scholarly journals Spatial Distribution and Development of Sequential Sampling Plans for Diaphorina citri Kuwayama (Hemiptera: Liviidae)

Agronomy ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1434
Author(s):  
Gabriel Díaz-Padilla ◽  
J. Isabel López-Arroyo ◽  
Rafael A. Guajardo-Panes ◽  
Ignacio Sánchez-Cohen
Keyword(s):  
Spatial Distribution ◽  
Sequential Sampling ◽  
Field Evaluation ◽  
Production Costs ◽  
Ratio Test ◽  
Operational Characteristic ◽  
Diaphorina Citri ◽  
Sample Number ◽  
Sampling Plans ◽  
Sequential Probability

Vector control in huanglongbing management has been conducted on a calendar basis resulting in high production costs. We addressed this issue and proposed a sequential sampling plan to support decision making for intervention against Diaphorina citri Kuwayama, which is involved in the transmission of the bacteria Candidatus Liberibacter asiaticus, associated with such lethal disease. We analyzed 3,264,660 records from samples gathered from the Mexican trapping program for the monitoring of D. citri; it included weekly inspection of 86,004 yellow sticky traps distributed in the country. Spatial distribution of the insect, estimation of a common k (kc), and sequential sampling plans based on Sequential Probability Ratio Test (SPRT) were determined. Taylor’s power law coefficients were ≥1 indicating aggregation in the spatial distribution of the insect. Common k ranged from 0.0183 to 0.2253 and varied independently of geographic zone or citrus species. We obtained 18 sequential sampling plans, one for each state. In the Average Sample Number (ASN) function, the minimal number of samples to make a decision ranged from 17 to 65. In the Operational Characteristic (OC) function, probabilities for a correct intervention at the threshold of 0.2 D. citri adults/trap in most cases were above 80%. In a field evaluation, the application of sampling plans yielded savings obtained by reduction in the number of interventions for insect control.

Accuracy of sequential sampling plans based on Wald's sequential probability ratio test

1983 ◽  
Vol 13 (6) ◽  
pp. 1197-1203 ◽  
Author(s):  
Gary W. Fowler
Keyword(s):  
Monte Carlo ◽  
Sequential Sampling ◽  
Sequential Probability Ratio Test ◽  
Ratio Test ◽  
Type I ◽  
Sample Number ◽  
Sampling Plans ◽  
Probability Ratio ◽  
Sequential Probability ◽  
Relative Errors

Monte Carlo operating characteristic (OC) and average sample number (ASN) functions were compared with Wald's OC and ASN equations for sequential sampling plans based on Wald's sequential probability ratio test (SPRT) using the binomial, negative binomial, normal, and Poisson distributions. This comparison showed that the errors inherent in Wald's equations as a result of "overshooting" the decision boundaries of the SPRT can be large. Relative errors increased for the OC and ASN equations as the difference between the null (θ0)) and alternative (θ1) test parameter values increased. Relative errors also increased for the ASN equation as the probabilities of type I (α) and type II (β) errors increased. For discrete distributions, the relative errors also increased as θ0 increased with θ1/θ0 fixed. Wald's equations, in general, overestimate the true error probabilities and underestimate the true ASN. For the values of θ0, θ1, α, and β used in many sequential sampling plans in forestry, Wald's equations may not be adequate. For those cases where the errors in Wald's equations are important compared with the other errors associated with the sampling plan, two alternative Monte Carlo OC and ASN functions are proposed.

