scholarly journals General bias/variance decomposition with target independent variance of error functions derived from the exponential family of distributions

2002 ◽  
Author(s):  
J.V. Hansen ◽  
T. Heskes
Keyword(s):  
Exponential Family ◽  
Variance Decomposition ◽  
Error Functions ◽  
Bias Variance ◽  
Exponential Family Of Distributions ◽  
Family Of Distributions

scholarly journals Asymptotic approximations to the Bayes posterior risk

1990 ◽  
Vol 3 (2) ◽  
pp. 99-116
Author(s):  
Toufik Zoubeidi
Keyword(s):  
Parameter Space ◽  
Exponential Family ◽  
Distribution Functions ◽  
Independent Random Variables ◽  
Asymptotic Approximations ◽  
Prior Density ◽  
Posterior Probabilities ◽  
Exponential Family Of Distributions ◽  
Family Of Distributions ◽  
Convex Subsets

Suppose that, given ω=(ω1,ω2)∈ℜ2, X1,X2,… and Y1,Y2,… are independent random variables and their respective distribution functions Gω1 and Gω2 belong to a one parameter exponential family of distributions. We derive approximations to the posterior probabilities of ω lying in closed convex subsets of the parameter space under a general prior density. Using this, we then approximate the Bayes posterior risk for testing the hypotheses H0:ω∈Ω1 versus H1:ω∈Ω2 using a zero-one loss function, where Ω1 and Ω2 are disjoint closed convex subsets of the parameter space.

9. Models for Generalized Location Systems

2007 ◽  
Vol 37 (1) ◽  
pp. 283-348 ◽  
Author(s):  
Carter T. Butts
Keyword(s):  
Exponential Family ◽  
Social Systems ◽  
System Model ◽  
Social Phenomena ◽  
Location System ◽  
Formal Framework ◽  
Model Complex ◽  
Exponential Family Of Distributions ◽  
Residential Settlement ◽  
Family Of Distributions

A formal framework is introduced for a general class of assignment systems that can be used to characterize a range of social phenomena. An exponential family of distributions is developed for modeling such systems, allowing for the incorporation of both attributional and relational covariates. Methods are shown for simulation and inference using the location system model. Two illustrative applications (occupational stratification and residential settlement patterns) are presented, and simulation is employed to show the behavior of the location system model in each case; a third application, involving occupancy of positions within an organization, is used to demonstrate inference for the location system. By leveraging established results in the fields of social network analysis, spatial statistics, and statistical mechanics, it is argued that sociologists can model complex social systems without sacrificing inferential tractability.

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