Sequential Sampling Method Research Articles

Sampling for Conditional Inference on Case–Control Data

The problem of exact conditional inference for discrete multivariate case-control data has two forms. The first is grouped case-control data, where Monte Carlo computations can be done using the importance sampling method of Booth and Butler (1999, Biometrika86, 321-332), or a proposed alternative sequential importance sampling method. The second form is matched case-control data. For this analysis we propose a new exact sampling method based on the conditional-Poisson distribution for conditional testing with one binary and one integral ordered covariate. This method makes computations on data sets with large numbers of matched sets fast and accurate. We provide detailed derivation of the constraints and conditional distributions for conditional inference on grouped and matched data. The methods are illustrated on several new and old data sets.

후보점과 대표점 교차검증에 의한 순차적 실험계획

Recently simulation model becomes an essential tool for analysis and design of a system but it is often expensive and time consuming as it becomes complicate to achieve reliable results. Therefore, high-fidelity simulation model needs to be replaced by an approximate model, the so-called metamodel. Metamodeling techniques include 3 components of sampling, metamodel and validation. Cross-validation approach has been proposed to provide sequnatially new sample point based on cross-validation error but it is very expensive because cross-validation must be evaluated at each stage. To enhance the cross-validation of metamodel, sequential sampling method using candidate points and representative cross-validation is proposed in this paper. The candidate and representative cross-validation approach of sequential sampling is illustrated for two-dimensional domain. To verify the performance of the suggested sampling technique, we compare the accuracy of the metamodels for various mathematical functions with that obtained by conventional sequential sampling strategies such as maximin distance, mean squared error, and maximum entropy sequential samplings. Through this research we learn that the proposed approach is computationally inexpensive and provides good prediction performance.

크리깅 모델을 이용한 순차적 근사최적화

Nowadays, it is performed actively to optimize by using an approximate model. This is called the approximate optimization. In addition, the sequential approximate optimization (SAO) is the repetitive method to find an optimum by considering the convergence of an approximate optimum. In some recent studies, it is proposed to increase the fidelity of approximate models by applying the sequential sampling. However, because the accuracy and efficiency of an approximate model is directly connected with the design area and the termination criteria are not clear, sequential sampling method has the disadvantages that could support an unreasonable approximate optimum. In this study, the SAO is executed by using trust region, Kriging model and Optimal Latin Hypercube design (OLHD). Trust region is used to guarantee the convergence and Kriging model and OLHD are suitable for computer experiment. Finally, this SAO method is applied to various optimization problems of highly nonlinear mathematical functions. As a result, each approximate optimum is acquired and the accuracy and efficiency of this method is verified by comparing with the result by established method.

Stopping-Time Resampling for Sequential Monte Carlo Methods

Summary Motivated by the statistical inference problem in population genetics, we present a new sequential importance sampling with resampling strategy. The idea of resampling is key to the recent surge of popularity of sequential Monte Carlo methods in the statistics and engin-eering communities, but existing resampling techniques do not work well for coalescent-based inference problems in population genetics. We develop a new method called ‘stopping-time resampling’, which allows us to compare partially simulated samples at different stages to terminate unpromising partial samples and to multiply promising samples early on. To illustrate the idea, we first apply the new method to approximate the solution of a Dirichlet problem and the likelihood function of a non-Markovian process. Then we focus on its application in population genetics. All our examples show that the new resampling method can significantly improve the computational efficiency of existing sequential importance sampling methods.

Reweighting for nonequilibrium Markov processes using sequential importance sampling methods

We present a generic reweighting method for nonequilibrium Markov processes. With nonequilibrium Monte Carlo simulations at a single temperature, one calculates the time evolution of physical quantities at different temperatures, which greatly saves computational time. Using the dynamical finite-size scaling analysis for the nonequilibrium relaxation, one can study the dynamical properties of phase transitions together with the equilibrium ones. We demonstrate the procedure for the Ising model with the Metropolis algorithm, but the present formalism is general and can be applied to a variety of systems as well as with different Monte Carlo update schemes.