The use of Wald's sequential probability ratio test to develop composite three-decision sampling plans

1985 ◽  
Vol 15 (2) ◽  
pp. 326-330
Author(s):  
Gary W. Fowler
Keyword(s):  
Monte Carlo ◽  
Negative Binomial ◽  
Sequential Sampling ◽  
Ratio Test ◽  
Sample Number ◽  
Sampling Plans ◽  
Probability Ratio ◽  
Sequential Probability ◽  
Error Probabilities ◽  
Decision Boundaries

Many sequential sampling plans used in forest sampling are composite three-decision plans based on the simultaneous use of two of Wald's sequential probability ratio tests (SPRTs). Wald's operating characteristic (OC) and average sample number (ASN) equations for each SPRT are used to describe the properties of the composite sampling plan. Wald's equations are only approximate because of "overshooting" of the decision boundaries of the SPRTs and the two SPRTs operate simultaneously in the composite plan. Wald's and Monte Carlo OC and ASN functions were developed for (i) two SPRTs used to develop a three-decision composite plan and (ii) the three-decision composite plan based on the negative binomial distribution. Wald's equations, in general, overestimate the true error probabilities and underestimate the true ASN for a given SPRT. Wald's equations are less accurate in describing the properties of the three-decision plan. Monte Carlo functions are more accurate than Wald's functions. Recommendations are made regarding the choice between Wald's and Monte Carlo functions. A Monte Carlo procedure to modify the decision boundaries of the plan to yield actual error probabilities approximately equal to the desired error probabilities is suggested.

SEQUENTIAL SAMPLING OF ADULT NORTHERN AND WESTERN CORN ROOTWORMS (COLEOPTERA: CHRYSOMELIDAE) IN SOUTHERN ONTARIO

1987 ◽  
Vol 119 (6) ◽  
pp. 577-585 ◽  
Author(s):  
H.J. McAuslane ◽  
C.R. Ellis ◽  
O.B. Allen
Keyword(s):  
Negative Binomial ◽  
Sequential Sampling ◽  
Ratio Test ◽  
Economic Threshold ◽  
Diabrotica Barberi ◽  
Southern Ontario ◽  
Sampling Plans ◽  
Field Corn ◽  
Corn Rootworms ◽  
Sequential Probability

AbstractThree sequential-sampling plans were developed for adult Diabrotica barberi Smith and Lawrence and D. virgifera virgifera LeConte in field corn in southern Ontario. The distribution of both species was well approximated by the negative binomial distribution and obeyed Taylor’s power law. Two plans, following the methods of Kuno (1969) and Green (1970), estimated populations with predetermined precision. The third plan, based on Wald’s (1947) sequential probability ratio test, categorized populations relative to an economic threshold. Different sequential-sampling plans were constructed for 1st-year fields and for all other fields because the parameter k, measuring the extent of aggregation of the beetles, differed between these two classes of fields. Decision equations for Wald’s plan in 1st-year fields were: D1 = 0.98n − 17.75 and D2 = 0.98n + 13.82. Decision equations for 2nd-year or older fields were: D1 = 0.99n − 13.42 and D2 = 0.99n + 10.45. The use of Wald’s plan reduced the required sample size by 55% in 1st-year fields, and by 48% in all other fields. The savings associated with the other sequential-sampling plans were not significant.

scholarly journals Spatial distribution pattern and sequential sampling plans for Bactrocera oleae (Gmelin) (Dip: Tephritidae) in olive orchards

2016 ◽  
Vol 48 (1) ◽  
pp. 23
Author(s):  
A. Arbab ◽  
F. Mirphakhar
Keyword(s):  
Spatial Distribution ◽  
Sample Size ◽  
Sequential Sampling ◽  
Bactrocera Oleae ◽  
Sampling Plans ◽  
Optimum Sample Size ◽  
Precision Level ◽  
The Individual ◽  
Optimum Sample ◽  
Basic Distribution

