A SAMPLING SYSTEM FOR ESTIMATING EGG AND LARVAL POPULATIONS OF AGROMYZA FRONTELLA (DIPTERA: AGROMYZIDAE) IN ALFALFA

1980 ◽  
Vol 112 (4) ◽  
pp. 375-385 ◽  
Author(s):  
D. G. Harcourt ◽  
M. R. Binns
Keyword(s):  
Negative Binomial ◽  
Population Estimates ◽  
Sampling System ◽  
Components Of Variance ◽  
Binomial Distributions ◽  
Efficient Sampling ◽  
The Mean ◽  
Sampling Procedures ◽  
Alfalfa Blotch Leafminer ◽  
Agromyza Frontella

AbstractDuring 1977, a detailed study was undertaken to develop efficient sampling procedures for estimating egg and larval populations of the alfalfa blotch leafminer, Agromyza frontella (Rond.), in Vernal alfalfa. Distributions of the stages within and between stems were contagious and stem totals tended to follow negative binomial distributions. Within stems, the density of eggs and larval mines increased exponentially from base to tip. Taking these patterns and the costs of sampling into account, and using the relevant components of variance, four leaves taken systematically from a single stem is proposed as the appropriate sample unit for both eggs and mines. On this basis, 200 stems per field will give adequate precision (less than 10% of the mean with confidence probability 90%) for population estimates. However, the propensity of the leafminer to prefer the middle leaflet to the basal leaflets in the approximate ratio 3:4:3 suggests that sampling costs may be further reduced by restricting counts to the middle leaflet and raising them by a factor of 2.5.

scholarly journals INFLUENCE OF STATISTICAL FLUCTUATIONS ON K/π RATIOS IN RELATIVISTIC HEAVY ION COLLISIONS

2001 ◽  
Vol 16 (07) ◽  
pp. 1227-1235 ◽  
Author(s):  
C. B. YANG ◽  
X. CAI
Keyword(s):  
Negative Binomial ◽  
Heavy Ion ◽  
Relativistic Heavy Ion Collisions ◽  
Relative Variance ◽  
Ion Collisions ◽  
Statistical Fluctuations ◽  
Binomial Distributions ◽  
The Mean ◽  
Multiplicity Distributions ◽  
Statistical Background

The influence of pure statistical fluctuations on K/π ratio is investigated in an event-by-event way. Poisson and the modified negative binomial distributions are used as the multiplicity distributions since they both have statistical background. It is shown that the distributions of the ratio in these cases are Gaussian, and the mean and relative variance are given analytically.

A SEQUENTIAL DECISION PLAN FOR MANAGEMENT OF THE ALFALFA BLOTCH LEAFMINER, AGROMYZA FRONTELLA (DIPTERA: AGROMYZIDAE)

1983 ◽  
Vol 115 (11) ◽  
pp. 1513-1518 ◽  
Author(s):  
D. G. Harcourt
Keyword(s):  
Lead Time ◽  
Negative Binomial ◽  
Sampling Time ◽  
Sequential Decision ◽  
Southern Ontario ◽  
Alternative Action ◽  
Action Strategies ◽  
Alfalfa Blotch Leafminer ◽  
Agromyza Frontella ◽  
Infestation Status

AbstractA sequential decision plan, based on the negative binomial distribution and providing for two infestation classes, has been derived for use in management of the alfalfa blotch leafminer, Agromyza frontella (Rond.), in southern Ontario. It utilizes counts of the eggs in leaflets of alfalfa, and in economic situations will provide growers with sufficient lead time to consider alternative action strategies. An appraisal of the plan by field scouts showed that it rated the infestation status of the leafminer correctly in 48 of 51 cases. Sampling time averaged 25 min per scout per field.

Microstructural Characterisation of a Syntactic Foam

2001 ◽  
Vol 9 (7) ◽  
pp. 449-458 ◽  
Author(s):  
E. Lawrence ◽  
D. Wulfsohn ◽  
R. Pyrz
Keyword(s):  
Volume Fraction ◽  
Syntactic Foam ◽  
Major Axis ◽  
Number Density ◽  
Sampling Protocol ◽  
Polyethylene Matrix ◽  
Efficient Sampling ◽  
Microstructural Characterisation ◽  
The Mean ◽  
Sampling Procedures

Stereological sampling procedures were used to characterize the geometry of the cells of a syntactic foam. The foam, formed by extrusion, consisted of hollow polymeric microballoons in a low-density polyethylene matrix. Estimates of cell volume fraction, number density and the mean and standard deviation of volumes of cells were made using design-based methods, which are generally valid without any assumptions about cell shape. Additionally, the distribution of cell aspect ratio was estimated, assuming ellipsoidal cells with the major axis in the direction of extrusion. In addition to describing the stereological methods used, this paper illustrates how the results of a pilot study can be used to design an efficient sampling protocol.

