Likelihood, Advanced Statistics

Likelihood is the probability of a set of observations provided the value of some parameter or the set of parameters. For instance, the likelihood of the random sample of n observations

450_likelihood.png 

with probability distribution, f(x,θ) which can be  given by
403_likelihood1.png 
This function is the basis of the maximum likelihood estimation. In number of applications the likelihood includes number of parameters, only a few of which are of interest to investigator. The remaining nuisance parameters are essential in order that the model makes the sense physically, but their values are largely irrelevant of the investigation and the conclusions to be made. Since there are troubles in dealing with likelihoods which depend on a large number of incidental parameters (for instance, maximizing the likelihood will be more tough) some form of modified likelihood is sought which comprises as few of the uninteresting parameters as possible. The number of possibilities is available. For instance, the marginal likelihood, removes the nuisance parameters by integrating them out of the likelihood. The profile likelihood with respect to parameters of interest, is the original likelihood, partly maximized with respect to the nuisance parameters. 

Posted Date: 7/30/2012 2:08:02 AM | Location : United States







Related Discussions:- Likelihood, Assignment Help, Ask Question on Likelihood, Get Answer, Expert's Help, Likelihood Discussions

Write discussion on Likelihood
Your posts are moderated
Related Questions
Method of moments   is the procedure for estimating the parameters in a model by equating sample moments to the population values. A famous early instance of the use of the proced

elements , importance, limitation, and theories

a researcher is interested in whether students who attend privte high schools have higher average SAT Scores than students in the general population. a random sample of 90 student

Yate s' continuity correction : When the testing for independence in contingency table, a continuous probability distribution, known as chi-squared distribution, is used as the app

Infant mortality rate is the ratio of the number of deaths during the calendar year among the infants under one year of age to the total number of live births during that particul

Quasi-experiment is a term taken in use for studies which resemble experiments but are weak on some of the characteristics, particularly that allocation of the subjects to groups

Categorical variable : A variable which provides the appropriate label of observation after the allocation to one of the several possible categories, for instance, the respiratory

Intention-to-treat analysis is the process in which all the patients randomly allocated to a treatment in the clinical trial are analyzed together as representing that particular


Chebyshev's inequality: A statement about the proportion of the observations which fall within some number of the standard deviations of the mean for any of the probability distri