Attributes
From a practical and mathematical standpoint, a valid reason to use this non-informative prior instead of others, like the ones obtained through a limit in conjugate families of distributions, is that it is not dependent upon the set of parameter variables that is chosen to describe parameter space.
Sometimes the Jeffreys prior cannot be normalized, and thus one must use an improper prior. For example, the Jeffreys prior for the distribution mean is uniform over the entire real line in the case of a Gaussian distribution of known variance.
Use of the Jeffreys prior violates the strong version of the likelihood principle, which is accepted by many, but by no means all, statisticians. When using the Jeffreys prior, inferences about depend not just on the probability of the observed data as a function of, but also on the universe of all possible experimental outcomes, as determined by the experimental design, because the Fisher information is computed from an expectation over the chosen universe. Accordingly, the Jeffreys prior, and hence the inferences made using it, may be different for two experiments involving the same parameter even when the likelihood functions for the two experiments are the same—a violation of the strong likelihood principle.
Read more about this topic: Jeffreys Prior
Famous quotes containing the word attributes:
“Even though fathers, grandparents, siblings, memories of ancestors are important agents of socialization, our society focuses on the attributes and characteristics of mothers and teachers and gives them the ultimate responsibility for the child’s life chances.”
—Sara Lawrence Lightfoot (20th century)
“Why does not the kitten betray some of the attributes common to the adult puss? A puppy is but a dog, plus high spirits, and minus common sense. We never hear our friends say they love puppies, but cannot bear dogs. A kitten is a thing apart; and many people who lack the discriminating enthusiasm for cats, who regard these beautiful beasts with aversion and mistrust, are won over easily, and cajoled out of their prejudices, by the deceitful wiles of kittenhood.”
—Agnes Repplier (1858–1950)
“God is the efficient cause not only of the existence of things, but also of their essence.
Corr. Individual things are nothing but modifications of the attributes of God, or modes by which the attributes of God are expressed in a fixed and definite manner.”
—Baruch (Benedict)