Showing papers on "Sampling (statistics) published in 1971"

Sampling Procedures for Coarse Fluvial Sediments

Abstract: Procedures for sampling the bed material of gravel-bed rivers consist of five independent steps: selection of site and time, collection of a sample, determination of grain size, computation of size distribution, and presentation of results. Because several choices of methods are available at each step, much confusion exists in the literature. Simple geometric arguments, illustrated with a model based on densely packed cubes, are used to develop weighting factors to convert from one sampling procedure to another. Comparison with several sets of field data shows that the conversion method is applicable to gravel deposits. Differences remaining after conversion are attributable to random differences between samples, or to population differences. The grid-by-number procedure is the only surface-oriented procedure directly comparable (equivalent) to customary bulk sieve analysis. It is, therefore, the only correct sampling procedure for the study of surface-dependent phenomena. Additional field data are presented to compare three equivalent procedures.

The Weighted Likelihood Ratio, Linear Hypotheses on Normal Location Parameters

Abstract: Raiffa and Schlaifer's theory of conjugate prior distributions is here applied to Jeffrey's theory of tests for a sharp hypothesis, for simple normal sampling, for model I analysis of variance, and for univariate and multivariate Behrens-Fisher probelms. Leonard J. Savage's Bayesianization of Jeffrey's theory is given with new generalizations. A new conjugate prior family for normal sampling which allows prior independence of unknown mena and variance is given.

Optimal linear regulators: The discrete-time case

Abstract: In this paper the optimal discrete-time linear-quadratic regulator problem is carefully presented and the basic results are reviewed. Dynamic programming is used to determine the optimization equations. Special attention is given to problems unique to the discrete-time case; this includes, for example, the possibility of a singular system matrix and a singular control-effort weighting matrix. Some problems associated with sampled-data systems are also summarized, e.g., sensitivity to sampling time, and loss of controllability due to sampling. Computational methods for the solution of the optimization equations are outlined and a simple example is included to illustrate the various computational approaches.

Alias-free sampling of neuronal spike trains

Abstract: Spectral analysis provides powerful techniques for describing the lower order moments of a stochastic process and interactions between two or more stochastic processes. A major problem in the application of spectral analysis to neuronal spike trains is how to obtain equispaced samples of the spike trains which will give unbiased and alias-free spectral estimates. Various sampling methods, which treat the spike train as a continuous signal, a point process and as a series of Dirac delta-functions, are reviewed and their limitations discussed. A new sampling technique, which gives unbiased and alias-free estimates, is described. This technique treats the spike train as a series of delta functions and generates samples by digital filtering. Implementation of this technique on a small computer is simple and virtually on-line.

Evaluation of a kicking technique for sampling stream bottom fauna

Abstract: A square-framed, conical net (300-μ pores) was used in the kicking technique described herein for sampling the larger invertebrates of stony streams. Small samples have consistent percentage popula...

Regression with non-Gaussian Stable Disturbances: Some Sampling Results

Abstract: The following sections are included:INTRODUCTIONALTERNATIVE ESTIMATORSSAMPLING RESULTSCONCLUSIONSREFERENCES (This abstract was borrowed from another version of this item.)

On the behaviour of optimal linear sampled-data regulators†

Abstract: Optimal sampled-data controls for linear processes with quadratic criteria are determined through application of the discrete minimum principle. The effect of sampling on the closed-loop system's performance is investigated and the asymptotic behaviour of the optimal cost for large sampling periods is determined. The resulting design method is applicable to continuous, sampled-data and discrete regulators.

Phytoplankton sampling with the sedgwick-rafter cell1

Abstract: Quantitative processing of large numbers of phytoplankton collections requires a sampling method that will yield precise and reproducible estimates of abundance within an acceptably short counting time. A two-stage sampling plan was developed, using the Sedgwick-Rafter cell, which satisfies these criteria. The sampling design is appropriate for larger phytoplankton species (> 10–15 µ) having relatively high population densities (⩾ 105 cells/liter) .

Estimating Sample Size in Computing Simulation Experiments

Abstract: A method is described for estimating and collecting the sample size needed to estimate the mean of a process (with a specified level of statistical precision) in a simulation experiment. Steps are also discussed for incorporating the determination and collection of the sample size into a computer library routine that can be called by the ongoing simulation program. We present the underlying probability model that enables us to denote the variance of the sample mean as a function of the autoregressive representation of the process under study and describe the estimation and testing of the parameters of the autoregressive representation in a way that can easily be “built into” a computer program. Several reliability criteria are discussed for use in determining sample size. Since these criteria assume that the variance of the sample mean is known, an adjustment is necessary to account for the substitution of an estimate for this variance. It is suggested that Student's distribution be used as the sampling d...

