Loss Functions in Bayesian Statistics
One of the consequences of Bayesian inference is that in addition to experimental data, the loss function does not in itself wholly determine a decision. What is important is the relationship between the loss function and the prior probability. So it is possible to have two different loss functions which lead to the same decision when the prior probability distributions associated with each compensate for the details of each loss function.
Combining the three elements of the prior probability, the data, and the loss function then allows decisions to be based on maximizing the subjective expected utility, a concept introduced by Leonard J. Savage.
Read more about this topic: Loss Function
Famous quotes containing the words loss, functions and/or statistics:
“... the loss of belief in future states is politically, though certainly not spiritually, the most significant distinction between our present period and the centuries before. And this loss is definite. For no matter how religious our world may turn again, or how much authentic faith still exists in it, or how deeply our moral values may be rooted in our religious systems, the fear of hell is no longer among the motives which would prevent or stimulate the actions of a majority.”
—Hannah Arendt (1906–1975)
“When Western people train the mind, the focus is generally on the left hemisphere of the cortex, which is the portion of the brain that is concerned with words and numbers. We enhance the logical, bounded, linear functions of the mind. In the East, exercises of this sort are for the purpose of getting in tune with the unconscious—to get rid of boundaries, not to create them.”
—Edward T. Hall (b. 1914)
“July 4. Statistics show that we lose more fools on this day than in all the other days of the year put together. This proves, by the number left in stock, that one Fourth of July per year is now inadequate, the country has grown so.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)