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  • 1
    Electronic Resource
    Electronic Resource
    The MAP test for multimodality (1994)
    Springer
    Journal of classification 11 (1994), S. 5-36 
    Details
    ISSN: 1432-1343
    Keywords: Minimal constrained spanning trees ; Nearest neighbor density estimates ; Minimal ascending path spanning trees ; Tests for modes ; The MAP test
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We introduce a test for detecting multimodality in distributions based on minimal constrained spanning trees. We define a Minimal Ascending Path Spanning Tree (MAPST) on a set of points as a spanning tree that has the minimal possible sum of lengths of links with the constraint that starting from any link, the lengths of the links are non-increasing towards a root node. We define similarly MAPSTs with more than one root. We present some algorithms for finding such trees. Based on these trees, we devise a test for multimodality, called the MAP Test (for Minimal Ascending Path). Using simulations, we estimate percentage points of the MAP statistic and assess the power of the test. Finally, we illustrate the use of MAPSTs for determining the number of modes in a distribution of positions of galaxies on photographic plates from a rich galaxy cluster.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01201021
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  • 2
    Electronic Resource
    Electronic Resource
    Bloc Voting in the United States Senate (2000)
    Springer
    Journal of classification 17 (2000), S. 29-49 
    Details
    ISSN: 1432-1343
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: blocs and legislative measures are partitioned into types so that, as nearly as possible, votes by each bloc for each type of measure are either all YEAs or all NAYs. A probability model is given for the partitions into blocs and types, and for the pattern of YEAs and NAYs given the partitions. The Alternating Randomized Combination algorithm is presented for searching for high probability partition pairs. The probability of each bloc and type in the final optimal partition pair is estimated by Markov Chain Monte Carlo. The final partition identifies 18 blocs of Senators, and 14 types of legislative measures. The blocs and types are delineated in a table reporting all decisive votes in the 103rd Congress. The blocs are characterized by the types of measures in which they vote against the majority party.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s003570000003
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  • 3
    Electronic Resource
    Electronic Resource
    Statistical theory in clustering (1985)
    Springer
    Journal of classification 2 (1985), S. 63-76 
    Details
    ISSN: 1432-1343
    Keywords: Theory of clustering ; High density clusters ; Tests of unimodality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A number of statistical models for forming and evaluating clusters are reviewed. Hierarchical algorithms are evaluated by their ability to discover high density regions in a population, and complete linkage hopelessly fails; the others don't do too well either. Single linkage is at least of mathematical interest because it is related to the minimum spanning tree and percolation. Mixture methods are examined, related to k-means, and the failure of likelihood tests for the number of components is noted. The DIP test for estimating the number of modes in a univariate population measures the distance between the empirical distribution function and the closest unimodal distribution function (or k-modal distribution function when testing for k modes). Its properties are examined and multivariate extensions are proposed. Ultrametric and evolutionary distances on trees are considered briefly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01908064
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