Pooled mean

Zinc absorption (%) (standard error of pooled mean 3.54)... 

Because of the too slow cooling rate of the High Pressure Freezing technique (10,000 K/s), water pools mean sizes were overestimated by TEM. Indeed, HPF essentially guarantees to produce a snapshot of the reverse microemulsion phase though this... 

Kirschbaimi et al. (1998) used a somewhat different modeling approach to simulate the effects of phosphorus availability on temperate forest COi-induced growth responses. But similar to the results here, they concluded that the presence of the secondary (labile) pool means that, in the short term, phosphorus availability should not constrain the ability of these forests to respond to [CO2]. They also concluded, however, that marked phosphorus constraints should become apparent on a time scale of... 

Pooled mean value of 8 animals for the entire period of 12 days. 

Statistics. Data for Expt. 1 were analyzed by one-way analysis of variance (26). Differences among means were checked by least significant difference. In Expt. 2 the repeated measurement design (i.e. three balance periods) was subjected to a split-plot analysis of variance as outlined by Gill and Hafs (27). Differences among pooled means were verified by least significant difference. 

P = and assume ti = 1 for all i. Therefore, the pool mean will be equal to a, the weight for the observed frequency depends only on and 8 becomes ... 

The range of theoretical values of plus or minus 50% of the target value of a pool means that there will be overlap of the pools. For example, the range of values for the medium-low pool for cadmium in blood is 3.5 to 10.5 [ig/l while the range of values for the medium-high pool is 5 to 15 ng/l. Therefore, it is possible for a quality control sample from the medium-low pool to have a higher concentra-... 

This model is expressed in terms of the parameters (a,b) which are common to the pool and so the pooled empirical data can be used to obtain estimates of these parameters using either maximum likelihood estimation or moment matching methods. Once the pool parameters have been estimated, Bayes Theorem can be used to update the prior for each asset to obtain its posterior based on the individual asset experience. The resulting posterior distribution for the failure frequencies over a given time horizon for a particular asset is a Poisson distribution with a mean that is a weighted average of the pooled mean and the individual asset experience. 

For the situation where we have the lowest level of the intensity at 0.0008 failures per annum, then we inevitably simulate many asset sample data sets with zero observed failures in a given year. For example, in some years we find that none of the assets experienced a failure event, but in other years only a single asset experienced a failure. Due to the properties of empirical Bayes estimation we find that in such circumstances an average weighted towards the pooled mean is allocated for zero event assets. In years when there is a failure event, even if only for one out of say the 20 assets in the pool, then this tends to increase the pool mean and hence the year ahead predicted number of failures. Equally in years where there are no observed failure events then the pooled mean decreases due to the additional exposure accumulated. It is also clear that the predicted number of failures for those particular assets which experience events are increased above the pool mean to account for their local history. 

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