A comparison of soil sampling procedures used to monitor soil fertility in permanent pastures

Soil Research ◽  
1984 ◽  
Vol 22 (1) ◽  
pp. 81 ◽  
Author(s):  
DK Friesen ◽  
GJ Blair
Keyword(s):  
Sampling Method ◽  
Nutrient Status ◽  
Temporal Variations ◽  
Cluster Sampling ◽  
Soil Test ◽  
Sampling Strategies ◽  
Grazed Pasture ◽  
The Mean ◽  
Sampling Procedures ◽  
Bray 1

Soil testing programs are often brought in disrepute by unexplained variability in the data. The deposition of dung and urine onto grazed pasture brings about marked variation in the chemical status of soils which contributes to this variability. A study was undertaken to compare a range of sampling procedures to estimate Colwell-P, Bray-1 P, bicarbonate K and pH levels in adjacent low and high P status paddocks. The sampling strategies used consisted of 75 by 50 m grids; whole and stratified paddock zig-zag and cluster (monitor plot) samplings. Soil test means for the various parameters did not vary among sampling methods. The number of grid samples required to estimate within 10% of the mean varied from 121 for Bray-1 P down to 1 for soil pH. Sampling efficiencies were higher for cluster sampling than for whole paddock zig-zag path sampling. Stratification generally did not improve sampling efficiency in these paddocks. Soil test means declined as sampling depth increased, but the coefficient of variation remained constant for Colwell-P and pH. The results indicate that cluster sampling (monitor plots) is the most appropriate procedure for estimating the nutrient status of grazed pastures. This sampling method enables a more accurate measure to be taken of the nutrient status of a paddock and should allow more reasonable estimates to be made of the temporal variations in soil test.

A Negative Binomial Regression Model for Accuracy Tests

2012 ◽  
Vol 36 (2) ◽  
pp. 88-103 ◽  
Author(s):  
Lai-Fa Hung
Keyword(s):  
Negative Binomial ◽  
Social Science Research ◽  
Poisson Model ◽  
Negative Binomial Regression ◽  
Science Research ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Negative Binomial Regression Model ◽  
Marginal Maximum Likelihood ◽  
The Mean

Rasch used a Poisson model to analyze errors and speed in reading tests. An important property of the Poisson distribution is that the mean and variance are equal. However, in social science research, it is very common for the variance to be greater than the mean (i.e., the data are overdispersed). This study embeds the Rasch model within an overdispersion framework and proposes new estimation methods. The parameters in the proposed model can be estimated using the Markov chain Monte Carlo method implemented in WinBUGS and the marginal maximum likelihood method implemented in SAS. An empirical example based on models generated by the results of empirical data, which are fitted and discussed, is examined.

scholarly journals Effects of cell cycle variability on lineage and population measurements of mRNA abundance

2020 ◽  
Author(s):  
Ruben Perez-Carrasco ◽  
Casper Beentjes ◽  
Ramon Grima
Keyword(s):  
Gene Expression ◽  
Cell Cycle ◽  
Negative Binomial ◽  
Eukaryotic Cell ◽  
Cycle Duration ◽  
Cell Cycle Duration ◽  
Monotonically Decreasing Function ◽  
Binomial Mixture ◽  
A Cell ◽  
The Mean

AbstractMany models of gene expression do not explicitly incorporate a cell cycle description. Here we derive a theory describing how mRNA fluctuations for constitutive and bursty gene expression are influenced by stochasticity in the duration of the cell cycle and the timing of DNA replication. Analytical expressions for the moments show that omitting cell cycle duration introduces an error in the predicted mean number of mRNAs that is a monotonically decreasing function of η, which is proportional to the ratio of the mean cell cycle duration and the mRNA lifetime. By contrast, the error in the variance of the mRNA distribution is highest for intermediate values of η consistent with genome-wide measurements in many organisms. Using eukaryotic cell data, we estimate the errors in the mean and variance to be at most 3% and 25%, respectively. Furthermore, we derive an accurate negative binomial mixture approximation to the mRNA distribution. This indicates that stochasticity in the cell cycle can introduce fluctuations in mRNA numbers that are similar to the effect of bursty transcription. Finally, we show that for real experimental data, disregarding cell cycle stochasticity can introduce errors in the inference of transcription rates larger than 10%.

scholarly journals Coverage versus Confidence

2021 ◽  
Vol 23 ◽  
Author(s):  
Peyton Cook
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Coverage Probability ◽  
Negative Binomial ◽  
Asymptotic Confidence Interval ◽  
Population Proportion ◽  
Coverage Probabilities ◽  
The Mean

This article is intended to help students understand the concept of a coverage probability involving confidence intervals. Mathematica is used as a language for describing an algorithm to compute the coverage probability for a simple confidence interval based on the binomial distribution. Then, higher-level functions are used to compute probabilities of expressions in order to obtain coverage probabilities. Several examples are presented: two confidence intervals for a population proportion based on the binomial distribution, an asymptotic confidence interval for the mean of the Poisson distribution, and an asymptotic confidence interval for a population proportion based on the negative binomial distribution.

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