Proper Local Scoring Rules on Discrete Sample Spaces

Details Proper Local Scoring Rules on Discrete Sample Spaces Proper Local Scoring Rules on Discrete Sample Spaces

2011-04-12

arxiv.org/abs/1104.2224v2

Mathematics

Statistics Theory

Scientific paper

A scoring rule is a loss function measuring the quality of a quoted probability distribution $\bq$ for a random variable $X$, in the light of the realised outcome $x$ of $X$; it is proper if the expected score, under any distribution $\bp$ for $X$, is minimised by quoting $\bq = \bp$. Using the fact that any differentiable proper scoring rule on a finite sample space ${\cal X}$ is the gradient of a concave homogeneous function, we consider when such a rule can be local in the sense of depending only on the probabilities quoted for points in a nominated neighbourhood of $x$. Under mild conditions, we characterise such a proper local scoring rule in terms of a collection of homogeneous functions on the cliques of an undirected graph on the space $\cX$. A useful property of such rules is that the quoted distribution $\bq$ need only be known up to a scale factor. Examples of the use of such scoring rules include Besag's pseudo-likelihood and Hyv\"arinen's method of ratio matching.

Affiliated with

Also associated with

No associations

Rating

Proper Local Scoring Rules on Discrete Sample Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Proper Local Scoring Rules on Discrete Sample Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Proper Local Scoring Rules on Discrete Sample Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-731067