Recursive and nonrecursive realizations of digital filters designed by frequency sampling techniques

Abstract: A great deal of work has been done recently on techniques for optimally designing finite duration impulse response (FIR) filters. One of these techniques, called frequency sampling, is a method for designing a digital filter from a set of samples of the desired filter frequency response. In this paper we present a unified discussion of the various types of frequency sampling designs and show how to realize them, both recursively and nonrecursively.

A second look at analysis of variance on dichotomous data

Abstract: The work of Lunney (1970) concerning the appropriateness of analysis of variance (ANOVA) techniques on dichotomous data is discussed and extended. Relations between standard statistical techniques for analyzing dichotomous data and ANOVA procedures are indicated. The need for usefulness of analyzing transformed data as opposed to direct analysis of dichotomous data are discussed. Required statistical procedures employing transformed data are outlined.

MIL-STD-414 Sampling Procedures and Tables for Inspection by Variables for Percent Defective

Abstract: (1975). MIL-STD-414 Sampling Procedures and Tables for Inspection by Variables for Percent Defective. Journal of Quality Technology: Vol. 7, Standards and Specifications, pp. 51-60.

A computer model study of zooplankton patchiness and its effects on sampling error1

Abstract: A computer model using estimates of patch structure parameters determined from an ocean study was developed to study the effects of spatial structure on the error of replicate net tows. The precision of nine replicate tows increases with increasing patch size, regardless of the position of the patch centers, and the largest net provides the most precise estimates. Lengthening the tow also results in significant increases in precision (up to a factor of 2 ), not related directly to increases in the volume of water filtered, but apparently to the increase in the probability of sampling the “right” number of patches. When, spatial structure is homogeneous, increasing tow length results in a larger reduction of sampling error than dots a comrresponding increase in net diameter. In general, better estimates of species proportions are obtained when the numbers of individuals per species are inequitably distributed and the degree of patch overlap is the greatest. INTRODUCIXON In this paper I shall examine the interactions of the patch structure variables, size, distribution, and density (i.e., numbers of individuals per volume) with net size and tow length, and their relation to the precision of net tows. The results of these experiments can be used to qualify only one of the assumptions basic to survey samples ( Taft 1960; Wiebe 1970) ; that is, that plankton samples taken with nets represent quantitatively population and community parameters in the parcel of water sampled. The term parcel refers to the water body that would be sampled if a series of replicate tows were taken at a geographic location. None of the work reported here relates to the other basic assumption: that the parcel itself contains numbers and kinds of organisms representative of the general arca of the station. My approach to the study of sampling error associated with the patchiness of zoo

Radioecological investigations of plutonium in an arctic marine environment.

Abstract: Samples of the human food chain at Thule, Greenland, were collected during the summer of 1968, after the nuclear weapon incident in January. As was to be expected from the increased plutonium levels in bottom sediments, the highest animal levels were found in bivalves, crustacea, polychaeta, and echinodermata. The levels in these bottom animals were on the average two orders of magnitude as high as the fall-out background, in a few cases four orders of magnitude. Fish from the bottom water also showed an increased plutonium content whereas sea weed, plankton, sea birds, seals, and walruses did not differ significantly from the fall-out background. The plutonium concentration in sea water was twice the fall-out background. No samples displayed plutonium levels that were considered hazardous to man or higher animals in the Thule district or in any other part of Greenland.

Method of sampling in a study of older people with a comparison of respondents and non-respondents.

