[edit] 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.
Loss Functions. In standard multiple regression we estimate the regression coefficients by "finding" those coefficients that minimize the residual variance (sum of squared residuals) around the regression line.
The Loss Function
In order to make precise what we mean by being a "good predictor", we define a loss (also called objective or error) function E over the model parameters. A popular choice for E is the sum-squared error:
(2) ...
SVMs can also be applied to regression problems by the introduction of an alternative loss function. The loss function must be modified to include a distance measure. The regression can be linear and non linear.
If a is an estimate for theta and L(theta,a) is a real-valued loss function, the expected loss of choosing a before observing any data is E(L(theta,a)) = Integral_{Omega_theta} L(theta,a) xi(theta) or, after observing the data x, ...
the probability that the true effect lies within a "practically small" distance of the null hypothesis - where "practically small" is defined relative to the question being asked, and could be extended to a formal decision-theoretic loss function - ...
It is thus the most basic (and naive) estimation heuristic. This method only uses a loss function appropriate for the problem and does not utilize a probabilistic model for the data.
 See also: Distribution, Regression, Variance, Outlier, Estimation
  
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