuff, before gallivanting into the weeds of the infeasible".
"ceteris paribus" is an unusual Latin phrase in English. For clarity, a native English phrase may be better. Could go literal, changing "ceteris paribus be," to ", all other conditions remaining the same," or a bit more idiomaticly ", normally, be,".
I, in general, think things are clearer when real world examples like this are given in the beginning, rather than after the abstract explanation. I think most people find the same thing.
Unlike the verbal incoherence of the previous commenter.
Whoever wrote this knows what he is doing.
Possible inferential gap given just the pages I saw on my path to this one: the notion of "causally downstream" and the reason why "observed temperatures for the last 200 years" are causally downstream from "simple models of geophysics constructed to explain data about Earth and other planets".