Abstract: Edinburgh is divided into 23 city wards in 10 of which one of us (J.W.) and colleagues provide a geriatric service. The sample was drawn from these 10 wards, contact being made with persons in the sample through their general practitioners. Ninetyfive general practitioners were working in 50 practices with premises in this area. The plan was explained to the doctors, 91 of whom agreed to co-operate and allowed us access to their lists of patients held by the Edinburgh Executive Council. A census was made from the records of the Executive Council of the name, address, date of birth, and National Health Service number of all those persons born in 1905 or earlier who lived in the defined area and who were on the list of a doctor with a surgery address in that area. There were 26,903 such persons. This population excludes those who were not on a doctor's list and those who lived in the area but attended a doctor with a surgery address outside the area. The National Health Service number helps to trace persons who have died

Multiphase Sampling in Nonresponse Problems

Abstract: The sampling procedure involving subsampling of nonrespondents is discussed. A rule for selecting a subsample of nonrespondents is proposed under which the subsampling fraction is not kept constant, but varied according to the sample nonresponse rates. Using this sampling rule, the variance of the estimator of the population mean is independent of the unknown rate of nonresponse in the population. This rule provides a procedure for determining the initial sample size and subsampling fraction in order to have a desired precision of the estimator when the rate of nonresponse is not accurately known. Similar sampling rules for the selection of subsamples when several attempts are made for obtaining information are also proposed.

Random sampling and reconstruction of spectra

Abstract: This paper deals with the problem of perfect reconstruction of the spectrum of a weakly stationary stochastic process x ( t ) from a set of random samples { x ( t n )}. A broad class of random sampling schemes, for which the sampling intervals are dependent, is constructed. It is shown that this class is “alias free≓ relative to various families of spectra. It is further shown that the alias free property of this class of sampling schemes is invariant under random deletion of samples.

Play-the-Winner Rule and Inverse Sampling in Selecting the Better of Two Binomial Populations

Abstract: In this article two sampling rules are analyzed for the problem of selecting the better of two binomial populations. The first is alternate sampling (vector-at-a-time) and the second is the “play-the-winner” rule introduced by Robbins [3], and discussed by Zelen [8]. The termination rule studied is inverse sampling. One result is that the probabilities of correct selection for these two methods of sampling are exactly equal. It is also found that the play-the-winner sampling is uniformly preferable to the vector-at-a-time sampling rule in the sense that for the same probability requirement the expected number of trials on the poorer population is always smaller.

Retaining Units aFter Changing Strata and Probabilities

Abstract: Survey samples are often based on primary sampling units selected from initial strata with probabilities pj proportional to initial measures. However, later samples can be better served with new strata and new probabilities, Pj, based on new information. The differences between the initial and new strata and measures may be due to changes either in population distributions or in survey objectives. It is efficient to retain in the new sample the maximum permissible number of initial selections. Procedures are presented first for changing measures within fixed strata, then for strata with changed units. Modifications, improvements and simplifications are also introduced.

Sampling series for band-limited generalized functions

Abstract: For an arbitrary band-limited generalized function H(t) a representation is obtained that is a combination of a Taylor series and a conventional sampling series A parameter N that enters can be chosen such as to make the series rapidly convergent Furthermore, it is shown that, for suitably restricted test functions, H(t) can be represented by a conventional sampling series and by a series of delta functions with weights equal to the sampling values The results apply also to ordinary band-limited functions

Deficiency of Gravity Corers for sampling Meiobenthos and Sediments

Abstract: GRAVITY corers are widely used1,2 for the collection of the smallest marine metazoans (meiofauna) from subtidal grounds, and it has been generally accepted that cores which appear undisturbed give reasonably representative samples. But, after comparing gravity cores with samples collected by SCUBA divers, I suggest that this is not so.

Method of digitally processing sinusoidal ac signals

Abstract: A sinusoidal ac signal is subjected to periodic sampling having a period Delta t. There is made a product of one sampled value of the signal taken at a certain sampling point and another sampled value at the next sampling point apart, by an interval of time equal to the period Delta t, from the previous sampling point. If the product is of negative value, a zero point of the signal must lie between the two sampling points. The zero point can equivalently be obtained by drawing a straight line passing the two sampled values. On the basis of the zero points of sinusoidal ac signals obtained in such a manner as above, the frequencies, phase differences, powers and the impedances of the associated transmission lines are obtained by means of a digital computer.

On Selecting the Most Probable Category

Abstract: A sequential procedure is given for selecting from a given multinomial distribution with k cells, the cell with the largest probability, which is called the “most probable” category. Observations being taken sequentially from the given distribution, the sampling is terminated when the difference between the highest and the next highest cell counts is equal to a positive integer r. The cell with the highest count when the sampling is terminated, is selected as the most probable category. It is shown that the sampling terminates with probability 1. The probability of a correct selection and the expected total number of observations are given. The given procedure is compared with other known procedures.