Binned histogram

Figure 22.4 Monte Carlo techniques were used to simulate different hypothetical individuals for different instances of the trial design, using variability and uncertainty distributions from the model analysis. The result is a collection of predicted outcomes, shown as a binned histogram (top figure). Success was defined as a difference in end point measurement of X or smaller between drug and comparator. Likelihood of success (shown in the bottom figure as a cumulative probability) for this example (low/medium drug dose and high comparator dose) is seen to be low, about 33%.

The analysis from the P passes are combined to give an overall multiple pass analysis of the data. The result is an MP bin histogram and a measure of the amount of the signal that is due to "dust". 

The only density estimators discussed in the protein literature are histogram estimates. However, these are nonsmooth and thus not suitable for global optimization techniques that combine local and global search. Moreover, histogram estimates have, even for an optimally chosen bin size, the extremely poor accuracy of only, for a sample of size n. The theo-... 

One therefore needs a smooth density estimation techniques that is more reliable than the histogram estimates. The automatic estimation poses additional problems in that the traditional statistical techniques for estimating densities usually require the interactive selection of some smoothing parameter (such as the bin size). Some publicly available density estimators are available, but these tended to oversmooth the densities. So we tried a number of ideas based on numerical differentiation of the empirical cdf to devise a better density estimator. 

Each bin is connected to a memory location in a computer so that each event can be stored additively over a period of time. All the totaled events are used to produce a histogram, which records ion event times versus the number of times any one event occurs (Figure 31.5).With a sufficiently large number of events, these histograms can be rounded to give peaks, representing ion m/z values (from the arrival times) and ion abundances (from the number of events). As noted above, for TOP instruments, ion arrival times translate into m/z values, and, therefore, the time and abundance chart becomes mathematically an m/z and abundance chart viz., a normal mass spectrum is produced. 

The overall x-range (which scales the plot) and that part of the x-range, which is to be subdivided into B classes (bins) can be individually defined essentially, this means that the plotted window can be adjusted to be the same for comparing several histograms, while bins need only be defined in that part of the x-axis where the measurements are concentrated. The optimal number of bins is suggested as B -Vn, but can be adjusted. 

Stack) a selected range of columns is automatically mapped into a stack of histograms on common x- and y-scales the vertical offset between histograms corresponds to the largest frequency found in all bins. 

In practice, the continuous function p( ) is represented as a histogram consisting of M bins. If all bins have equal size Z = ( i - 0) /M then... 

Time-domain detection results in histograms of photon arrival times. In time-correlated SPC, the time-bins correspond to the analog-to-digital conversion levels, whereas in time-gated SPC, the time-bins are the time-windows during which the photoncounting gate is activated. 

In the left panel of Fig. 1 we present the [Fe/H] distributions for planet host stars (hashed histogram) included in the CORALIE planet-search sample [25], when compared with the same distribution for 900 stars in the whole CORALIE program (open histogram). The knowledge of the uniformly determined metallicity distribution for stars in the solar neighborhood (and included in the CORALIE sample) permits us to determine the percentage of planet host stars per metallicity bin. 

The 2D conductance-distance histogram shows the logarithm of the experimentally obtained conductance in units of Go plotted vs distance [54, 63, 142], The distance axis is normalized with respect to the atomic contact rupture, to align the experimental traces to a common point. Examples are z = 0 at G = 0.7 G0 [54], Individual conductance-distance traces obtained in this manner are binned in 2D space (usually 1,000 x 1,000 bins), and then all individual 2D histograms are added together. The result represents statistically significant conductance-distance trends. 

Fig. 10 Two-dimensional (2D) histograms (plateau scattering vs position) at various electrode potentials for Au(l 11) in 0.1 M H2SO4. The statistical analysis is based on 2D bins...

These ten results represent a sample from a much larger population of data as, in theory, the analyst could have made measurements on many more samples taken from the tub of low-fat spread. Owing to the presence of random errors (see Section 6.3.3), there will always be differences between the results from replicate measurements. To get a clearer picture of how the results from replicate measurements are distributed, it is useful to plot the data. Figure 6.1 shows a frequency plot or histogram of the data. The horizontal axis is divided into bins , each representing a range of results, while the vertical axis shows the frequency with which results occur in each of the ranges (bins). 

Figure 1.8. Histogram for sub-grid-scale distribution of

Likewise, in the limit of large numbers of samples and bins, the bi-variate histogram can be used to compute an estimate for the joint PDF of [Pg.40]

For the moment estimates, we have seen that the composition PDF, /, (delta functions (i.e., the empirical PDF in (6.210)). However, it should be intuitively apparent that this representation is unsatisfactory for understanding the behavior of fyiir) as a function of fj. In practice, the delta-function representation is replaced by a histogram using finite-sized bins in composition space (see Fig. 6.5). The histogram h, (k) for the /ctli cell in composition space is defined by... 

Fig. 6.1 Activity histogram (left Y axis) and cumulative frequency curve (right Y axis) versus binned percent inhibition (X axis) for a recent primary HTS run at Wyeth. Note the sudden spike in the cumulative frequency curve for compounds with >100% inhibition, corresponding to the 0.2% most active compounds.

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