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**Comparisons of new nonlinear modeling techniques with applications to infant respiration.**
*(English)*
Zbl 1041.62523

Summary: This paper concerns the application of new nonlinear time-series modeling methods to recordings of infant respiratory patterns. The techniques used combine the concept of minimum description length modeling with radial basis models. Our first application of the methods produced results that were not entirely satisfactory, particularly with respect to accurately modeling long term quantitative and qualitative features of respiration patterns. This paper describes a number of modifications of the original methods and makes a comparison of the improvements the various modifications gave. The modifications made were increasing the class of basis function, broadening the range of possible embedding strategies, improving the optimization of the likelihood of the model parameters and calculating a closer approximation to description length. The criteria used in the comparisons were description length, root-mean-square prediction error, model size, free-run behavior and amplitude size and variation.

We use surrogate data analysis to confirm the hypothesis that the recorded data are consistent with the nonlinear models we construct, and not consistent with simpler models. We also investigate the free-run dynamics of the model systems to see if the models exhibit features consistent with physiological characteristics observed independently in the respiratory recording. This involved modeling breathing patterns prior to a sigh and onset of a phenomenon called ”periodic breathing”; and comparing the period of ”cyclic amplitude modulation” of the free-run dynamics of the models and the period of the subsequent periodic breathing observed in respiration recording. The periods were consistent in six out of seven recordings.

We use surrogate data analysis to confirm the hypothesis that the recorded data are consistent with the nonlinear models we construct, and not consistent with simpler models. We also investigate the free-run dynamics of the model systems to see if the models exhibit features consistent with physiological characteristics observed independently in the respiratory recording. This involved modeling breathing patterns prior to a sigh and onset of a phenomenon called ”periodic breathing”; and comparing the period of ”cyclic amplitude modulation” of the free-run dynamics of the models and the period of the subsequent periodic breathing observed in respiration recording. The periods were consistent in six out of seven recordings.

### MSC:

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

92C30 | Physiology (general) |

37N25 | Dynamical systems in biology |

### Keywords:

Radial basis modeling; Description length; Surrogate analysis; Infant respiratory patterns; Periodic breathing
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\textit{M. Small} and \textit{K. Judd}, Physica D 117, No. 1--4, 283--298 (1998; Zbl 1041.62523)

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### References:

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