First of all we have to know the meaning of Inference.
Inference is defined as a process of drawing conclusions based on evidence and reasoning. Here the conclusions are drawn with the help of statistical tools.
Broadly speaking, inference is mainly two category.
1) Classical inference
2) Bayesian inference
Classical inference is only applicable in frequency probability ie; in term of repeated sampling from population. In Classical inference, we are deal with the prior probabilities. And in case of Bayesian inference our main aim is to deal with the posterior(conditional) probabilities. As we all know that the conditional probability is evaluated with the help of the prior probabilities.
The similarity in classical inference and Bayesian inference is that both are based on probability.
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