November 22, 2018 Thursday
Bedtime Story
Bayesian Probability and Bayesian Inference
With the latest data available now to our
friend interested in purchasing a lottery his probability now has increased
dramatically.
Not the objective probability but the
subjective probability.
His degree of belief would change or rather
should change as he comes across incidences of more wins.
I would not like to go into the mathematics
of Bayesian probability in spite of the fact that it is perhaps one of the most
counter-intuitive areas of mathematical probability.
Yet I would like to linger on a little bit
on Bayesian inference because it is one of those revolutionary ideas that even
without exact use of mathematics has its applications in everyday life besides
its formal application in science, engineering and medicine.
It can and must be applied in subjects as
variable as philosophy, sport and law.
One thing that I would like to point out is
that when Bayes wrote his treatise “An Essay towards solving a problem in the
Doctrine of chances” even though he came to the conclusion that the value of
the conditional probability value p is variable one that changes on observation
it cannot be said that he himself had developed a Bayesian kind of thinking.
After all, he was trying to counter Hume
and trying to prove the existence of miracles and god.
So what exactly is Bayesian inference?
Bayesian inference is a method of
statistical inference wherein the probability of a hypothesis is updated each
time new information or new evidence or a contradiction becomes available
concerning it.
As you can see from the very definition
that its use can be universal (but rarely applied by us average apes) but
perhaps an example will clarify that.
We shall consider the matter of a criminal
court where the prosecution has to establish culpability of the accused ‘beyond
a reasonable doubt’.
Of course what constitutes the definition
of ‘beyond a reasonable doubt’ is itself open to interpretations and is subjective
to a much larger extent than desirable.
‘Reasonable doubt’ is considered with
reference to a ‘reasonable man’ (sometime I wonder what that means considering
the way we apes think and behave) that the evidence against the accused should
convince a ‘reasonable man’ that there is no ‘reasonable doubt’ regarding the
guilt of the accused.
It is the highest burden of proof that the
prosecution has to establish in a criminal court of most modern systems of
jurisprudence.
It is not surprising then that the
conviction rates in a third-world country with sparse resources extremely
tightly stretched and prosecution highly-vulnerable to corruption the
conviction rate for the violations of Indian Penal Code (even for crimes of
serious nature) is dramatically low.
In the state of Maharashtra alone according
to the data collected by a NGO Praja Foundation there is an astounding 77%
acquittal in cases of serious crimes.
Stay tuned to the voice of an
average story storytelling chimpanzee or login at http://panarrans.blogspot.com
Good night Mon Ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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