Binomial Sampling Research Articles

Coverage‐adjusted Confidence Intervals for a Binomial Proportion

ABSTRACTWe consider the classic problem of interval estimation of a proportion p based on binomial sampling. The ‘exact’ Clopper–Pearson confidence interval for p is known to be unnecessarily conservative. We propose coverage adjustments of the Clopper–Pearson interval that incorporate prior or posterior beliefs into the interval. Using heatmap‐type plots for comparing confidence intervals, we show that the coverage‐adjusted intervals have satisfying coverage and shorter expected lengths than competing intervals found in the literature.

Penehcyclidine and awareness during anaesthesia: caution with zero numerators

Throughout the article ‘penehyclidine’ is misspelled as ‘penehcyclidine’. The colours in Table 1 were accidentally omitted and this Table is printed here in its correct form. The x-axis label and legend to Figure 2 were incorrectly reproduced. The x-axis title should read “Number of red balls”, and the legend should read as below. The Figure and Legend are printed here in their correct form. The text in the second column, 3rd page of this paper [1] should read as follows: This is the distribution obtained when performing binomial sampling without replacement; for example, the probabilities of obtaining 0, 1, 2, 3, 4 and 5 red balls from an urn of 15 red and 5 white balls. The authors and publishers apologise for these errors.

A sequential binomial sampling plan for potato psyllid (Hemiptera: Triozidae) on bell pepper (Capsicum annum )

Potato psyllids (Bactericera cockerelli Sulc) are a pest on solanaceous crop plants, including bell peppers. Potato psyllids vector Candidatus Liberibacter psyllaurous, but bell peppers (Capsicum annum L.) do not exhibit symptoms from infection. Potato psyllids show variation in spatial patterns and host choice with cultivar and plant species. Consequently, a study of spatial distribution and sampling plan specific to bell peppers is necessary for management of this insect pest, as those developed for other crops are unlikely to transfer among crops. Potato psyllids were evenly distributed on both sides of leaves but prefer the top two-thirds of pepper plants. Within fields, psyllids demonstrated an aggregated spatial distribution, but the edge effect observed in other crop plants was absent. Eggs and nymphs had similar spatial distributions that differed from adults. A series of nymph-based sampling plans were examined. Sampling plans based on an infestation of less than 41% of plants infested (5 nymphs plant(-1)) were statistically unacceptable, while little difference was found between the 41% infestation plan and 56% (20 nymphs plant(-1)) infestation plan. At 41%, an average of 11 and maximum of 49 samples would be necessary to make a treatment decision. The binomial sequential sampling plan presented here offers an important yet simple tool for managing potato psyllids in bell pepper.

The Sudden Infant Death Syndrome is a Probability Process

The Sudden Infant Death Syndrome (SIDS) is sudden-unexpected death of an infant that remains unexplained after thorough forensic autopsy, death scene investigation and review of the infant's medical history. As the results of a few spins of a roulette wheel cannot establish whether the wheel is honest (uniform value distribution), medical investigations of a few SIDS cases have not been able to uncover the mechanistic cause of death. We propose that this is because statistical analyses of large numbers of independent observations may be required to unmask the apparent probability processes that govern these quite different phenomena. The SIDS male fraction ~0.60 appears as a binomial probability sample characteristic of a condition caused by an Xlinked gene. The unique SIDS age distribution (minimum at birth, mode ~63 days, median ~94 days, falling exponentially to zero at ~41.2 months) appears as a probability sample from an underlying Johnson SB (4-parameter lognormal) distribution of ages. The presence of this lognormal distribution is prima facie evidence that a probability process is involved. Matching binomial and SB distribution equations to these physiological phenomena, we propose: The SIDS binomial gender distributions arises from an Xlinked recessive allele (q ≈ 2/3) non-protective against acute anoxic encephalopathy; and SIDS Johnson SB age distributions arise from such genetically susceptible infants having Research Article British Journal of Medicine & Medical Research, 3(1): 80-93, 2013 81 three independent risk factors: neurological prematurity (m + 0.31) decreasing with age in months m; risk of respiratory infection increasing with age (41.2 m); and risk of physiological anemia rising and falling with age (2ᴨσ)[exp(-0.5[(y-μ)/σ])] , where y = Log[(m + 0.31)/(41.2 m)] = μ + σ z, μ is median of y, σ is standard deviation of y, with z a standard normal deviate. We show infant Respiratory Distress Syndrome and Suffocation by Inhalation of Food or Foreign Object have approximately the same male fractions as SIDS, supporting the hypothesis that the same allele of an X-linked gene is responsible for death in all these cases.

