Likelihood Ratio Test of Hardy-Weinberg Equilibrium Using Uncertain Genotypes for Sibship Data

Testing for Hardy-Weinberg equilibrium of genotype frequencies is a crucial first step in the study of population genetics. In this paper, we develop an Expectation-Maximization algorithm to estimate the genotype frequencies for sibship data with genotype uncertainty. We also develop a likelihood ratio test of Hardy-Weinberg equilibrium for sibships with no parental genotypes available and with possible genotyping errors. Simulations show that our likelihood ratio test maintains valid control of the type I error rate and good statistical power. Finally, the likelihood ratio test is extended across strata when a sample is stratified by multiple ethnic populations with different genotype frequencies.

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Understanding Dive Computers

Modern digital dive computers date to the early 80s, though analog devices simulating tissue gas uptake and elimination through porous membranes date back to the 70s. Analog devices were limited to nonstop diving and had a short shelf life. 

Digital dive computers proved highly successful and very useful right from the start, progressing from just table emulators to full up algorithmic staging devices across mixed gas, open circuit (OC), re breather (RB), nonstop, decompression, deep, and shallow diving. Dive computers are moderately expensive items these days, and high end units range beyond $1500. Basically, a decompression computer is a microprocessor consisting of a power source, pressure transducer, analog to digital signal converter, internal clock, chip with RAM (random access memory) and ROM (read only memory), and pixel display screen.