Surface Profiling Using Sequential Sampling and Inverse Methods. Part II: Implementation and Experimental Results

Surface Profiling Using Sequential Sampling and Inverse Methods. Part II: Implementation and Experimental Results

Surface profiling using sequential sampling and inverse methods. Part I: Mathematical background

A novel method is presented for measuring the height profile of the surface of an object, even in the presence of relative motion between the surface and the height sensors. The method involves making height measurements of the surface using several sensors arranged along the scanned surface. The surface profile and the relative motions are mathematically separated by observing that the surface features appear sequentially among the sensor data, while the relative motions appear simultaneously. The proposed linear inverse technique overcomes several limitations of existing profiling methods based on curvature measurements. In contrast with other inverse calculations, the results are quite stable, with noise in the results only about twice the measurement noise. Regularization is introduced as a means of smoothing noise and for achieving solutions for ill-posed cases. This paper focuses on the profile calculation of one-sided objects, and initially uses the assumption that the rigid relative motion between object and sensors is purely translational.

Surface Profiling Using Sequential Sampling and Inverse Methods. Part I: Mathematical Background

Surface Profiling Using Sequential Sampling and Inverse Methods. Part I: Mathematical Background

Surface profiling using sequential sampling and inverse methods. Part II: Implementation and experimental results

Sequential sampling with inverse calculation is demonstrated to provide a practical and reliable method for profiling surfaces, independent of rigid-body motions. Examples are given where various arrangements of displacement sensors can provide single-sided, double-sided, and parallel profilling. Double-sided measurements also give specimen thickness, and parallel measurements give surface twist. In common with other inverse calculation methods, there is a tradeoff between achievable spatial resolution and sensitivity to measurement noise. Such sensitivity, which typically doubles the measurement noise in the computed profiles, can be minimized by appropriate choice of sensor configuration, measurement method, and use of regularization. Practical guidelines for all these features are given, together with example experimental results for four typical sensor configurations.

Estimation of the density of nymphs of the bush tick, Haemaphysalis longicornis (Acari: Ixodidae), by the catch effort method.

The density of nymphs of the bush tick, Haemaphysalis longicornis, was investigated by the catch effort method with flagging. The spatial distribution of H. longicornis nymphs fit the model of contagiously distributed colonies by Iwao's m*-m analysis (Iwao 1968). A sequential sampling method was used to predict the theoretical point at which to stop sampling. Our analysis showed that five quadrats (4 m x 4 m) were sufficient to estimate the density of H. longicornis nymphs with a mean density of 5.39 per quadrat. We estimated the tick density by two methods with respect to the sampling interval. The estimated density of ticks based on ticks collected during short sampling intervals (within a half hour) was 511.34 in the 18 quadrats with the extrapolation of the linear regression equation. On the other hand, for the long interval sampling, the total number of ticks estimated by the linear regression equation was 635.47 in six quadrats in which ticks had been collected by long interval sampling. There was a significant difference between the slopes of the two linear regression equations, suggesting that the rate of reduction in the number of H. longicornis nymphs in the study area by the catch effort method differed between the two sampling methods.

