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Commonly used speech enhancement algorithms estimate the power spectral density of the noise to be removed, or make a decision about the presence of speech in a particular frame, and estimate the clean speech based on these. Errors in a noise estimate or speech activity decision may result in undesirable artifacts, and some errors may be more damaging than others. Robust Bayesian Analysis is used to analyze the sensitivity of algorithms to errors in noise estimates and improve signal-to-noise ratio while mitigating artifacts in the enhanced speech. The findings explain why some common heuristic changes to the Wiener filter algorithm are effective. A standard Wiener algorithm is used for comparison, objective quality measures are used to quantify improvement, and insights into the underlying mechanisms of heuristic methods are offered.