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21 For the employed, this approximation is exact under the assumption of constant wages.
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This means that the symmetric approximation is exact for any value of d for any quadratic; no need to make d small; and this is not true for the asymmetric formula.
The approximation is exact when there is one single instrument and no covariates.
As the likelihood is Gaussian, the Laplace approximation is exact and hence its accuracy comes from the numerical integration scheme.
This approximation is the more exact the smaller β value, however, the value of β should not be necessary very small.
Numerical results show that this approximation is very close to the exact solution.
We show in this section that another form of approximation provides closer results in this case, and that this approximation is actually based on the exact same coefficients as the asymptotic approximation described above.
Our algorithm strictly generalizes previous adaptive caching algorithms for exact copies: we can set parameters to require that all approximations be exact, in which case our algorithm dynamically chooses whether or not to cache each data value.
In general, while MCMC inference approximations are exact in the limit of large running time, it is very hard even for experts to assess at which point an MCMC estimate can be considered reliable.
As this threshold corresponds to a certain genomic distance to the local tree, this approximation is equivalent to an 'exact window' sliding along the sequence.
Below, we will discuss the mean field approximation, which is exact for the global hopping dynamics but it is only an approximation for the model with local hopping dynamics.
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