Validation of the MAC technique in dogs and rabbits

Minimum alveolar concentrations (MAC) are determined using one of the different noxious stimuli (clamping, electrical stimulation, or surgical incision), based on a study conducted in the 1960s with three dogs. This study compares different noxious stimuli applied in a randomized order in dogs (n = 10) anesthetized with isoflurane (I) and halothane (H), and in rabbits (n = 10) anesthetized with I. Anesthesia was induced with the anesthetic in oxygen and maintained with mechanical ventilation. End-tidal anesthetic (Fe′A) and CO2 (Pe′CO2) concentrations were monitored with a calibrated infrared gas analyzer. Pe′CO2 and body temperature were maintained within normal limits. Noxious stimuli included skin incision on the lateral chest (SI), clamping of the tail (TC), fore- (FC) and hindlimb paw (HC), and electrical current (50 V at 50 cycles second for 10 msecond pulses) applied to the fore- (FE) and hindlimb (HE), and oral mucosa (OE) (except rabbits). SI was applied first and only for the first two consecutive measurements using the up–down method for sequential sampling of quantal-response data. After an initial equilibration period of at least 20 minutes at an Fe′A of 1.4% (H) or 1.7% (I), the Fe′A was decreased in the first animal to 0.85% of H (dog) or 1% of I (dog and rabbit) and maintained for at least 20 minutes before the noxious stimuli. If the animal responded or did not respond, the stimuli were then tested at an Fe′A 0.1% higher or lower, respectively. The new Fe′A was kept constant for at least 20 minutes and the noxious stimuli repeated until purposeful movement ceased or returned, respectively. MAC was defined as the Fe′A mid-way between the value permitting and preventing purposeful movement. Data were analyzed using an anova. MAC for I in dogs was 1.27 ± 0.047 (mean ± SEM) for TC, FC, and HC; 1.36 ± 0.035 for OE; 1.35 ± 0.040 for FE and HE; and 0.99 for SI. MAC for H in dogs was 0.97 ± 0.028 for TC; 0.96 ± 0.032 for FC and HC; 1.04 ± 0.033 for OE, FE, and HE; and 0.73 for SI. MAC for I in rabbits was 2.08 ± 0.021 for TC, FC, and HC; 2.04 ± 0.023 for FE and HE; and 0.90 for SI. MAC for SI was significantly lower than the other methods. In conclusion, electrical current and clamping resulted in similar MAC values.

Distribuição espacial de Alabama argillacea (Hübner) (Lepidoptera: Noctuidae) em algodoeiro

O conhecimento do modelo de distribuição espacial de pragas na cultura é fundamental para estabelecer um plano adequado de amostragem seqüencial e, assim, permitir a correta utilização das estratégias de controle e a otimização das técnicas de amostragem. Esta pesquisa objetivou estudar a distribuição espacial de lagartas de Alabama argillacea (Hübner) na cultura do algodoeiro, cultivar CNPA ITA-90. A coleta de dados ocorreu durante o ano agrícola de 1998/99 na Fazenda Itamarati Sul S.A., localizada no município de Ponta Porã, MS, em três diferentes áreas de 10.000 m² cada uma. Cada área amostral foi composta de 100 parcelas com 100 m² cada. Foi realizada semanalmente a contagem das lagartas pequenas, médias e grandes, encontradas em cinco plantas por parcela. Os índices de agregação (razão variância/média e índice de Morisita), o teste de qui-quadrado com o ajuste dos valores encontrados e esperados às distribuições teóricas de freqüência (Poisson, binomial positiva e binomial negativa), mostraram que todos os estádios das lagartas estão distribuídos de acordo com o modelo de distribuição contagiosa, ajustando-se ao padrão da Distribuição Binomial Negativa durante todo o período de infestação.

A new sequential importance sampling method and its application to the two-dimensional hydrophobic–hydrophilic model

The sequential importance sampling method and its various modifications have been developed intensively and used effectively in diverse research areas ranging from polymer simulation to signal processing and statistical inference. We propose a new variant of the method, sequential importance sampling with pilot-exploration resampling (SISPER), and demonstrate its successful application in folding polypeptide chains described by a two-dimensional hydrophobic-hydrophilic (HP) lattice model. We show by numerical results that SISPER outperformed several existing approaches, e.g., a genetic algorithm, the pruned-enriched Rosenbluth method, and the evolutionary Monte Carlo, in finding the ground folding states of 2D square-lattice HP sequences. In a few difficult cases, the new method can find the ground states without using any prior structural information on the chain. We also discuss the potential applications of SISPER in more general problems.

Sampling for Plant Disease Incidence

ABSTRACT 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, rho). Based on direct estimates of rho (determined from the theta parameter of the beta-binomial distribution or from the observed variance) or a model predicting rho 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 rho or a rho that depends on incidence.

