Conditioning Chance & Probability by Bayes Theorem
* Probability is one of the most key important factors that takes into effect the condition of time and space but there are other measures which go hand in hand with the measures that go into calculation of probability values and that is Conditional Probability which takes into effect the chance of occurrence of one particular event with effect to occurrence of some other events that may also affect the possibility and probability of the other event .
* When one would like to
estimate the probability of any given event , one may believe the probability
of some value to be applicable to some values which one may calculate upon a
set of possible events or situations . This term is used to express a belief of
"apriori probability"
which means general probability of any given event .
* For example , in the condition
of a throw of a coin ... if the coin thrown is a fair coin , then it could be
said that the apriori probability of occurrence of a head is around 50 percent
. This means that when someone would go for tossing a coin , he already knows
what is the probability of occurrence of a positive ( in other words .. desired
outcome ) otherwise occurrence of a negative outcome ( in other words ..
undesired outcome ) .
* Therefore , no matter how many
times one would toss a coin .. whenever faced with a new toss the probability
of occurrence of a heads is still 50 percent and the probability of occurrence
of a tail is still 50 percent .
* But consider a situation where
if someone wishes to change the context , then the subject of apriori probability is not valid
anymore .. because something subtle has happened and changed the outcome as we
all know there are some prerequisites and conditions that must satisfy so that
the general experiment could be carried out and come to fruitition. In such a
case , one can express the belief as a form of posteriori probability which is the priori probability after
something has happened that would tend to modify the count or outcome of the
event .
* For instance , gender estimation for a person being either a male or a female is the same which is about 50 percent in almost all of the cases . But this general assumption that any population taken into account would be having the same demography is wrong as I happened to come across my referenced article that what generally happens in a demographic population is that generally the women are the ones who tend to live longer and exceed their counterpart males in most of the cases in all of human existence .. as they are mostly the ones who tend to live longer and exceed their counterpart males in most of the factors that contribute to the general well being , and as a result of which the population demographic tilt is more towards the female gender .
Hence , putting all these factors into account
that contribute to the general estimate of any population , one should not
ideally take gender as a main parameter for determination of population data
because this factor is tilted in age-brackets and hence an overall idea for
generalisation of this factor should not be considered .
* Again , taking this factor of
gender into account , the posteriori probability is different from the expected apriori one which in this
example can consider gender to be the parameter for estimation of population
data and thus estimate somebody's probability of gender on the belief that
there are 50 percent males and 50 percent females in a given population data .
* One can view cases of conditional probability in the given manner P(y(x)) which in mathematical sense can be read as probability of the event y given the probability of occurrence of event x takes place . For the great relevance Conditional Probability plays in the concepts and studies of machine learning , learning and understanding the syntax of representation , expression and comprehension of the given equation is of great paramount importance to any newbie or virtuoso in the field of maths , statistics and machine learning . Hence , again if someone comes across a notation for conditional probability in the form P(y(x)) which can be read as the probability of event Y happening given X has already happened .
* As mentioned earlier in the
above paragraph , because of its dependence on possibility of occurrence on
single or multiple prior conditions , the role of conditional probability is of
paramount importance for machine learning which takes into effect statistical
conditions of occurrence of any event . If the apriori probability can change
because of circumstances, knowing the possible circumstances can give a big
push in one's chances of correctly predicting any event by observing the
underlying examples - exactly what machine learning generally intends to do .
* Generally , the possibility of finding a random person's gender as a male or female is around 50 percent . But , in case one would like to take into consideration the mortal aspects and age factor of any population , we have seen that the demographic tilt is more in favour of females . If under all such conditions , one would take into consideration the female population , and then dictate a machine learning algorithm to find out the gender of the considered person on the basis of their apriori conditions like length of hair , mortality rate etc , the ML algorithm would be able to very well determine the solicited answer
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