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Bayesian inference: An approach to the inference based largely on Bayes' Theorem and comprising of the below stated principal steps:
(1) Obtain the likelihood, f x q describing the process increasing the data x in terms of unknown parameters q.
(2) Obtain the previous distribution, f q expressing what is known about the q, previous to observing the data.
(3) Apply Bayes' theorem to derive posterior distribution f q x expressing that what is known about q after observing the given data.
(4) Derive suitable inference statements from posterior distribution. These might include speci?c inferences like interval estimates, point estimates or probabilities of the hypotheses or asumptions. If interest centres on particular components of q their posterior distribution is formed by the integrating out of the other parameters.
This form of inference varies from classical form of the frequentist inference in the various respects, particularly the use of prior distribution which is not present in the classical inference. It represents the investigator's knowledge and wisdom about the parameters before seeing data.
Classical statistics only makes use of the likelihood. As a result to the Bayesian every problem is unique and is considered by the investigator's beliefs about parameters expressed in the prior distribution for the speci?c or particular investigation.
Genetic algorithms: The optimization events motivated by the biological analogies. The prime idea is to try to mimic the 'survival of the fittest' rule of the genetic mutation in
Cluster analysis : A set of methods or techniques for constructing a sensible and informative classi?cation of an initially unclassi?ed set of data, using variable values observed
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Nuisance parameter : The parameter of the model in which there is no scienti?c interest but whose values are generally required (but in usual are unknown) to make inferences about
The Null Hypothesis - H0: γ 1 = γ 2 = ... = 0 i.e. there is no heteroscedasticity in the model The Alternative Hypothesis - H1: at least one of the γ i 's are not equal
Difference b/w historigram and histogram
Introduction to Generalized Linear Models (GLM) We introduce the notion of GLM as an extension of the traditional normal-theory-based linear regression models. This will be very
The more effective display than a number of other methods or techniques, for instance, pie charts and bar charts, for displaying the quantitative data which are labeled. An instanc
1) Let N1(t) and N2(t) be independent Poisson processes with rates, ?1 and ?2, respectively. Let N (t) = N1(t) + N2(t). a) What is the distribution of the time till the next epoch
The Null Hypothesis - H0: β 1 = 0 i.e. there is homoscedasticity errors and no heteroscedasticity exists The Alternative Hypothesis - H1: β 1 ≠ 0 i.e. there is no homoscedasti
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