KINETICS OF SINGLE AND MULTIPLE METAL ION SORPTION PROCESSES ON HUMIC SUBSTANCES

Single and multiple metal ion reaction processes were studied on humic acids (HA) from various sources. A sequential sampling method (samples periodically removed from the bulk reaction volume) was used. Experimental parameters studied included pH, temperature, HA and peat sources, metal type and concentration. The Langmuir-Hinshelwood (LH) kinetics approach was used to describe the sorption kinetics of metal ions onto HA. Great differences were found among the metals in the extent of reaction and sorption kinetics. The extent of reaction was Cr(III) > Pb(II) > Cu(II) > Ag(I) > Cd(II) = Co(II) = Li(I) for single metal adsorption and Cr(III) > Pb(II) > Cu(II) = Ag(I) = Cd(II) = Co(II) = Li(I) for multiple metal adsorption on Humic Acid No. 1. The multiple ion sorption kinetics were similar between HA from different sources. For peat reactions, the extent of multiple metal ion sorption was Cr(III) > Pb(II) > Cu(II) > Ag(I) > Co(II) = Cd(II) = Li(I). The sorption rates of all metal ions on HA were very rapid. Most adsorption occurred within 2 minutes, but sorption did not reach equilibrium in 1 day under competitive conditions. The presence of Cr(III) greatly decreased the adsorption of all other metals to the extent that some were not adsorbed at all. For all metal ions studied, less total sorption of each metal ion occurred in the presence of multiple competing ions than with single metal ions. Pearson's Hard Soft Acid Base principles and Klopman's generalized perturbation theory of chemical reactivity generally predicted the sorption preference between metal ions and humic substances. A nonlinearity concept was used to rationalize the use of the LH kinetic model.

An analytical approximation and a neural network model for optimal sample size in vendor selection

A Company wants to order at most M items from one of two competing vendors. The problem is to identify the best sequential sampling procedure and an optimal sample sizeN, that can aid the company to select that vendor such that the overall expected number of non-conforming items ordered is minimized. In this paper Monte Carlo simulation is used to compare the effectiveness of several sequential sampling methods for choosing between two competing vendors (Bernoulli populations). A simple expression is proposed that approximates the optimal sample size, given the values of M and the success probabilities of the two Bernoulli populations. A neural network model is also developed for the purpose of finding out the approximate value of optimal sample size. Optimal sample sizes obtained by both of the proposed methods are compared with the exact values and the results are encouraging both in terms of complexity and accuracy.

Frequency distribution of weed counts and applicability of a sequential sampling method to integrated weed management

Summary: Résumé: ZusammenfassungWeed density was sampled in a number of quadrats in five crops and at eight locations in Italy. For every location and species of crop and weed, a mean/variance pair was calculated. The relationship between these two parameters was significantly influenced by crop and, to a lesser extent, by site, but not by species of weed. The goodness of fit of the negative binomial distribution to the samples was assessed. Its k exponent was estimated on the basis of the observed variance/mean regression. A good fit was found for weed populations with fewer than 10 plants m−2. The applicability of a sequential sampling procedure based on the negative binomial distribution to a weed control strategy that uses a threshold density is discussed. Denombrement de la fréquence des adventices et applicabilité a une méthode d'échantillonnage séquentiel pour un desherbage integré La densité en adventices a étééchantillonnée dans plusieurs cadres dans 5 cultures et à 8 endroits en Italic. Pour chaque lieu et espèce de culture et de mauvaise herbe un couple moyenne/variance a été calculé. La relation entre ces deux paramètres était très dépendante de la culture et à un degré moindre du lieu, mais n'était pas influencé par l'espèce d'adventice. La validité de l'application de la distribution binomiale négative aux échantillons a été estimée. Son coefficient k était estimé sur la base de la regression observée sur variance/ moyenne. Une bonne adéquation a été mise en évidence pour des populations inférieures à 10 plantes m−2 L'applicabilité d'un protocole d'échantillonnage séquentiel basé sur la distribution binomiale négative, à une stratégic de désherbage utilisant un seuil de densité est discutée. Frequenzverteilung in Unkraut‐Vegetationsaufnahmen und Aufnahmemethode im Rahmen der integrierten Unkrautbekämpfung Auf der Basis der Dichte von Unkräutern in 5 Kulturen an 8 Orten in Italien wurden Mittelwert und Varianz berechnet. Das Verhältnis dieser beiden Parameter wurde durch die Kulturpflanzenart signifikant, weniger durch den Ort und gar nicht durch die Unkrautart beeinflußt. Die Güte der Anpassung an dienegative Binomialverteilung der Erhebungsdaten wurde bestimmt. Ihr k‐Exponent wurde nach der beobachteten Varianz/Mittelwerts‐Regression bestimmt. Für Populationsdichten von < 10 Pflanzen m−2 ergab sich eine gute Anpassung. Die sich aus der negativen Binomialverteilung ergebende Bekämpfungsstrategie aufgrund von Schadensschwellen wird diskutiert.

