We propose to characterize the burstiness of packet arrival processes with indices of dispersion for intervals and for counts. These indices, which are functions of the variance of intervals and counts, are relatively straightforward to estimate and convey much more information than simpler indices, such as the coefficient of variation, that are often used to describe burstiness quantitatively.

[Read before The Royal Statistical Society at a meeting organized by the Research Section on

2. Wavelets for time series functions and moments. Wavelet analysis provides a means of parameterizing such quantities in the nonstationary case. By wavelet jk=ZT

A framework within which to generate and characterize populations of correlated spike trains is presented. Spike trains are generated using integrate to threshold and ®re type encoders. Spectral analysis techniques form the basis for specifying the strength of correlation within the population. To accurately specify weak correlation, a combined coherence estimate is formed between several independent pairs of spike trains from a population. The aim is to produce populations of spike trains which have a realistic stochastic correlation structure and which can be used to explore the role of correlated neuronal discharge in information processing in neuronal systems. # 1998 Elsevier

Data of process type are now routinely collected and analyzed in the environmental sciences. This is a consequence, in part, of today’s general availabilty of sophisticated computing, storage, display and analysis equip-ment. At the same time stochastic models have been developed that take

For any point process in R d that has a Papangelou conditional intensity λ, we define a random measure of ‘innovations ’ which has mean zero. When the point process model parameters are estimated from data, there is an analogous random measure of ‘residuals’. We analyse properties of the innovations and residuals, including first and second moments, conditional independence, a martingale property, lack of correlation, and marginal distributions. Keywords: Georgii-Nguyen-Zessin formula; Gibbs point process; set-indexed martingale; Papangelou conditional intensity; Pearson residuals; scan statistic;

A procedure is developed to probe the changes in the functional interactions among neurons in primary motor cortex of the monkey brain during adaptation. A monkey is trained to learn a new skill, moving its arm to reach a target under the influence of external perturbations. The spike trains of multiple neurons in the primary motor cortex are recorded simultaneously. We utilize the methodology of directed transfer function, derived from a class of linear stochastic models, to quantify the causal interactions between the neurons. We find that the coupling between the motor neurons tends to increase during the adaptation but return to the original level after the adaptation. Furthermore, there is evidence that adaptation tends to affect the topology of the neural network, despite the approximate conservation of the average coupling strength in the network before and after the adaptation.

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