By J. K. Lindsey
This advent to methods of modelling a large choice of phenomena that ensue over the years is available to an individual with a simple wisdom of statistical principles. J.K. Lindsey concentrates on tractable types regarding uncomplicated techniques for which particular likelihood types, consequently chance capabilities, should be specific. (These types are the main invaluable in statistical purposes modelling empirical data.) Examples are drawn from actual, organic and social sciences, to teach how the book's underlying principles could be utilized, and information units and R code are provided for them. writer source web page: http://popgen.unimaas.nl/~jlindsey/books.html
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Additional resources for Statistical Analysis of Stochastic Processes in Time
Example text
2 Basics of statistical modelling In this chapter, I shall review some of the elementary principles of statistical modelling, not necessarily specifically related to stochastic processes. In this way, readers may perhaps more readily understand how models of stochastic processes relate to other areas of statistics with which they are more familiar. At the same time, I shall illustrate how many of these standard procedures are not generally applicable to stochastic processes using, as an example, a study of the duration of marriages before divorce.
Does a record at a given time point indicate a new value in the series then or only that it changed some time since the previous observation? Is the process stationary? – Is the process increasing or decreasing systematically over time, such as a growth curve? – Is there periodic (daily, seasonal) variation? – Does the process change abruptly at some time point(s)? – Are there long-term changes? Is more than one (type of) response recorded at each time point? – Can several events occur simultaneously?
Thus, in many longitudinal studies, certain individuals tend to drop out (in similar ways to those described above for survival data). One may want to model the time until dropout as a survival process. However, most individuals will (hopefully) never drop out of a study. Thus, there will be a mixture of two subpopulations: those with a potential to drop out (who may or may not) and those who will always stay in the study until the end. 4). Stopping rules In the collection of duration data, two basic types of planned censoring have usually been distinguished: (i) All recording may be stopped after a fixed interval of time, called Type I or time censoring, used most often in medical studies.