Question

Bayesian analysis is a probabilistic classification method based on Bayes' theorem

(postulated by an English Mathematician named Thomas Bayes). In summary, the

Bayesian theory rests on the belief that the evidence about the true state of a given

problem can be expressed in term of the degree of understanding of the underlying

issues. That degree of understanding can in turn be expressed in terms of probability.

And based on the observation, the theorem provides the relationship between the

probabilities of two possible events and their conditional probabilities.

The formula for Bayes Theorem is given as: P(A|B) = P(B|A) * P(A)/P(B)

Question:

Discuss the reasons for using Bayesian analysis when faced with uncertainty in

making decisions.

Discussion Requirements:

How would you describe Bayesian Theorem?

Describe the assumptions of Bayesian analysis.

Provide the example of problem where one can use Bayesian analysis in Big Data Analytics.

Describe the the problems with Bayesian analysis.

Answer 1

• In statistical inference, there are two ways for interpretations of probability include Frequentist (or Classical) inference and Bayesian inference. It usually is unlike each other in the classical nature of probability. Classical inference defines probability as the limit of an event’s relative frequency for a large number of experiments and only in the sense of random experiments which are well defined. Another side, Bayesian inference can impose probabilities to each statement when a random process is not associated. In the sense of Bayesian, the probability is a way to show an individual’s degree of beliefs in a statement. Bayesian inferences are different interpretations of probability, and also different approaches depend on those interpretations. Bayes’ theorem presents the relativity about two conditional probabilities that are the reverse of anything other. The initials of the term Bayes’ theorem is in honour of Reverend Thomas Bayes and is referred to as Bayes’ law. This theorem shows the conditional probability or posterior probability of an event A after B is observed in terms of the prior probability of A, the prior probability of B and the conditional probability of B given A. It is valid in all interpretations of probability. Bayes’ formula is how to revise probability statements using data. The Bayes’ law (or Bayes’ rule) is

P(A|B) = P(B|A) * P(A)/P(B)

• Bayesian analysis has a strong assumption of an underlying distributional assumption of selecting prior when calculating for the Posterior distribution, i.e. the conditional probability distribution is supported by an underlying suitable choice of distribution which in general depends on the situation and nature of the likelihood.
• In Big Data Analysis, the most used analysis is Bayesian analysis. We can have several examples of big data analysis. Suppose we are considering the "Next text prediction" feature of Google's search results. Here the data which is already inserted in the database of Google (Or the database which is constantly being built in the server database) will be treated as the supporting "prior knowledge" and the likelihood of the text will give you the posterior distributional outcome which is the "Next text prediction".
• Problems with the Bayesian analysis: the main problem of the Bayesian analysis is the underlying distributional assumption which should be suitably chosen to have a proper posterior outcome. The prior distribution mainly depends upon the nature of the likelihood of the data and if the prior distribution is not properly chosen, the result will be an erroneous one.