Typically, maximum-likelihood estimates are asymptotically unbiased.

That is they converge to the unknown 'true' value of a parameter (if that concept applies) as the quantity of observed data (sample size) increases.

However, rarely do we have sufficient data to assume negligible biasedness.

A conceptual challenge in statistical inference is judging the degree to which we accept the trade-off between bias and uncertainty.

Bias and parsimony are interconnected - as with parsimony, diagnostic tools such as AIC (or AICc, QAIC, QAICc) and BIC assist investigators in formally deciding upon the 'best' model.

However, the 'best' model may not be a good enough model if it fails goodness-of-fit diagnostics or retrospective analysis.

Bias in parameter estimates is defined as the difference between the 'true' value and the expected value of the parameter (as defined by the deterministic model and its error specification).

Bias can sometimes be determined analytically, but for other than simple models is almost always determined by simulations, where those simulations use 'known' (as defined by the analyst) values of those parameters, 'known' being a proxy term for unknown 'true' values.

Repeated analyses of these simulated data provide a distribution of parameter estimates which are judged for their ability to unbiasedly and confidently estimate the 'known' value.