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D R Brillinger

Publications and source records attributed to D R Brillinger.

9 recordsLinked to original sources
PubMed1988

Maximum likelihood analysis of spike trains of interacting nerve cells.

Suppose that a neuron is firing spontaneously or that it is firing under the influence of other neurons. Suppose that the data available are the firing times of the neurons present. An "integrate several inputs and fire" model is developed and studied empirically. For the model a neuron's firing occurs when an internal state variable crosses a random threshold. This conceptual model leads to maximum likelihood estimates of internal quantities, such as the postsynaptic potentials of the measured influencing neurons, the membrane potential, the absolute threshold and also estimates of derived quantities such as the strength-duration curve and the recovery process of the threshold. The model's validity is examined via an estimate of the conditional firing probability. The approach appears useful for estimating biologically meaningful parameters, for examining hypotheses re these parameters, for understanding the connections present in neural networks and for aiding description and classification of neurons and synapses. Analyses are presented for a number of data sets collected for the sea hare, Aplysia californica, by J. P. Segundo. Both excitatory and inhibitory examples are provided. The computations were carried out via the Glim statistical package. An example of a Glim program realizing the work is presented in the Appendix.

Animals↗
PubMed1988

The maximum likelihood approach to the identification of neuronal firing systems.

The concern of this work is the identification of the (nonlinear) system of a neuron firing under the influence of a continuous input in one case, and firing under the influence of two other neurons in a second case. In the first case, suppose that the data consist of sample values Xt, Yt, t = 0, +/- 1, +/- 2,... with Yt = 1 if the neuron fires in the time interval t to t + 1 and Yt = 0 otherwise, and with Xt denoting the (sampled) noise value at time t. Suppose that Ht denotes the history of the process to time t. Then, in this case the model fit has the form Prob[Yt = 1/Ht] = phi(Ut-theta) where (formula; see text) where gamma t denotes the time elapsed since the neuron last fired and phi denotes the normal cumulative. This model corresponds to quadratic summation of the stimulus followed by a random threshold device. In the second case, a network of three neurons is studied and it is supposed that (formula; see text) with Xt and Zt zero-one series corresponding to the firing times of the two other neurons. The models are fit by the method of maximum likelihood to Aplysia californica data collected in the laboratory of Professor J.P. Segundo. The paper also contains some general comments of the advantages of the maximum likelihood method for the identification of nonlinear systems.

Animals↗
PubMed1986

The natural variability of vital rates and associated statistics.

The first concern of this work is the development of approximations to the distributions of crude mortality rates, age-specific mortality rates, age-standardized rates, standardized mortality ratios, and the like for the case of a closed population or period study. It is found that assuming Poisson birthtimes and independent lifetimes implies that the number of deaths and the corresponding midyear population have a bivariate Poisson distribution. The Lexis diagram is seen to make direct use of the result. It is suggested that in a variety of cases, it will be satisfactory to approximate the distribution of the number of deaths given the population size, by a Poisson with mean proportional to the population size. It is further suggested that situations in which explanatory variables are present may be modelled via a doubly stochastic Poisson distribution for the number of deaths, with mean proportional to the population size and an exponential function of a linear combination of the explanatories. Such a model is fit to mortality data for Canadian females classified by age and year. A dynamic variant of the model is further fit to the time series of total female deaths alone by year. The models with extra-Poisson variation are found to lead to substantially improved fits.

Age Factors↗
PubMed1981

Some aspects of modern population mathematics.

"The purpose of this paper is to survey a number of the technical tools and models that have found use in the study of human and other populations, and to indicate some problems of current interest. These tools and models are varied: integral equations, nonlinear oscillations, differential geometry, dynamical systems, nonlinear operation, bifurcation theory, semigroup theory, martingale theory, Markov processes, diffusion processes, branching processes, ergodic theory, prediction theory and state-space models. A fairly extensive bibliography is provided. Also an Appendix has been added describing the analysis of a classical entomological data set." (summary in FRE)

Demography↗
PubMed1979

Empirical examination of the threshold model of neuron firing.

An elementary model of neuronal activity involves temporal and spatial summation of postsynaptic currents that are elicited by presynaptic spikes and that, in turn, elicit postsynaptic potentials at a trigger zone; when the potential at the trigger zone exceeds a "threshold" level, a postsynaptic spike is generated. This paper describes three methods of estimating the "summation function", that is, the function of time that converts the synaptic current into potential at the trigger zone: namely, maximum likelihood, cross-correlation analysis and cross-spectral analysis. All three methods, when applied to input-output data collected on various neurons of Aplysia californica, give comparable results. As estimated, the summation function involved in the explored cells has an early positive-going swing that is large and brief. In the cell L5, but not in R2, there was also a late negative-going swing of longer duration.

Animals↗
PubMed1978

A note on the estimation of evoked response.

The traditional average evoked response is compared and contrasted with several alternate estimates, derived from frequency domain considerations, for a model of evoked responses superimposed upon a stationary noise series. Further, a means of constructing approximate confidence intervals for the values of an evoked response is indicated. The case of several simultaneously recorded series is also considered.

Evoked Potentials↗