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:
“We feel public misfortunes just so far as they affect our private circumstances, and nothing of this nature appeals more directly to us than the loss of money.”
—Titus Livius (Livy)
“Nobody is so constituted as to be able to live everywhere and anywhere; and he who has great duties to perform, which lay claim to all his strength, has, in this respect, a very limited choice. The influence of climate upon the bodily functions ... extends so far, that a blunder in the choice of locality and climate is able not only to alienate a man from his actual duty, but also to withhold it from him altogether, so that he never even comes face to face with it.”
—Friedrich Nietzsche (1844–1900)
“We ask for no statistics of the killed,
For nothing political impinges on
This single casualty, or all those gone,
Missing or healing, sinking or dispersed,
Hundreds of thousands counted, millions lost.”
—Karl Shapiro (b. 1913)