Question

Which are the similarities of Classical and Bayesian approaches of Inference?

And when we use this for a data in what will be differ and why?

Answer 1

Use

.Frequentist inference, objectivity, and decision theory

One interpretation of frequentist inference (orclassical inference) is that it is applicable only in terms of frequency probability; that is, in terms of repeated sampling from a population

Probability statements made in Bayesian and classical approaches to inference of- ten look similar, but they carry different meanings.

Bayesian inference is a method of statistical inference in which Bayes' theorem is used toupdate the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics.

Frequentist inference, objectivity, and decision theory

One interpretation of frequentist inference (orclassical inference) is that it is applicable only in terms of frequency probability; that is, in terms of repeated sampling from a population.

Difference....

The differences have roots in their definition of probability i.e., Bayesian statistics defines it as a degree of belief, while classical statistics defines it as a long run relative frequency of occurrence.

One important consequence of the probability definition is that Bayesian statisticians assign probability distributions to uncertain variables such as parameters, predictions etc, while classical statisticians cannot assign probabilities to all uncertain variables e.g., parameters, instead confidence intervals and regions are used to quantify the parameters uncertainty.