A Data-Driven Framework for Uncertainty Assessment

Statistical inference is an important part of statistics and is broadly classified into two categories namely Bayesian and non-Bayesian inference. Non-Bayesian inference thinks of probability as the limit of an event's relative rate of recurrence when the experiment is repeated large number of times and does not take into account the prior knowledge related to the experiment. Also, the non-Bayesian approach considers parameters as fixed. While as in Bayesian inference,the probability reflects one's degree of belief in the occurrence of event and hence consists of current data (represented by a likelihood function) and prior (represents degree of belief). Bayesian approach considers parameters as random variable. Taking in context of data analysis, Bayesian approach has far reaching results than non-Bayesian counterpart. Therefore, in Bayesian opinion, probabilities are not properties of random variables but a measurable coding of one's degree of knowledge. Bayesian statistics is a method where estimates are entirely dependent on prior distribution and current sample data. Bayesian method gives a complete model for both decision making and statistical inference. Many commonly used classical procedures are contained in the Bayesian analysis and it provides solution to many questions where the Non-Bayesian approach fails. So, by means of Bayesian analysis it is possible to include scientific hypothesis in the study (by means of prior distribution) and many complex problems which are difficult to solve by conventional approach can be easily handled. So this model is grounded on an interpretation of probability as a conditional measure of uncertainty, which matches the meaning of the 'probability' in everyday language. So, the statistical inference regarding the point of interest is defined in terms of the uncertainty about its value while taking into considerationthe evidence and the way of modifying it defined by Bayes theorem.