Bajesov kriterijum odlučivanja u izboru pouzdanih isporučioca

Competitive terms and conditions on the market force organizations to find a way to reduce price of nonconformance increase productivity and improve service to customers. Orientation to customer needs requires continuous improvement of quality of products and services, lower costs, shorter delivery time and the optimal inventory of materials in stock. Company's decision whether certain components should be bought or produced represents a significant dilemma in terms of uncertainty of the market itself. The paper explains the technique to choose a reliable supplier of castings for the production of heating plate - an alternative to using a priori probability, which are reviewed by the sampling process. The paper presents us with the technique of data collection - binomial sampling, with all the appropriate elements of decision-making analysis. The model based on a combination of a priori distribution of the sampling process, using Bayes's theorem for compliance and audit subjective beliefs and information from the a priori probability of the empirical data. The resulting revised or posterior probabilities are then used to find the expected costs of non-compliance for each alternative and the choice of optimal strategy dedicated.

Bajesov kriterijum odlučivanja u izboru pouzdanih isporučilaca

Competitive terms and conditions on the market force organizations to find a way to reduce price of nonconformance increase productivity and improve service to customers. Orientation to customer needs requires continuous improvement of quality of products and services, lower costs, shorter delivery time and the optimal inventory of materials in stock. Company's decision whether certain components should be bought or produced represents a significant dilemma in terms of uncertainty of the market itself. The paper explains the technique to choose a reliable supplier of castings for the production of heating plate - an alternative to using a priori probability, which are reviewed by the sampling process. The paper presents us with the technique of data collection - binomial sampling, with all the appropriate elements of decision-making analysis. The model based on a combination of a priori distribution of the sampling process, using Bayes's theorem for compliance and audit subjective beliefs and information from the a priori probability of the empirical data. The resulting revised or posterior probabilities are then used to find the expected costs of non-compliance for each alternative and the choice of optimal strategy dedicated.

Foliar physiognomic climate estimates for the Late Cretaceous (Cenomanian–Turonian) Lark Quarry fossil flora, central-western Queensland, Australia

Although there is a broad knowledge of Cretaceous climate on a global scale, quantitative climate estimates for terrestrial localities are limited. One source of terrestrial palaeoproxies is foliar physiognomy. The use of foliar physiognomy to explore Cretaceous assemblages has been limited, and some of its potential sources of error have not been fully explored. Although museum collections house a wealth of material, collection bias toward particular taxa or preservation qualities of specimens further magnifies existing taphonomic bias to cold temperatures. As a result, specific collection for foliar physiognomy can be necessary. Here, we conduct three foliar physiognomic analyses on the early Late Cretaceous Lark Quarry flora and assess the results in the context of other proxies from the same formation. Our results suggest that the climate at the Cenomanian–Turonian boundary in central western Queensland was warm and had high precipitation (leaf-area analysis: 1321 mm + 413 mm – 315 mm mean annual precipitation; leaf-margin analysis: 16.4°C mean annual temperature, 5.3°C binomial sample error; climate leaf-analysis multivariate program: 16 ± 2°C for mean annual temperature, 9-month growth season, 1073 ± 483 mm growth-season precipitation). Our analysis also gave higher mean annual temperature estimates than did a previous analysis by climate leaf-analysis multivariate program, based on museum collections for the Winton Formation.

Phototactic personality in fruit flies and its suppression by serotonin and white

Drosophila typically move toward light (phototax positively) when startled. The various species of Drosophila exhibit some variation in their respective mean phototactic behaviors; however, it is not clear to what extent genetically identical individuals within each species behave idiosyncratically. Such behavioral individuality has indeed been observed in laboratory arthropods; however, the neurobiological factors underlying individual-to-individual behavioral differences are unknown. We developed "FlyVac," a high-throughput device for automatically assessing phototaxis in single animals in parallel. We observed surprising variability within every species and strain tested, including identically reared, isogenic strains. In an extreme example, a domesticated strain of Drosophila simulans harbored both strongly photopositive and strongly photonegative individuals. The particular behavior of an individual fly is not heritable and, because it persists for its lifetime, constitutes a model system for elucidating the molecular mechanisms of personality. Although all strains assayed had greater than expected variation (assuming binomial sampling), some had more than others, implying a genetic basis. Using genetics and pharmacology, we identified the metabolite transporter White and white-dependent serotonin as suppressors of phototactic personality. Because we observed behavioral idiosyncrasy in all experimental groups, we suspect it is present in most behaviors of most animals.

