SUMMARY A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed. For numerical problems in a large number of dimensions, Monte Carlo methods are often more efficient than conventional numerical methods. However, implementation of the Monte Carlo methods requires sampling from high dimensional probability distributions and this may be very difficult and expensive in analysis and computer time. General methods for sampling from, or estimating expectations with respect to, such distributions are as follows. (i) If possible, factorize the distribution into the product of one-dimensional conditional distributions from which samples may be obtained. (ii) Use importance sampling, which may also be used for variance reduction. That is, in order to evaluate the integral J = X) p(x)dx = Ev(f), where p(x) is a probability density function, instead of obtaining independent samples XI, ..., Xv from p(x) and using the estimate J, = Zf(xi)/N, we instead obtain the sample from a distribution with density q(x) and use the estimate J2 = Y{f(xj)p(x1)}/{q(xj)N}. This may be advantageous if it is easier to sample from q(x) thanp(x), but it is a difficult method to use in a large number of dimensions, since the values of the weights w(xi) = p(x1)/q(xj) for reasonable values of N may all be extremely small, or a few may be extremely large. In estimating the probability of an event A, however, these difficulties may not be as serious since the only values of w(x) which are important are those for which x -A. Since the methods proposed by Trotter & Tukey (1956) for the estimation of conditional expectations require the use of importance sampling, the same difficulties may be encountered in their use. (iii) Use a simulation technique; that is, if it is difficult to sample directly from p(x) or if p(x) is unknown, sample from some distribution q(y) and obtain the sample x values as some function of the corresponding y values. If we want samples from the conditional dis

https://www.jstor.org/stable/pdfplus/2334940.pdf

Monte Carlo Sampling Methods Using Markov Chains and Their Applications

For various reasons individuals in a sample survey may prefer not to confide to the interviewer the correct answers to certain questions. In such cases the individuals may elect not to reply at all or to reply with incorrect answers. The resulting evasive answer bias is ordinarily difficult to assess. In this paper it is argued that such bias is potentially removable through allowing the interviewee to maintain privacy through the device of randomizing his response. A randomized response method for estimating a population proportion is presented as an example. Unbiased maximum likelihood estimates are obtained and their mean square errors are compared with the mean square errors of conventional estimates under various assumptions about the underlying population.

Randomized response: a survey technique for eliminating evasive answer bias.

A method of sample selection for household telephone interviewing via random digit dialing is developed which significantly reduces the cost of such surveys as compared to dialing numbers completely at random. The sampling is carried out through a two-stage design and has the unusual feature that although all units have the same probability of selection, it is not necessary to know the probabilities of selection of the first-stage or the second-stage units. Simple random sampling of possible telephone numbers, within existing telephone exchanges, is inefficient because only about 20 percent of these numbers are actually telephone numbers assigned to households. The method of selection proposed reduces the proportion of unused numbers sharply.

https://www.jstor.org/stable/pdfplus/2286513.pdf

Sampling Methods for Random Digit Dialing

The lack of full participation in sample surveys threatens the inferential value of the survey method. We review a set of conceptual developments and experimental findings that appear to be informative about causes of survey participation; offer an integration of that work with findings from the more traditional statistical and survey methodological literature on nonresponse; and, given the theoretical structure, deduce potentially promising paths of research toward the understanding of survey participation.

Understanding the decision to participate in a survey

Part 1 Aggregated analysis - standard errors and significance tests: introduction, C.J.Skinner domain means, regression and multivariate analysis, C.J.Skinner chi-squared tests for contigency tables, J.N.K.Rao and D.R.Thomas measures of association for contingency tables, E.A.Molina. Part 2 Aggregated analysis - point estimation and bias: introduction, T.M.F.Smith the effect of selection of regression analysis, G.Nathan and T.M.F.Smith multivariate analysis, T.M.F.Smith and D.J.Holmes selection based on the response variable in logistic regression, A.J.Scott and C.J.Wild. Part 3 Disaggregated analysis - modelling structured populations: introduction, D.Holt multilevel and multivariate models in survey analysis, H.Goldstein and R.Silver regression models for stratified multistage cluster samples, D.Pfeefferman and L.LaVange logistic models for contingency tables, D.Holt and P.D.Ewings.

Analysis of complex surveys

Sample Survey Methods and Theory

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Sample Survey Methods and Theory