Background μ, σ2• Few observations made by a black box• What is the distribution behind the black box?• E.g., with what probability will it output a number bigger than 5?
Approach• Easy to determine with many observations• With few observations..• Assume a canonical distribution based on prior knowledge• Determine parameters of this distribution using the observations, e.g., mean, variance
Estimating the variance σ2 Chi-Square if the original distribution was Normal
Microarray Data• Many genes, 25000• 2 conditions (or more), many replicates within each condition• Which genes are differentially expressed between the two conditions?
More Specifically• For a particular gene – Each condition is a black box – Say 3 observations from each black box• Do both black boxes have the same distribution? – Assume same canonical distribution – Do both have the same parameters?
Which Canonical Distribution• Use data with many replicates• 418.0294, 295.8019, 272.1220, 315.2978, 294.2242, 379.8320, 392.1817, 450.4758, 335.8242, 265.2478, 196.6982, 289.6532, 274.4035, 246.6807, 254.8710, 165.9416, 281.9463, 246.6434, 259.0019, 242.1968• Distribution??