Randomization and Monte Carlo Methods in Biology.
Part 1 Randomization tests and confidence intervals: the idea of a randomization test examples of a randomization test aspects of randomization testing raised by the examples confidence intervals from randomization. Part 2 Monte Carlo and other computer intensive methods: Monte Carlo tests jackknifing bootstrapping bootstrap tests of significance and confidence intervals. Part 3 Some general considerations: power determining how many randomizations are needed determining a randomization distribution exactly the computer generation of pseudo-random numbers generating random permutations. Part 4 One and two sample tests: the paired comparisons design the one sample randomization test the two sample randomization test the comparison of two samples on multiple measurements. Part 5 Analysis of variance: one factor analysis of variance Bartlett's test for constant variance examples of more complicated types of analysis of variance discussion computer program. Part 6 Regrssion analysis: simple regression testing for a non-zero beta value confidence limits for beta multiple linear regression randomizing X variable values. Part 7 Distance matrices and spatial data: testing for association between distance matrices Mantel's test determining significance by sampling randomization distribution confidence limits for a matrix regression coefficient problems involving more than two matrices. Part 8 Other analyses on spatial data: the study of spatial point patterns Mead's randomization test a test based on nearest neighbour distances testing for an association between two point patterns the Besag-Diggle test tests using distances between points. Part 9 Time series: randomization and time series randomization tests for serial correlation randomization tests for trend randomization tests for periodicity irregularly spaced series tests on times of occurence discussion of procedures for irregular series bootstrap and Monte Carlo tests. Part 10 Multivariate data: univariate and multivariate tests sample means and covariance matrices comparison on sample means vectors chi-squared analyses for count data principal component analysis and other one sample methods discriminate function analysis. Part 11 Ad hoc methods: the construction of tests in non-standard situations testing for randomness of species co-occurences on islands examining time change in niche ovelap probing multivariate data with random skewers other examples. Part 12 Conclusion: randomization methods bootstrap and Monte Carlo methods.
A Simplified Monte Carlo Significance Test Procedure
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Wiley and Royal Statistical Society are collaborating with JSTOR to digitize, preserve and extend access to Journal of the Royal Statistical Society. Series B (Methodological). SUMMARY The use of Monte Carlo test procedures for significance testing, with smaller reference sets than are now generally used, is advocated. It is shown that, for given oX = l/n, n a positive integer, the power of the Monte Carlo test procedure is a monotone increasing function of the size of the reference set, the limit of which is the power of the corresponding uniformly most powerful test. The power functions and efficiency of the Monte Carlo test to the uniformly most powerful test are discussed in detail for the case where the test criterion is N(y, 1). The cases when the test criterion is Student's t-statistic and when the test statistic is exponentially distributed are considered also.
Simple Monte Carlo Tests for Spatial Pattern
The Monte Carlo approach to testing a simple null hypothesis is reviewed briefly and several examples of its application to problems involving spatial distributions are presented. These include spatial point pattern, pattern similarity, space‐time interaction and scales of pattern. The aim is not to present specific “recommended tests” but rather to illustrate the value of the general approach, particularly at a preliminary stage of analysis.
A Review Of Monte Carlo Tests Of Cluster Analysis.
A review of Monte Carlo validation studies of clustering algorithms is presented. Several validation studies have tended to support the view that Ward's minimum variance hierarchical method gives the best recovery of cluster structure. However, a more complete review of the validation literature on clustering indicates that other algorithms may provide better recovery under a variety of conditions. Applied researchers are cautioned concerning the uncritical selection of Ward's method for empirical research. Alternative explanations for the differential recovery performance are explored and recommendations are made for future Monte Carlo experiments.
Monte Carlo tests of renormalization-group predictions for critical phenomena in Ising models
A critical review is given of status and perspectives of Monte Carlo simulations that address bulk and interfacial phase transitions of ferromagnetic Ising models. First, some basic methodological aspects of these simulations are briefly summarized (single-spin flip vs. cluster algorithms, finite-size scaling concepts), and then the application of these techniques to the nearest-neighbor Ising model in d=3 and 5 dimensions is described, and a detailed comparison to theoretical predictions is made. In addition, the case of Ising models with a large but finite range of interaction and the crossover scaling from mean-field behavior to the Ising universality class are treated. If one considers instead a long-range interaction described by a power-law decay, new classes of critical behavior depending on the exponent of this power law become accessible, and a stringent test of the e-expansion becomes possible. As a final type of crossover from mean-field type behavior to two-dimensional Ising behavior, the interface localization–delocalization transition of Ising films confined between “competing” walls is considered. This problem is still hampered by questions regarding the appropriate coarse-grained model for the fluctuating interface near a wall, which is the starting point for both this problem and the theory of critical wetting.
Monte Carlo Tests of the Accuracy of Cluster Analysis Algorithms: A Comparison of Hierarchical and Nonhierarchical Methods.
Nine hierarchical and four nonhierarchical clustering algorithms were compared on their ability to resolve 200 multivariate normal mixtures. The effects of coverage, similarity measures, and cluster overlap were studied by including different levels of coverage for the hierarchical algorithms, Euclidean distances and Pearson correlation coefficients, and truncated multivariate normal mixtures in the analysis. The results confirmed the findings of previous Monte Carlo studies on clustering procedures in that accuracy was inversely related to coverage, and that algorithms using correlation as the similarity measure were significantly more accurate than those using Euclidean distances. No evidence was found for the assumption that the positive effects of the use of correlation coefficients are confined to unconstrained mixture models.
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