Simultaneous Con dence Intervals for Linear Estimates of Linear Functionals
نویسنده
چکیده
This note presents three ways of constructing simultaneous condence intervals for linear estimates of linear functionals in inverse problems, including \Backus-Gilbert" estimates. Simultaneous con dence intervals are needed to compare estimates, for example, to nd spatial variations in a distributed parameter. The notion of simultaneous con dence intervals is introduced using coin tossing as an example before moving to linear inverse problems. The rst method for constructing simultaneous con dence intervals is based on the Bonferroni inequality, and applies generally to con dence intervals for any set of parameters, from dependent or independent observations. The second method for constructing simultaneous con dence intervals in inverse problems is based on a \global" measure of t to the data, which allows one to compute simultaneous con dence intervals for any number of linear functionals of the model that are linear combinations of the data mappings. This leads to con dence intervals whose widths depend on percentage points of the chi-square distribution with n degrees of freedom, where n is the number of data. The third method uses the joint normality of the estimates to nd shorter con dence
منابع مشابه
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