Rejoinder: The 2005 Neyman Lecture: Dynamic Indeterminism in Science

Rejoinder to ``The 2005 Neyman Lecture: Dynamic Indeterminism in Science'' [arXiv:0808.0620]Comment: Published in at http://dx.doi.org/10.1214/08-STS246REJ the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Examining an Irregularly Sampled Time Series for Whiteness

Suppose it is of interest whether the series itself is white noise. The empirical Fourier transform is proposed to address this question

The 2005 Neyman Lecture: Dynamic Indeterminism in Science

Jerzy Neyman's life history and some of his contributions to applied statistics are reviewed. In a 1960 article he wrote: ``Currently in the period of dynamic indeterminism in science, there is hardly a serious piece of research which, if treated realistically, does not involve operations on stochastic processes. The time has arrived for the theory of stochastic processes to become an item of usual equipment of every applied statistician.'' The emphasis in this article is on stochastic processes and on stochastic process data analysis. A number of data sets and corresponding substantive questions are addressed. The data sets concern sardine depletion, blowfly dynamics, weather modification, elk movement and seal journeying. Three of the examples are from Neyman's work and four from the author's joint work with collaborators.Comment: This paper commented in: [arXiv:0808.0631], [arXiv:0808.0638]. Rejoinder in [arXiv:0808.0639]. Published in at http://dx.doi.org/10.1214/07-STS246 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic normality of finite Fourier transforms of stationary generalized processes

AbstractThis paper indicates a mixing condition under which a net of Fourier transforms, of a stationary generalized process over an abelian locally compact group, has a limiting normal distribution

Synthetic plots: some history and examples

Jerzy Neyman and Elizabeth Scott developed the idea of synthetic plots. These plots are a display of the data values of an experiment side by side with a display of simulated data values, with the simulation-based on a considered stochastic model. The Neyman and Scott work concerned the distribution of galaxies on the celestial sphere. A review of their wo is presented here followed by personal examples from hydrology, neuroscience, and animal motion.Jerzy Neyman and Elizabeth Scott developed the idea of synthetic plots. These plots are a display of the data values of an experiment side by side with a display of simulated data values, with the simulation-based on a considered stochastic model. The Neyman and Scott work concerned the distribution of galaxies on the celestial sphere. A review of their wo is presented here followed by personal examples from hydrology, neuroscience, and animal motion

Comparative Aspects of the Analysis of Stationary Time Series, Point Processes and Hybrids

This paper brings out comparative aspects of the analysis of time series, point processes and hybrids such as sampled time series and marked point processes. Secondand third-order moments and spectra prove useful tools for addressing certain scientific problems involving such processes. Illustrative analyses are presented for data on tides, neurons and earthquakes

Three months journeying of a Hawaiian monk seal

Hawaiian monk seals (Monachus schauinslandi) are endemic to the Hawaiian Islands and are the most endangered species of marine mammal that lives entirely within the jurisdiction of the United States. The species numbers around 1300 and has been declining owing, among other things, to poor juvenile survival which is evidently related to poor foraging success. Consequently, data have been collected recently on the foraging habitats, movements, and behaviors of monk seals throughout the Northwestern and main Hawaiian Islands. Our work here is directed to exploring a data set located in a relatively shallow offshore submerged bank (Penguin Bank) in our search of a model for a seal's journey. The work ends by fitting a stochastic differential equation (SDE) that mimics some aspects of the behavior of seals by working with location data collected for one seal. The SDE is found by developing a time varying potential function with two points of attraction. The times of location are irregularly spaced and not close together geographically, leading to some difficulties of interpretation. Synthetic plots generated using the model are employed to assess its reasonableness spatially and temporally. One aspect is that the animal stays mainly southwest of Molokai. The work led to the estimation of the lengths and locations of the seal's foraging trips.Comment: Published in at http://dx.doi.org/10.1214/193940307000000473 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Special Issue Paper

An exploratory data analysis of the temperature fluctuations in a spreading fir

Nonparametric directionality measures for time series and point process data

The need to determine the directionality of interactions between neural signals is a key requirement for analysis of multichannel recordings. Approaches most commonly used are parametric, typically relying on autoregressive models. A number of concerns have been expressed regarding parametric approaches, thus there is a need to consider alternatives. We present an alternative nonparametric approach for construction of directionality measures for bivariate random processes. The method combines time and frequency domain representations of bivariate data to decompose the correlation by direction. Our framework generates two sets of complementary measures, a set of scalar measures, which decompose the total product moment correlation coefficient summatively into three terms by direction and a set of functions which decompose the coherence summatively at each frequency into three terms by direction: forward direction, reverse direction and instantaneous interaction. It can be undertaken as an addition to a standard bivariate spectral and coherence analysis, and applied to either time series or point-process (spike train) data or mixtures of the two (hybrid data). In this paper, we demonstrate application to spike train data using simulated cortical neurone networks and application to experimental data from isolated muscle spindle sensory endings subject to random efferent stimulation

Gridded and direct Epoch of Reionisation bispectrum estimates using the Murchison Widefield Array

We apply two methods to estimate the 21~cm bispectrum from data taken within the Epoch of Reionisation (EoR) project of the Murchison Widefield Array (MWA). Using data acquired with the Phase II compact array allows a direct bispectrum estimate to be undertaken on the multiple redundantly-spaced triangles of antenna tiles, as well as an estimate based on data gridded to the $uv$-plane. The direct and gridded bispectrum estimators are applied to 21 hours of high-band (167--197~MHz; $z$=6.2--7.5) data from the 2016 and 2017 observing seasons. Analytic predictions for the bispectrum bias and variance for point source foregrounds are derived. We compare the output of these approaches, the foreground contribution to the signal, and future prospects for measuring the bispectra with redundant and non-redundant arrays. We find that some triangle configurations yield bispectrum estimates that are consistent with the expected noise level after 10 hours, while equilateral configurations are strongly foreground-dominated. Careful choice of triangle configurations may be made to reduce foreground bias that hinders power spectrum estimators, and the 21~cm bispectrum may be accessible in less time than the 21~cm power spectrum for some wave modes, with detections in hundreds of hours.Comment: 19 pages, 10 figures, accepted for publication in PAS