The distribution of adult and larvae <em>Bactrocera oleae</em> (Diptera: Tephritidae), a key pest of olive, was studied in olive orchards. The first objective was to analyze the dispersion of this insect on olive and the second was to develop sampling plans based on fixed levels of precision for estimating <em>B. oleae</em> populations. The Taylor’s power law and Iwao’s patchiness regression models were used to analyze the data. Our results document that Iwao’s patchiness provided a better description between variance and mean density. Taylor’s <em>b</em> and Iwao’s <em>β</em> were both significantly more than 1, indicating that adults and larvae had aggregated spatial distribution. This result was further supported by the calculated common <em>k</em> of 2.17 and 4.76 for adult and larvae, respectively. Iwao’s a for larvae was significantly less than 0, indicating that the basic distribution component of <em>B. oleae</em> is the individual insect. Optimal sample sizes for fixed precision levels of 0.10 and 0.25 were estimated with Iwao’s patchiness coefficients. The optimum sample size for adult and larvae fluctuated throughout the seasons and depended upon the fly density and desired level of precision. For adult, this generally ranged from 2 to 11 and 7 to 15 traps to achieve precision levels of 0.25 and 0.10, respectively. With respect to optimum sample size, the developed fixed-precision sequential sampling plans was suitable for estimating flies density at a precision level of D=0.25. Sampling plans, presented here, should be a tool for research on pest management decisions of <em>B. oleae</em>.

scholarly journals Action Thresholds for Summer Fungicide Sprays and Sequential Classification of Apple Scab Incidence

Plant Disease ◽  
2009 ◽  
Vol 93 (5) ◽  
pp. 490-498 ◽  
Author(s):  
Odile Carisse ◽  
Catherine Meloche ◽  
Guy Boivin ◽  
Tristan Jobin
Keyword(s):  
Decision Making ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Sequential Sampling ◽  
Apple Scab ◽  
Parameter Estimates ◽  
Ratio Test ◽  
Sample Number ◽  
Action Thresholds

The objectives of this study were to establish scab incidence thresholds at which summer fungicide sprays should be initiated and to develop sequential sampling for classification plans to facilitate decision making. The relationship between proportion of scabbed leaves per shoot and percent scabbed fruits at harvest was established based on data collected in both experimental and commercial orchards. Action threshold at which fungicide spray program should be initiated in order to maintain fruit scab at harvest below 2% was established at 0.006 scabbed leaves per shoot; hence incidence thresholds of 0.005 and 0.01 scabbed leaves per shoot were evaluated. Sequential sampling for classification procedures (SSCP), using the Wald's sequential probability ratio test (SPRT), were developed based on a beta-binomial distribution and using parameter estimates of the binary power law. Monte Carlo simulations were used to establish the probability of classifying mean scab incidence as less than the action thresholds (pth = 0.005 and pth = 0.01). Operating characteristic (OC) and average sample number (ASN) curves were established for eight combinations of stop lines and error levels (α and β). Based on the results of the Monte Carlo simulations, four sets of stop lines (two for each pth threshold) were selected for further evaluation. Bootstrap simulations of 50 data sets indicated that both the OC and ASN curves for each of the four pairs of stop lines were similar to OC and ASN values determined by Monte Carlo simulation. When validated with data not used to construct the models, the SSCPs provided the appropriate classification in 98 and 95% of the simulations for the pth = 0.005 and pth = 0.01 (α = 0.05 and β = 0.10), respectively. The sequential sampling plans developed in this study should allow for rapid and accurate classification of the incidence of apple scab on leaves, and aid in sampling for summer scab management decision making.

scholarly journals Control of Traffic Intensity in Hyperexponential and Mixed Erlang Queueing Systems with a Method Based on SPRT

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Müjgan Zobu ◽  
Vedat Sağlam
Keyword(s):  
Operating Characteristic ◽  
Queueing Systems ◽  
Ratio Test ◽  
Traffic Intensity ◽  
Sample Number ◽  
Average Sample Number ◽  
Phase Type ◽  
Sequential Probability ◽  
Matlab Programming ◽  
Average Sample

The control of traffic intensity is one of the important problems in the study of queueing systems. Rao et al. (1984) developed a method to detect changes in the traffic intensity in queueing systems of the and types based on the Sequential Probability Ratio Test (SPRT). In this paper, SPRT is theoretically investigated for two different phase-type queueing systems which consist of hyperexponential and mixed Erlang. Also, for testing against , Operating Characteristic (OC) and Average Sample Number (ASN) functions are obtained with numerical methods using multipoint derivative equations according to different situations of and type errors. Afterward, numerical illustrations for each model are provided with Matlab programming.

