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In artificial neural networks, the variance increases and the bias decreases as the number of hidden units increase, [12] although this classical assumption has been the subject of recent debate. [4] Like in GLMs, regularization is typically applied. In k-nearest neighbor models, a high value of k leads to high bias and low variance (see below).
For a normal distribution with unknown mean and variance, the sample mean and (unbiased) sample variance are the MVUEs for the population mean and population variance. However, the sample standard deviation is not unbiased for the population standard deviation – see unbiased estimation of standard deviation.
In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an objective property of an estimator.
This is known as the bias–variance tradeoff. Keeping a function simple to avoid overfitting may introduce a bias in the resulting predictions, while allowing it to be more complex leads to overfitting and a higher variance in the predictions. It is impossible to minimize both simultaneously.
Illustration of regression dilution (or attenuation bias) by a range of regression estimates in errors-in-variables models. Two regression lines (red) bound the range of linear regression possibilities. The shallow slope is obtained when the independent variable (or predictor) is on the abscissa (x-axis).
Detection bias occurs when a phenomenon is more likely to be observed for a particular set of study subjects. For instance, the syndemic involving obesity and diabetes may mean doctors are more likely to look for diabetes in obese patients than in thinner patients, leading to an inflation in diabetes among obese patients because of skewed detection efforts.
A typical measure of bias of forecasting procedure is the arithmetic mean or expected value of the forecast errors, but other measures of bias are possible. For example, a median-unbiased forecast would be one where half of the forecasts are too low and half too high: see Bias of an estimator .
Generally Bessel's correction is an approach to reduce the bias due to finite sample size. Such finite-sample bias correction is also needed for other estimates like skew and kurtosis, but in these the inaccuracies are often significantly larger. To fully remove such bias it is necessary to do a more complex multi-parameter estimation.