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:
“If but some vengeful god would call to me
From up the sky, and laugh: “Thou suffering thing,
Know that thy sorrow is my ecstasy,
That thy love’s loss is my hate’s profiting!””
—Thomas Hardy (1840–1928)
“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)
“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)