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Unformatted text preview: ECEN 689 - Statistical Computation in Genomic Signal Processing Fall 2009 Homework 2 – Solutions 1. (a) Technical variability comes from uncontrollable/unknown changes that happen be- tween experimental set-ups, which have nothing to do with the biological phenomenon under study itself; biological variability comes from the biological differences between individuals/specimens under study. (b) Fold change does not take into account variability, and thus has poor reproducibility. (c) The sensitivity of a test is the probability that it will reject a false null hypothesis; it is equal thus to 1 - the false negative rate. The specificity of a test is the probability that it will not reject a true null hypothesis; it is equal thus to 1 - the false positive rate. A good test has both large sensitivity and specificity; however, these are often competing requirements. (d) A uniformly most powerful test is more sensitive at any level of specificity than any other test. The t-test is UMP under the assumption of Gaussian populations with the same variance (Technically speaking, this is true in the one-sided case and in the class of similar tests, but, except for very small sample sizes, this caveat may often be ignored). (e) The deviation distribution is the probability density function of the difference ˆ- ˆ over all possible sample training data. This difference should be small around its mean with high probability (small variance) and centered around zero (unbiasedness). Thewith high probability (small variance) and centered around zero (unbiasedness)....
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- Fall '10
- Signal Processing, Null hypothesis, Type I and type II errors, α, Bayes error, COR COR COR