scholarly journals Sampling for Plant Disease Incidence

1999 ◽  
Vol 89 (11) ◽  
pp. 1088-1103 ◽  
Author(s):  
L. V. Madden ◽  
G. Hughes
Keyword(s):  
Power Law ◽  
Binomial Distribution ◽  
Disease Incidence ◽  
Sequential Sampling ◽  
Cluster Sampling ◽  
Diseased Plant ◽  
Ratio Test ◽  
Wide Range ◽  
Sequential Probability ◽  
The Relationship

Knowledge of the distribution of diseased plant units (such as leaves, plants, or roots) or of the relationship between the variance and mean incidence is essential to efficiently sample for diseased plant units. Cluster sampling, consisting of N sampling units of n individuals each, is needed to determine whether the binomial or beta-binomial distribution describes the data or to estimate parameters of the binary power law for disease incidence. The precision of estimated disease incidence can then be evaluated under a wide range of settings including the hierarchical sampling of groups of individuals, the various levels of spatial heterogeneity of disease, and the situation when all individuals are disease free. Precision, quantified with the standard error or the width of the confidence interval for incidence, is directly related to N and inversely related to the degree of heterogeneity (characterized by the intracluster correlation, ρ). Based on direct estimates of ρ (determined from the θ parameter of the beta-binomial distribution or from the observed variance) or a model predicting ρ as a function of incidence (derived from the binary power law), one can calculate, before a sampling bout, the value of N needed to achieve a desired level of precision. The value of N can also be determined during a sampling bout using sequential sampling methods, either to estimate incidence with desired precision or to test a hypothesis about true disease incidence. In the latter case, the sequential probability ratio test is shown here to be useful for classifying incidence relative to a hypothesized threshold when the data follows the beta-binomial distribution with either a fixed ρ or a ρ that depends on incidence.

Development of Binomial Sequential Sampling Plans for Sugarcane Aphid (Hemiptera: Aphididae) in Commercial Grain Sorghum

2020 ◽  
Vol 113 (4) ◽  
pp. 1990-1998 ◽  
Author(s):  
Jessica C Lindenmayer ◽  
Kristopher L Giles ◽  
Norman C Elliott ◽  
Allen E Knutson ◽  
Robert Bowling ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Sequential Sampling ◽  
Grain Sorghum ◽  
Ratio Test ◽  
Test Model ◽  
Leaf Sample ◽  
Melanaphis Sacchari ◽  
Sampling Plans ◽  
Sugarcane Aphid ◽  
Economic Thresholds

Abstract The sugarcane aphid (Melanaphis sacchari Zehntner) is a significant economic pest of grain sorghum (Sorghum bicolor (L.) Moench) in the Southern United States. Current nominal and research-based economic thresholds are based on estimates of mean aphids per leaf. Because enumerating aphids per leaf is potentially time consuming, binomial sequential sampling plans for M. sacchari were developed that allow users to quickly classify the economic status of field populations and determine when an economic threshold has been exceeded. During 2016 and 2017, counts of M. sacchari were recorded from 281 sampling events in 140 sorghum fields located in six states (Oklahoma, Kansas, Texas, Arkansas, Louisiana, Mississippi) . Regression analysis was used to describe the relationships between the mean M. sacchari density per two-leaf sample and proportion of plants infested with one or more aphids. Tally thresholds of T50 and T100 aphids per two-leaf sample were selected based on goodness of fit and practicality. Stop lines for both tally thresholds were developed for selected economic thresholds using Wald’s sequential probability ratio test. Model validations using an additional 48 fields demonstrated that reliable classification decisions could be made with an average of 11 samples regardless of location. This sampling system, when adopted, can allow users to easily and rapidly determine when M. sacchari infestations need to be treated.

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