Measuring Field Variability of Disturbed Soils for Simulation Purposes

AbstractSpatial variation of soil profiles disturbed by leveling was inventoried on a field scale to obtain representative data for simulation purposes. Depth of occurrence, thickness, and morphology of functional layers, which are different pedogenetic horizons with comparable soil physical properties, were considered to be regionalized variables. The layers served as carriers of physical information, such as water‐retention and hydraulic‐conductivity characteristics and organic‐matter content. An impression of the variability within each layer was obtained by six fold sampling. Spatial variability, expressed by variations in thickness of functional layers, was inventoried in a two‐step soil survey. First, semivariograms were constructed using data obtained following a nested sampling scheme supplemented by a nugget estimation procedure. Variograms were used to evaluate cost/quality ratios at varying potential grid sampling densities, using the root of the prediction error variance (RPEV) to compare quality of interpolations. Based on these evaluations and a sequential sampling test, a grid mesh of 12 m was chosen. Second, a grid soil survey and an independent quality test were done, in which root mean square errors (RMSE) on test points were compared with RPEV. The RPEV to RMSE ratios varied between 0.7 and 1.1 for the sampled grid mesh, and had comparable values for other grid meshes. Estimations on test points by an hypothesized spatial mean, based on 26 measurements by a sequential sampling method, produced RMSE values not significantly different from RMSE values from kriging interpolations. However, sequential sampling required 26 observations whereas kriging required 153, a saving of 83%.

Binomial Sequential Sampling Methods for Cereal Aphids in Small Grains

Seventy-one samples of 200 to 400 tillers each were taken from small grain fields. An equation used to relate the proportion of infested tillers to the mean number of aphids per tiller fit the data well ( r 2 = 0.98). Although the equation was developed from pooled counts of four species of cereal aphids ( Schizaphis graminum (Rondani), Sitobion avenae (F.), Rhopalosiphum padi (L.), and R. maidis (Fitch)), it described the relationship between the proportion of infested tillers and mean number of aphids per tiller adequately for each species individually. When predictions from the equation were compared with independent data, the predicted and actual numbers of aphids per tiller were similar. Required sample sizes for estimation of the mean number of aphids per tiller with fixed average levels of precision (standard error /mean) were determined. Required sample sizes to achieve a precision level of 0.15 ranged from a low of approximately 110 tillers for intermediate aphid populations to >500 tillers for low and high aphid populations. A truncated sequential sampling plan was developed. Using this plan, from 25 to 100 tillers are inspected for the presence or absence of cereal aphids. The average number of tillers inspected to arrive at a control decision ranged from 25 to 76 tillers depending on aphid population density. The frequency of decision errors was high (approximately 0.9) for populations near the action threshold (12.5 aphids/tiller), but was otherwise acceptable.

Method for sequential sampling of cerebrospinal fluid in humans.

The authors describe a method for sequential cerebrospinal fluid sampling in humans by modifying the technique for continuous lumbar drainage.