Bayesian prior: Difference between revisions

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{{Drop|B|ayesian statistics have}}, in our dystopian techno-determinist age, a lot to answer for.
{{Drop|B|ayesian statistics have}}, in our dystopian techno-determinist age, a lot to answer for.


They take us from a surprising proof of how the odds work in a game of chance — that will help you choose wisely between goats and cars — but once it departs the tightly-controlled conditions of that statistical experiment, it is easily misapplied and may get badly lost in evaluating Shakespeare, our debt to distant future generations, and the onrushing [[apocalypse]], courtesy of which, it seems to say, there won’t ''be'' any distant future generations to worry about anyway.
In their place they can unravel surprising odds in a game of chance that human brains intuitively misapprehend this will help should you be asked to choose wisely between goats and cars — but outside the tight swim lanes of statistical experiment, they can be easily misapplied and may get badly lost in weighing up the risks of the market, the merits of Shakespeare, our debt to distant future generations, and the prospect of onrushing [[apocalypse]], courtesy of which, some theorists tell us, there won’t ''be'' many future generations to worry about anyway.
====Goats and sportscars====
====Goats and sportscars====
{{Drop|T|he neatest illustration}} of how Bayesian priors are meant to work is the “Monty Hall” problem, named for the ghost of the gameshow ''Deal or No Deal'':
{{Drop|T|he neatest illustration}} of how “Bayesian priors” work is the “Monty Hall” problem, named for the ghost of the gameshow ''Deal or No Deal'':
{{quote|
{{quote|
A game show invites a contestant to choose a prize by opening one of three doors. One door conceals s a sports car, the other two conceal goats. [''Why goats? — Ed'']  
A game show contestant is asked to choose a prize from behind one of three doors. She is told one door conceals s a sports car and the other two goats. [''Why goats? — Ed'']  


Once the contestant has made her choice, the host theatrically opens one of the ''other'' doors to reveal a goat.  
When the contestant has chosen, the host theatrically opens one of doors she did not choose, to reveal a goat.  


There are now two doors left; one concealing a goat, one concealing the car. Assume the host will never open the door the contestant chose, nor the one concealing the car, and the car will not move.
There are now two doors left; one concealing a goat, one concealing the car. Assume the host will never open the door the contestant chose, nor the one concealing the car, and the car will not move.