Test for conditional odds ratio in matching pairs inverse sampling design

Conditional odds ratio is often used in matched pair design to assess the equivalence of two treatments for both prospective and retrospective clinical trials. In this context some test procedures are available under binomial sampling scheme. The present study provides an alternative approach to the same problem under an inverse binomial sampling scheme. Various performance characteristics of the proposed procedure are examined through exact and simulation studies.

A Binomial Sampling Plans for Aphis gossypii (Hemiptera: Aphididae) in Greenhouse Cultivation of Cucumbers

Infestations of Aphis gossypii per leaf in greenhouse cultivation of cucumbers were investigated to develop binomial sampling plans. An empirical P T -m model, ln(m)=α +β1n[-1n(1-P T )], was used to evaluate relationship between the proportion of infested leaves with ≤ T aphids per leaf (P T ) and mean aphid density (m). Tally thresholds (T) were set to 1, 3, 5, 7, and 9 aphids per leaf to find appropriate T in greenhouse cultivation of cucumbers. Increasing sample size had little effect on the precision of the binomial sampling plan. However, the precision increased with tally threshold. The binomial model with T = 5 provided appropriate predictions of the mean densities of A. gossypii in the greenhouse cultivation of cucumbers. Using a binomial model with T = 5 (sample size = 200), a wide range of densities (1.2 - 222.8 aphids per leaf) could be estimated with precision levels of 0.346 - 0.380 for PT values between 0.15 and 0.96. Binomial models were validated at T = 5 and 7 using 12 independent data sets. Both binomial models were robust and adequately described aphid densities; most of the independent sampling data fell within 95% confidence intervals around the prediction model.

Elaboração de um plano de amostragem para Cigarrinha-Verde (Homoptera: Cicadellidae) em vinha no Vale do Lima

The aims of this work were: to study the spatial patterns of nymphal stages of the green-leafhopper Empoasca vitis using the regression models of Taylor's Power Law and Iwao, in vineyard cvs. Arinto and Vinhao in organic farming and integrated production systems; to develop a binomial sampling (presence-absence). The results showed that: i) Taylor's power law was more appropriate to describe the spatial pattern of E. vitis and indicated a random pattern; no statistically differences were detected between varieties and production systems, ii) the sample size required increases with the degree of accuracy, iii) it is possible to simplify the enumerative sampling plan; and iv) the sample size required to estimate population densities of this pest corresponding to the economic thresholds, ranges from 30 to 57 leaves.

An approach alternative to the binomial UMPU test

We consider a test based on a possible modification of the inverse binomial sampling procedure which has the same size and power as the binomial UMPU test. The proposed procedure leads to a considerable saving in trial size as compared to the fixed trial size binomial two-sided test procedure. We carry out a simulation study to evaluate the performance of the proposed methodology and compare it with a natural competitor.

Empirical Validation of Pooled Whole Genome Population Re-Sequencing in Drosophila melanogaster

The sequencing of pooled non-barcoded individuals is an inexpensive and efficient means of assessing genome-wide population allele frequencies, yet its accuracy has not been thoroughly tested. We assessed the accuracy of this approach on whole, complex eukaryotic genomes by resequencing pools of largely isogenic, individually sequenced Drosophila melanogaster strains. We called SNPs in the pooled data and estimated false positive and false negative rates using the SNPs called in individual strain as a reference. We also estimated allele frequency of the SNPs using “pooled” data and compared them with “true” frequencies taken from the estimates in the individual strains. We demonstrate that pooled sequencing provides a faithful estimate of population allele frequency with the error well approximated by binomial sampling, and is a reliable means of novel SNP discovery with low false positive rates. However, a sufficient number of strains should be used in the pooling because variation in the amount of DNA derived from individual strains is a substantial source of noise when the number of pooled strains is low. Our results and analysis confirm that pooled sequencing is a very powerful and cost-effective technique for assessing of patterns of sequence variation in populations on genome-wide scales, and is applicable to any dataset where sequencing individuals or individual cells is impossible, difficult, time consuming, or expensive.

