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4395 results in Advances in Applied Probability

Page 208 of 220

  • The sampling theory of selectively neutral alleles

  • G. A. Watterson
  • Journal:
    Advances in Applied Probability / Volume 6 / Issue 3 / September 1974
    Published online by Cambridge University Press:
    01 July 2016, pp. 463-488
    Print publication:
    September 1974

  • In a paper of the same title, Ewens has considered the problem of inferring whether the genotypic frequencies observed in a small sample are consistent with a particular population model, in which all types are selectively neutral. The present paper gives the general theory of such sampling schemes, when the sampling is from either a deterministic, or a stochastically varying, population.

    The theory is illustrated on a population model which was introduced by Karlin and McGregor. Various results are proved for both the population, and its sample. It is shown that Ewens' sampling theory applies to this population model, and conjectures as to why different population models may have the same sampling theory are made.

  • On discrete time extremal processes

  • R. W. Shorrock
  • Journal:
    Advances in Applied Probability / Volume 6 / Issue 3 / September 1974
    Published online by Cambridge University Press:
    01 July 2016, pp. 580-592
    Print publication:
    September 1974

  • Upper record values and times and inter-record times are studied in their rôles as embedded structures in discrete time extremal processes. Various continuous time approximations to the discrete-time processes are analysed, especially as processes over their state spaces. Discrete time processes, suitably normalized after crossing a threshold T, are shown to converge to limiting continuous time processes as T → ∞ under suitable assumptions on the underlying CDF F, for example, when 1 — F varies regularly at ∞, and more generally. Discrete time extremal processes viewed as processes over their state spaces are noted to have an interesting interpretation in terms of processes of population growth.

  • The statistical analysis of spatial pattern

  • M. S. Bartlett
  • Journal:
    Advances in Applied Probability / Volume 6 / Issue 2 / June 1974
    Published online by Cambridge University Press:
    01 July 2016, pp. 336-358
    Print publication:
    June 1974

  • A brief survey is made of the range of models and statistical techniques relevant to the analysis of spatial pattern, and more detailed discussion given to three specific classes of stochastic process in two dimensions viz. (i) continuous processes X(r), (ii) point processes N(r), (iii) lattice processes Xi. The appropriate theory for these classes of processes is indicated in Part I; and in Part II some examples of data are classified under these same three headings, and their statistical analysis discussed.

Page 208 of 220