Hypothesis testing and earthquake prediction.

Requirements for testing include advance specification of the conditional rate density (probability per unit time, area, and magnitude) or, alternatively, probabilities for specified intervals of time, space, and magnitude. Here I consider testing fully specified hypotheses, with no parameter adjustments or arbitrary decisions allowed during the test period. Because it may take decades to validate prediction methods, it is worthwhile to formulate testable hypotheses carefully in advance. Earthquake prediction generally implies that the probability will be temporarily higher than normal. Such a statement requires knowledge of "normal behavior"--that is, it requires a null hypothesis. Hypotheses can be tested in three ways: (i) by comparing the number of actual earth-quakes to the number predicted, (ii) by comparing the likelihood score of actual earthquakes to the predicted distribution, and (iii) by comparing the likelihood ratio to that of a null hypothesis. The first two tests are purely self-consistency tests, while the third is a direct comparison of two hypotheses. Predictions made without a statement of probability are very difficult to test, and any test must be based on the ratio of earthquakes in and out of the forecast regions.

Changes in global gene expression patterns during development and maturation of the rat kidney

We set out to define patterns of gene expression during kidney organogenesis by using high-density DNA array technology. Expression analysis of 8,740 rat genes revealed five discrete patterns or groups of gene expression during nephrogenesis. Group 1 consisted of genes with very high expression in the early embryonic kidney, many with roles in protein translation and DNA replication. Group 2 consisted of genes that peaked in midembryogenesis and contained many transcripts specifying proteins of the extracellular matrix. Many additional transcripts allied with groups 1 and 2 had known or proposed roles in kidney development and included LIM1, POD1, GFRA1, WT1, BCL2, Homeobox protein A11, timeless, pleiotrophin, HGF, HNF3, BMP4, TGF-α, TGF-β2, IGF-II, met, FGF7, BMP4, and ganglioside-GD3. Group 3 consisted of transcripts that peaked in the neonatal period and contained a number of retrotransposon RNAs. Group 4 contained genes that steadily increased in relative expression levels throughout development, including many genes involved in energy metabolism and transport. Group 5 consisted of genes with relatively low levels of expression throughout embryogenesis but with markedly higher levels in the adult kidney; this group included a heterogeneous mix of transporters, detoxification enzymes, and oxidative stress genes. The data suggest that the embryonic kidney is committed to cellular proliferation and morphogenesis early on, followed sequentially by extracellular matrix deposition and acquisition of markers of terminal differentiation. The neonatal burst of retrotransposon mRNA was unexpected and may play a role in a stress response associated with birth. Custom analytical tools were developed including “The Equalizer” and “eBlot,” which contain improved methods for data normalization, significance testing, and data mining.