DNA mixture genotyping by probabilistic computer interpretation of binomially-sampled laser captured cell populations: Combining quantitative data for greater identification information

Two person DNA admixtures are frequently encountered in criminal cases and their interpretation can be challenging, particularly if the amount of DNA contributed by both individuals is approximately equal. Due to an inevitable degree of uncertainty in the constituent genotypes, reduced statistical weight is given to the mixture evidence compared to that expected from the constituent single source contributors. The ultimate goal of mixture analysis, then, is to precisely discern the constituent genotypes and here we posit a novel strategy to accomplish this. We hypothesised that LCM-mediated isolation of multiple groups of cells ('binomial sampling') from the admixture would create separate cell sub-populations with differing constituent weight ratios. Furthermore we predicted that interpreting the resulting DNA profiling data by the quantitative computer-based TrueAllele® interpretation system would result in an efficient recovery of the constituent genotypes due to newfound abilities to compute a maximum LR from sub-samples with skewed weight ratios, and to jointly interpret all possible pairings of sub-samples using a joint likelihood function. As a proof of concept, 10 separate cell samplings of size 20 recovered by LCM from each of two 1:1 buccal cell mixtures were DNA-STR profiled using a specifically developed LCN methodology, with the data analyzed by the TrueAllele® Casework system. In accordance with the binomial sampling hypothesis, the sub-samples exhibited weight ratios that were well dispersed from the 50% center value (50±35% at the 95% level). The maximum log(LR) information for a genotype inferred from a single 20 cell sample was 18.5 ban, with an average log(LR) information of 11.7 ban. Co-inferring genotypes using a joint likelihood function with two sub-samples essentially recovered the full genotype information. We demonstrate that a similar gain in genotype information can be obtained with standard (28-cycle) PCR conditions using the same joint interpretation methods. Finally, we discuss the implications of this work for routine forensic practice.

Asymptotically optimum estimation of a probability in inverse binomial sampling under general loss functions

The optimum quality that can be asymptotically achieved in the estimation of a probability p using inverse binomial sampling is addressed. A general definition of quality is used in terms of the risk associated with a loss function that satisfies certain assumptions. It is shown that the limit superior of the risk for p asymptotically small has a minimum over all (possibly randomized) estimators. This minimum is achieved by certain non-randomized estimators. The model includes commonly used quality criteria as particular cases. Applications to the non-asymptotic regime are discussed considering specific loss functions, for which minimax estimators are derived.

Sample Size under Inverse Negative Binomial Group Testing for Accuracy in Parameter Estimation

BackgroundThe group testing method has been proposed for the detection and estimation of genetically modified plants (adventitious presence of unwanted transgenic plants, AP). For binary response variables (presence or absence), group testing is efficient when the prevalence is low, so that estimation, detection, and sample size methods have been developed under the binomial model. However, when the event is rare (low prevalence <0.1), and testing occurs sequentially, inverse (negative) binomial pooled sampling may be preferred.Methodology/Principal FindingsThis research proposes three sample size procedures (two computational and one analytic) for estimating prevalence using group testing under inverse (negative) binomial sampling. These methods provide the required number of positive pools (), given a pool size (k), for estimating the proportion of AP plants using the Dorfman model and inverse (negative) binomial sampling. We give real and simulated examples to show how to apply these methods and the proposed sample-size formula. The Monte Carlo method was used to study the coverage and level of assurance achieved by the proposed sample sizes. An R program to create other scenarios is given in Appendix S2.ConclusionsThe three methods ensure precision in the estimated proportion of AP because they guarantee that the width (W) of the confidence interval (CI) will be equal to, or narrower than, the desired width (), with a probability of . With the Monte Carlo study we found that the computational Wald procedure (method 2) produces the more precise sample size (with coverage and assurance levels very close to nominal values) and that the samples size based on the Clopper-Pearson CI (method 1) is conservative (overestimates the sample size); the analytic Wald sample size method we developed (method 3) sometimes underestimated the optimum number of pools.

Spatial dispersion and binomial sequential sampling for the potato psyllid (Hemiptera: Triozidae) on potato

The potato psyllid is a serious pest of potatoes. Sampling plans on potatoes for the potato psyllid have yet to be developed, thus the authors' objectives were (1) to determine the most efficient within-plant sampling unit, (2) to determine the spatial dispersion of potato psyllids in potato fields and (3) to develop a binomial sequential sampling plan for this pest. Significantly more potato plants were infested with potato psyllids on the edges of the field, and significantly more plants were infested with psyllids on the 'top' and 'middle' of the potato plant. Significantly more psyllids were also found on the undersides of leaves. The potato psyllid has an aggregated distribution in potato fields. Binomial sequential sampling plans were developed for three action thresholds representing 0.5, 1 and 5 psyllids per plant. The average sample numbers for these action thresholds were between 12 and 16 samples, depending on the action thresholds. However, based on the shape of the operating characteristic curve, the 0.5 and 1 sampling plans were more reliable than the 5 psyllids per plant plan. The binomial sequential sampling plans are useful for detecting potato psyllids at low levels of infestation, which will be useful for pest management purposes.

