F.R. Hampel. Data Analysis and Self-Similar Processes. Proc. of the 46th Session of ISI, Tokyo, Japan , Book 4, pp. 1--20, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(i.e. empirically observed characteristics spanning many time scales) from models used to describe them. Regarding the modeling of empirically observed phenomena, one should always keep in mind that . no model is ever correct all are but better or worse approximations of reality (see [12]) A. Extending Traditional Approaches The prevailing approach in the teletraffic literature to dealing with and describing the increasingly complex dynamics of today s traffic streams has been to model the observed traffic dynamics one time scale at a time, which typically results in Markovian ....

F.R. Hampel. Data Analysis and Self-Similar Processes. Proc. of the 46th Session of ISI, Tokyo, Japan , Book 4, pp. 1--20, 1987.

....where the available measurements are limited in scope, we argue here that for highly engineered complex systems such as the Internet, they are of little value. Ignoring the rich semantic context present in trac measurements means missing out on new discoveries. As is cogently discussed in [34], it seems to be the rule rather than the exception that many naturally occurring empirical records or time series violate the assumption of independence or correlations that decay exponentially fast. Instead, the data often suggest the presence of strong temporal correlations over large lags, ....

F. R. Hampel. Data analysis and self-similar processes. In Proceedings of the 46th Session of the International Statistical Institute, Tokyo, Japan, September 1987. International Statistical Institute.

....have 900 additional WWW data sets like this one available for analysis. 5 negative) reactions from statisticians as well as mathematical modelers and is typically accompanied by endless philosophical discussions about the (im)possibility of inferring true LRD from a finite data set (e.g. see [7, 5, 10]) In sharp contrast, in the present context of network traffic analysis, there exist very pragmatic reasons for moving beyond philosophical discussions towards the challenging problem of providing phenomenological explanations. For real world analysis, the philosophical points are moot: the ....

.... we deal with huge numbers of huge data sets How can we do reliable estimation in the presence of strong correlations and infinite variance How can we more formally assess heuristic arguments of similarity in inference across different data sets Although it is worthwhile to always heed Hampel s [5] advice that no model is ever correct all are but better or worse approximations of reality 2 , our decision as network researchers is obvious when given a choice between a 2 The same idea is often expressed in the well known saying All models are wrong, but some are useful. 8 black ....

F. R. Hampel. Data analysis and self-similar processes. In Proceedings of the 46th Session of the International Statistical Institute, Tokyo, Japan, September 1987. International Statistical Institute.

....to some statistical model, e.g. ARMA, 144] The first assumption can be totally fallacious as the above physical mechanisms suggest, and as substantiated by statistical studies in other fields [11] The general conclusion is that the (i.i. d) assumption rarely holds for real, practical situations [70]. The use of statistical models is also unsound, as there is no physical basis for the model, and it is totally data driven [189] An elegant method of modeling the long term dependence in data is the fractal based approach [102] The above background provides the physical motivations to adopt ....

....set equal to 0, and the frequency corresponding to the spectral peak is used as a preliminary estimate for f r . 7.5 Fractal Component The random components are usually assumed to be independent, identically distributed (i.i. d) 68] However, this assumption rarely holds in practical situations [11, 70], and is only an approximation. The intricate interplay of random and (remnant) deterministic effects, leading to spatial interdependence between the errors, has been described in Chapter 4. The fractal dimension is an effective descriptor for the structure resulting from such complex processes ....

F. Hampel. Data analysis and self-similar processes. In Bulletin of the International Statistical Institute, 46th Session, pages 235--264, Tokyo, September 1987. International Statistical Institute.

.... models are short range dependent (i.e. have exponentially decaying autocorrelations) measured packet traffic data are consistent with long range dependence (i.e. hyperbolically decaying autocorrelations) The probability theory of self similarity and long range dependence is discussed in [22, 24, 77, 171, 177, 287, 389, 390, 402]. The books [130, 178, 337, 338] also contain large sections on self similar processes, and extensive bibliographies can be found in [14, 22, 24, 287, 374, 389] Self similar stochastic processes were introduced by Kolmogorov [239] in a theoretical context and brought to the attention of ....

F. R. Hampel. Data analysis and self-similar processes. In Proceedings of the 46th Session of the International Statistical Institute, Tokyo, Japan, September 1987. International Statistical Institute.

.... Descriptions of Data Analytic Findings The ideas put forward in [13] that data analysis, like calculations, can profit from repeated starts and fresh approaches and that there is not just one analysis for a substantial problem are still relevant to traffic modeling, as is the statement in [7] that virtually no model is ever correct all are but better or worse approximations for reality . In particular, from a statistical viewpoint, a number of different models can be consistent with a given set of data (i.e. analyzing one and the same data set by different researchers can lead ....

F.R. Hampel, "Data Analysis and Self-Similar Processes", Proc. of the 46th Session of ISI, Tokyo, pp. 235--254, 1987.

.... me into statistics was my fascination with the statistical problems arising out of my early work in field ornithology, especially bird migration (cf. also Section 9) My statistical ideas in ornithology range from a simple but basic and general model to more sophisticated special ones (cf. Hampel 1987b, p. 109 ff) In recent years I noticed that one of the vague new concepts I had arrived at but never worked out while pondering over my data seems to be also the basic idea of the possibility theory ( th eorie des possibilit es ) by Dubois and Prade (1988) which shows how deep thinking in ....

Hampel, F. (1987a). Data analysis and self-similar processes, Bull. Internat. Statist. Inst., Tokyo 52: (Book 4) 235--264, (with discussion).

No context found.

F. R. Hampel, "Data Analysis and Self-Similar Processes", Proc. 46th Session ISI, Book 4, 235-254, 1987.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC