Probability ratio method

Cummings JR, Haynes JD, Lipchuck LM, Ronsberg MA (1960) A sequential probability ratio method for detecting compounds with diuretic activity in rats. J Pharmacol Exp Ther 128 414—418... 

This feasibility study shows that determination of pellet wt by fast neutron oxygen activation analysis can be used for quality assurance inspection of M34 primers. Either direct oxygen analysis, where a comparison standard (such as lucite) is used, or a ratio method, utilizing the Cu in the cup-anvil combination as an internal standard, can be applied. In general, the uniformity of production primers is quite satisfactory, as is usually the case where production procedures are standardized. It seems likely that the light pellet is one which has been improperly manufd and will probably be well below specifications in pellet wt. Production experience with such primers indicates that only one in 3x10s primers is expected to show low pellet wt therefore, one would not expect to find a reject in a small sampling. Nevertheless, detection and rejection of this one bad unit is critical for the prevention of weapon malfunctions and possible injuries to personnel... 

The accuracy of the ratio method improves if more recent plant cost data are available. This figure is probably accurate to within + 30%. The exchange rate used was taken at 16th October 1986 (US I = AsO.6332). 

The ratio method provides an estimate of AS1 2.9 million. This can be regarded as reasonably accurate ( 30%) considering the original plant cost data is 7 years old. The factorial method has produced a surprisingly similar result. This is probably due to the fact that the plant is not particularly large, and the possibility of estimation cost inaccuracies is reduced. The estimate of AS1 3.5 million determined by the factorial cost technique should therefore also be regarded as an acceptably accurate value. 

Das et al. [37] studied the coefficient of friction signal in order to determine the end-point detection more effectively. As shown in Fig. 4.35, the raw COF data were analyzed and the noise levels were filtered out to more precisely determine the end point of the process. The variance sequential probability ratio test (SPRT) method was adopted to analyze and filter the raw data. The coefficient of friction signal can thus be processed and analyzed to detect the end point more effectively. 

Bayes theorem provides a method to calculate the probability of a disease after the addition of new information to previously obtained information. These formulas can be incorporated into computer spreadsheets and other computer aids to help in the estimation of updated probabilities. One method, which can be performed without a computer, involves using the odds ratio version of Bayes theorem. The odds ratio of the occurrence of a disease is calculated before the test result is known this information is then combined with the results of the test in the form of a likelihood ratio. The final result is again in the form of an odds ratio this can be converted into a probability, if desired. The advantages of this method are that it is relatively easily memorized and that it requires little mathematical calculation. The odds ratio is useful when it is combined with the likelihood ratio in a more memorable form of Bayes theorem ... 

We prefer to determine the enzyme activity in three media one with a stimulating anion (mostly HCO3 ), one with a neutral anion (mostly Cl ) and one with an inhibitory anion (mostly SCN ). The enzyme activity in each of these media should be given. Some authors report only the difference between a stimulating and a neutral medium whereas others give the ratio of the activities. The differential method operates on the assumption that the activity in the medium with the neutral anion is due to other ATPase activities in the enzyme preparation. The ratio method assumes that the activity in the medium with the neutral anion is completely due to a low-activity form of the anion-sensitive ATPase. Since both assumptions are contradictory and probably not true for the relatively crude enzyme preparations, it is better not to give only the difference or the ratio of the activities in these media. 

Kulldorff M, Davis RL, Kolczak M. Lewis E, Lieu T, Platt R. 2011. A maximized sequential probability ratio test for drug and vaccine safety surveillance. Sequential Analysis Design, Methods and Applications. 30(l) 58-78. 

Due to influences of measurement error, manufacturing, assembly and other factors, there is uncertainty in mechanical components geometry size, material properties parameters (such as elastic modulus, Poisson s ratio), and so on. The uncertainty significantly affects the reliability of the mechanical components. Therefore, it is important to choose appropriate distributions of random variables before wear reliability analysis. The traditional probability theory method is one of common methods which are used to deal with the uncertainty of variables. However, the method of probability and statistics is subject to restrictions of sample size, sampling time and sample conditions. Sometimes, because sample size is too small, it is impossible to obtain the probability density functions of random variables. 

Once the bed is constructed, the grounding resistance must be checked for acceptance—a resistance of 2-5 Q. Existing beds should also be checked periodically to detect any changes in the resistance, especially when the soil is dry or the weather is cold. Several methods exist for measuring ground bed resistance, including the three-point method, the fall-of-potential method, and the ratio method. Of these three methods, the fall-of-potential is probably the most widely accepted. For this reason, we will describe only the fall-of-potential method here. 

Fig. 3 shows a result obtained by the variance to mean ratio (VIMR) analysis for the scaled data at Korean TRIGA Mk-II reactor with two neutron counters. The same data can be analyzed by correlation, count probability, FFT method, etc. Should this experiment be done by the conventional method, it needs two NKAs and a computer. Each MCA scales neutron pulse and sends data to the computer. Nowadays, a PC board type MCA is comnercially available and the external data transfer from the MCA to the PC which requires more time than the pulse scaling, is not needed. But a MCA board can receive only one pulse line and the MCA channel size is limited. 

When urainium foils are irradiated, a number of neutron-induced reactions occur. In the case of measuring resonance escape probability by the cadmium-ratio method only the Np activity is significant, yet other activities primarily due to fission will be present, having initial or Compton scattered rays within the 104-keV rainge. The greater the... 

Order-of-magnitude estimate (ratio estimate). Rule-of-thumb method based on cost data for previous similar types of plant probable error within 10 to 50 percent. 

In some cases, we may not be able to draw directly from the posterior distribution. The difficulty lies in calculating the denominator of Eq. (18), the marginal data distribution p(y). But usually we can evaluate the ratio of the probabilities of two values for the parameters, p(Q, y)/p(Qu y), because the denominator in Eq. (18) cancels out in the ratio. The Markov chain Monte Carlo method [40] proceeds by generating draws from some distribution of the parameters, referred to as the proposal distribution, such that the new draw depends only on the value of the old draw, i.e., some function We accept... 

Here AX is the acetyl compound (acetyl chloride or acetic anhydride), N is N-methylimidazole, I is the intermediate (presumably A -acetyl-A -methylimidazo-lium ion), X is the counterion (chloride or acetate), and ROH is the acetyl acceptor (alcohol or water). A general treatment of Scheme XXIII requires specification of the detailed nature of and k[ and is probably too complicated to be of practical use. However, several important special cases may arise from the operation of the ratio kxlk x, the behavior of apparent rate constants k /. and k, the relative magnitudes of k / and k, the relative concentrations of the reactants, the method of observation, and the nature of ROH. These cases are outlined in Scheme XXIV. 

In this context it is important to note that the detection of this land of alkali cation impurity in ionic liquids is not easy with traditional methods for reaction monitoring in ionic liquid synthesis (such as conventional NMR spectroscopy). More specialized procedures are required to quantify the amount of alkali ions in the ionic liquid or the quantitative ratio of organic cation to anion. Quantitative ion chromatography is probably the most powerful tool for this kind of quality analysis. 

Probably the most widely used method for estimating the drop in pressure due to friction is that proposed by LOCKHART and Martinelli(,5) and later modified by Chisholm(,8 . This is based on the physical model of separated flow in which each phase is considered separately and then a combined effect formulated. The two-phase pressure drop due to friction — APtpf is taken as the pressure drop — AP/, or — APG that would arise for either phase flowing alone in the pipe at the stated rate, multiplied by some factor 2L or . This factor is presented as a function of the ratio of the individual single-phase pressure drops and ... 

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