GROUP-SIZE DIVERSITY IN PUBLIC GOODS GAMES

Public goods games are models of social dilemmas where cooperators pay a cost for the production of a public good while defectors free ride on the contributions of cooperators. In the traditional framework of evolutionary game theory, the payoffs of cooperators and defectors result from interactions in groups formed by binomial sampling from an infinite population. Despite empirical evidence showing that group-size distributions in nature are highly heterogeneous, most models of social evolution assume that the group size is constant. In this article, I remove this assumption and explore the effects of having random group sizes on the evolutionary dynamics of public goods games. By a straightforward application of Jensen's inequality, I show that the outcome of general nonlinear public goods games depends not only on the average group size but also on the variance of the group-size distribution. This general result is illustrated with two nonlinear public goods games (the public goods game with discounting or synergy and the N-person volunteer's dilemma) and three different group-size distributions (Poisson, geometric, and Waring). The results suggest that failing to acknowledge the natural variation of group sizes can lead to an underestimation of the actual level of cooperation exhibited in evolving populations.

Cost-Effective Binomial Sequential Sampling of Western Bean Cutworm, Striacosta albicosta (Lepidoptera: Noctuidae), Egg Masses in Corn

Striacosta albicosta (Smith) (Lepidoptera: Noctuidae), is a native pest of dry beans (Phaseolus vulgaris L.) and corn (Zea mays L.). As a result of larval feeding damage on corn ears, S. albicosta has a narrow treatment window; thus, early detection of the pest in the field is essential, and egg mass sampling has become a popular monitoring tool. Three action thresholds for field and sweet corn currently are used by crop consultants, including 4% of plants infested with egg masses on sweet corn in the silking-tasseling stage, 8% of plants infested with egg masses on field corn with approximately 95% tasseled, and 20% of plants infested with egg masses on field corn during mid-milk-stage corn. The current monitoring recommendation is to sample 20 plants at each of five locations per field (100 plants total). In an effort to develop a more cost-effective sampling plan for S. albicosta egg masses, several alternative binomial sampling plans were developed using Wald's sequential probability ratio test, and validated using Resampling for Validation of Sampling Plans (RVSP) software. The benefit-cost ratio also was calculated and used to determine the final selection of sampling plans. Based on final sampling plans selected for each action threshold, the average sample number required to reach a treat or no-treat decision ranged from 38 to 41 plants per field. This represents a significant savings in sampling cost over the current recommendation of 100 plants.

Sampling of Cacopsylla pyri (Hemiptera: Psyllidae) and Pilophorus gallicus (Hemiptera: Miridae) in Pear Orchards

The psyllid Cacopsylla pyri L. (Hemiptera: Psyllidae), is one of the principal pests of pear (Pyrus spp.) orchards and, along with its natural enemies, needs to be carefully monitored for correct integrate pest management and biological pest control decision making. We compare sampling techniques and develop sampling methods for C. pyri and Pilophorus gallicus Remane (Heteroptera: Miridae). Four pear orchards were sampled periodically from 2007 to 2010 in southern Spain by beating branches into funnels or 45-cm-diameter nets and taking shoot samples. Different sampling techniques were compared, and several sampling methods were assayed for adults and nymphs of C. pyri and P. gallicus. Psylla adult and P. gallicus counts in the nets and funnels were similar and closely correlated. Counts of C. pyri adults in the funnels and nets were higher than on shoots, but all measures were closely correlated. The number of nymphs on shoots and leaves was correlated, as were the counts on leaves within shoots. A guide for choosing the sampling unit in cost/precision terms is given. C. pyri nymphs and adults showed an aggregated distribution, whereas P. gallicus had a less-crowded spatial distribution. Enumerative sequential sampling was evaluated for both insects by using the different sampling techniques by resampling experimental data. The negative binomial distribution fitted the experimental data gathered using the different sampling techniques for C. pyri adults and P. gallicus. The use of binomial sampling is discussed for the two insects and the costs involved are compared with those implied in the sequential enumerative method.