Theory repeated-sampling

The method of maximum likelihood is the standard estimation procedure in statistical inference. Whether one looks at the inference problem from the point of view of classical repeated-sampling theory or Bayesian theory or straightforward likelihood theory, maximizing the likelihood emerges as the preferred procedure. There really is no dispute about this in regular estimation problems, and phylogenetic inference does seem to be unexceptional from a statistical point of view, even though it took a little while for the initial difficulties in the application of maximum likelihood to be sorted out. This was mainly done by Felsenstein (1968) and Thompson (1974) in their Ph.D. dissertations and subsequent publications. 

Where you devise original solutions to the measurement of characteristics the theory and development of the method should be documented and retained as evidence of the validity of the measurement method. Any new measurement methods should be proven by rigorous experiment to detect the measurement uncertainty and cumulative effect of the errors in each measurement process. The samples used for proving the method should also be retained so as to provide a means of repeating the measurements should it prove necessary. 

Experiments at present are concentrated on sd-metals and Pt-group metals. The sp-metals, on which theories of the double layer have been based, are somewhat disregarded. In some cases the most recent results date back more than 10 years. It would be welcome if double-layer studies could be repeated for some sp-metals, with samples prepared using actual surface procedures. For instance, in the case of Pb, the existing data manifest a discrepancy between the crystalline system and the crystal face sequence of other cases (e.g., Sn and Zn) the determination of EgaQ is still doubtful. For most of sp-metals, there are no recent data on the electron work function. 

The statistician has tools available, first developed back in the 1930s by R. A. F. Fisher, a British statistician who undertook to analyze the effect of sample size on experimental results such as these. We have drawn a limited number of animals from what is, in theory, a huge pool of available subjects. If we were to repeat our experiment it is possible, because of chance alone, we could get a slightly different result, say 1/50 in C versus 41/50 in T. And if we were to repeat the experiment again and again and again, we would sometimes see the same result... 

Solid-state NMR has done much to dispel the mysteries of humin compositions, and significant advances have recently been made using proton NMR in the liquid state (see Section 15.3.3 of Chapter 15). Based on solid-state 13C NMR spectra, Hatcher et al. (1980) concluded that a repeating aliphatic structural unit, possibly attributable to branched and cross-linked algal or microbial lipids, is common to both soil and sediment humin samples. Hatcher et al. (1983) viewed the increase in humin relative to the other humic fractions as a selective preservation of the aliphatic compounds of the sediments and did not support condensation theories. 

In theory, Edman degradations could sequence a peptide of any length. In practice, however, the repeated cycles of degradation cause some internal hydrolysis of the peptide, with loss of sample and accumulation of by-products. After about 30 cycles of degradation, further accurate analysis becomes impossible. A small peptide such as bradykinin can be completely determined by Edman degradation, but larger proteins must be broken into smaller fragments (Section 24-9E) before they can be completely sequenced. 

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