Detecting Hidden Effects in High Dimensions

In this talk, I will discuss two problems. The first concerns the sample size that one would need in order for a simple epidemiological study of the association of genes and common diseases to produce meaningful results. This will be achieved by studying the power of the 2-sample Binomial test.

The second topic concerns the detection of a noisy signal hidden in a mass of random noise. I will discuss what happens if independent draws from a mixture density (1-p) f(x) + p f(x-μ) (μ>0) are observed and one would like to identify the observations coming from the second component of the mixture.

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