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Figure 4B displays the unit square bias coordinates, Poincare disk mapped coordinates, transducer ratio parameters, and relative distances (βL) from the angle equivalent quinpirole coordinates.
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where each of the mean square values can be decomposed via the squared bias and variance.
The mean square error (MSE) is a natural choice of optimization since it includes both variance and squared bias.
It can be shown that the expected test error is the sum of irreducible error, squared bias and variance (Hastie et al.[4] Eq 7.9).
Generally, (32) has a higher cost in terms of MSE (because we disregard two terms of (32)), however the squared bias term of (24) will be approximately zero.
While those estimators have desirable asymptotic properties under weak regularity conditions, simulation studies have shown these estimators to exhibit a small sample bias in the opposite direction of the least squares bias for censored data.
We will minimize the MSE between the estimated log-irradiance and its true value, which is defined by: MSE = E log E i ̂ − log E i 2 = Var log E i ̂ ⏟ variance term + E log E i ̂ − log E i 2 ⏟ squared bias term (24).
Lack of fit results in increased prediction squared bias, and overfitting results in increased prediction variance.
The idea is to exploit the relation between the parameters of the model and the least squares biases.
Our experimental results also demonstrate the 1/f noise power scales with the square of bias voltage, which is in agreement with the results of Fine et al. [17].
The MSE can be thought of as corresponding to the sum of the variance plus the square of bias of θ ^.
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