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# Inference in Dynamic Error-in-Variable-Measurement
Problems

**Joao Albuquerque, Lorenz T. Biegler and Robert E. Kass**

### Abstract:

*Efficient algorithms have been developed for estimating model
parameters from measured data, even in the presence of gross errors.
In addition to point estimates of parameters, however, assessments of
uncertainty are needed. Linear approximations provide standard errors,
but these can be misleading when applied to models that are
substantially nonlinear. To overcome this difficulty, ``profiling''
methods have been developed for the case in which the regressor
variables are error free. In this paper we extend profiling methods
to Error-in-Variable-Measurement (EVM) models. We use Laplace's method
to integrate out the incidental parameters associated with the
measurement errors, and then apply profiling methods to obtain
approximate confidence contours for the parameters. This approach is
computationally efficient, requiring few function evaluations, and can
be applied to large scale problems. It is useful when the certain
measurement errors (e.g., input variables) are relatively small, but
not so small that they can be ignored.
**
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