18th July Lecture 1

There are 3 Methods of estimation

1)    Ratios chance ( which vary from 0 to 1  eg.1/10)

     2)    Percentage chance ( which vary from  0 to 100  eg. 50% )                             3)   Probability (which vary from 0 to 1 eg. 0.1)

Probability Method of estimation

3 approaches to calculate Probability were showed

1.   A prior ( prior information )

        

     Probability calculated by logically examining existing information. A priori probability can most easily be described as making a conclusion based upon deductive reasoning rather than research or calculation. The largest drawback to this method of defining probabilities is that it can only be applied to a finite set of events.

     For example, consider how the price of a share can change. Its price can increase, decrease or remain the same. Therefore, according to a priori probability, we can assume that there is a 1-in-3, or 33%, chance of one of the outcomes occurring (all else remaining equal).

The probability that an event will reflect established beliefs about the event before the arrival of new evidence or information. Prior probabilities are the original probabilities of an outcome, which be will updated with new information to create posterior probabilities.

2.   Empirical approach ( information collected )

Also known as relative frequency, or experimental probability, is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, not in a theoretical sample space but in an actual experiment. In a more general sense, empirical probability estimates probabilities from experience and observation.

In statistical terms, the empirical probability is an estimate of a probability. In simple cases, where the result of a trial only determines whether or not the specified event has occurred, modelling using a binomial distribution might be appropriate and then the empirical estimate is the maximum liklihood. It is the Bayesian estimate for the same case if certain assumptions are made for the prior distribution of the probability. If a trial yields more information, the empirical probability can be improved on by adopting further assumptions in the form of a statistical model: if such a model is fitted, it can be used to derive an estimate of the probability of the specified event.

For example, let's say that a manufacturer tested 1000 radios, at random, and found 15 of them to be defective.
We can easily determine that the empirical probability that a radio is defective would be:
P(defective radio) = 15
                     1000
or...3/200. 
As a decimal it would be .015, and
as a percent it would be 1.5%
Now the manufacturer can use this result to predict that in the production of 7500 radios, 1.5% of them will probably be defective. Or, (.015)(7500) = 112.5 defective radios.

3.   Subjectivity ( Intuition )

A probability derived from an individual's personal judgment, understanding and experience  about whether a specific outcome is likely to occur. Subjective probabilities contain no formal calculations. This can be used to capitalize on background of experienced workers and managers in decision making.

It’s a way of tapping a persons knowledge to forecast the occurrence of an event.

Subjective probabilities differ from person to person. Because the probability is subjective, it contains a high degree of personal bias. An example of subjective probability could be asking New York Yankees fans, before the baseball season starts, the chances of New York winning the world series. While there is no absolute mathematical proof behind the answer to the example, fans might still reply in actual percentage terms, such as the Yankees having a 25% chance of winning the world series.

VENN DIAGRAM:

A Venn diagram or set diagram is a diagram that shows all possible logical relations between a finite collection of sets. Venn diagrams were conceived around 1880 by John Venn. They are used to teach elementary set theory, as well as illustrate simple set relationships improbablity, logic, statistics,linguistics and computer science.

Written By:

Pareena Neema

Group Members:

Abhishek Panwala

Raghav Kabra

Poorva Saboo

Parita Mandhana