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Papers by Priscilla Greenwood

Probab Theory Relat Field, 1973

Neural Computation, Nov 7, 2014

In this letter, we provide a stochastic analysis of, and supporting simulation data for, a stocha... more In this letter, we provide a stochastic analysis of, and supporting simulation data for, a stochastic model of the generation of gamma bursts in local field potential (LFP) recordings by interacting populations of excitatory and inhibitory neurons. Our interest is in behavior near a fixed point of the stochastic dynamics of the model. We apply a recent limit theorem of stochastic dynamics to probe into details of this local behavior, obtaining several new results. We show that the stochastic model can be written in terms of a rotation multiplied by a two-dimensional standard Ornstein-Uhlenbeck (OU) process. Viewing the rewritten process in terms of phase and amplitude processes, we are able to proceed further in analysis. We demonstrate that gamma bursts arise in the model as excursions of the modulus of the OU process. The associated pair of stochastic phase and amplitude processes satisfies their own pair of stochastic differential equations, which indicates that large phase slips occur between gamma bursts. This behavior is mirrored in LFP data simulated from the original model. These results suggest that the rewritten model is a valid representation of the behavior near the fixed point for a wide class of models of oscillatory neural processes.

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1973

... o H.*(dx) = G(dx). m=O This equation says that there are two ways of looking at the sum of th... more ... o H.*(dx) = G(dx). m=O This equation says that there are two ways of looking at the sum of the probabilities that S, E dx at an ascending ladder epoch before T. For one of these the 'ladder epoch' is replaced by 'n < N' using duality. Page 6. 772 PRISCILLA GREENWOOD ...

Mathematical and Statistical Estimation Approaches in Epidemiology, 2009

We review the topic of stochastic epidemic modeling with emphasis on compartmental stochastic mod... more We review the topic of stochastic epidemic modeling with emphasis on compartmental stochastic models. A main theme is the usefulness of the correspondence between these and their large population deterministic limits, which describe dynamical systems. The dynamics of an ODE system informs us of the deterministic skeleton upon which the behavior of corresponding stochastic systems are built. In this chapter

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1969

Let X(t) be a separable symmetric stable process of index c~. Let P be a finite partition of [0, ... more Let X(t) be a separable symmetric stable process of index c~. Let P be a finite partition of [0, 1], and .r a collection of partitions. The variation of a path X(t) is defined in three ways in terms of the sum ~ [X(t~)-X(q_l) f and the collection N. Under certain conditions on r and on the para-t~P meters ~ and/~, the distribution of the variation is shown to be a stable law. Under other conditions the distribution of the variational sum converges to a stable distribution.

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1976

... Priscilla Greenwood University of British Columbia, 2075 Wesbrook Place Vancouver, BC, Canada... more ... Priscilla Greenwood University of British Columbia, 2075 Wesbrook Place Vancouver, BC, Canada V6T 1W5 ... like Y(T+), IT(T) where T+, T are geometrically distributed and Y,, I~ are random walks with step-distributions appearing in Proposition 2. That the independent sum of Y ...

Probability Theory and Related Fields, 1993

Neural Computation, 2005

We study optimal estimation of a signal in parametric neuronal models on the basis of interspike ... more We study optimal estimation of a signal in parametric neuronal models on the basis of interspike interval data. Fisher information is the inverse asymptotic variance of the best estimator. Its dependence on the parameter value indicates accuracy of estimation. Our models assume that the input signal is estimated from neuronal output interspike interval data where the frequency transfer function is sigmoidal. If the coefficient of variation of the interspike interval is constant with respect to the signal, the Fisher information is unimodal, and its maximum for the most estimable signal can be found. We obtain a general result and compare the signal producing maximal Fisher information with the inflection point of the sigmoidal transfer function in several basic neuronal models.

Journal of Multivariate Analysis, 1979

Bivariate stable distributions are defined as those having a domain of attraction, where vectors ... more Bivariate stable distributions are defined as those having a domain of attraction, where vectors are used for normalization. These distributions are identified and their domains of attraction are given in a number of equivalent forms. In one case, marginal convergence implies joint convergence. A bivariate optional stopping property is given. Applications to bivariate random walk are suggested.

Journal of Mathematical Biology, 2012

We show that the stochastic Morris-Lecar neuron, in a neighborhood of its stable point, can be ap... more We show that the stochastic Morris-Lecar neuron, in a neighborhood of its stable point, can be approximated by a two-dimensional Ornstein-Uhlenbeck (OU) modulation of a constant circular motion. The associated radial OU process is an example of a leaky integrate-and-fire (LIF) model prior to firing. A new model constructed from a radial OU process together with a simple firing mechanism based on detailed Morris-Lecar firing statistics reproduces the Morris-Lecar Interspike Interval (ISI) distribution, and has the computational advantages of a LIF. The result justifies the large amount of attention paid to the LIF models.

Biosystems, 2007

We define an optimal signal in parametric neuronal models on the basis of interspike interval dat... more We define an optimal signal in parametric neuronal models on the basis of interspike interval data and rate coding schema. Under the classical approach the optimal signal is located where the frequency transfer function is steepest. Its position coincides with the inflection point of this curve. This concept is extended here by using Fisher information which is the inverse asymptotic variance of the best estimator and its dependence on the parameter value indicates accuracy of estimation. We compare the signal producing maximal Fisher information with the inflection point of the sigmoidal frequency transfer function.

Biological Cybernetics, 2005

How does the information about a signal in neural threshold crossings depend on the noise acting ... more How does the information about a signal in neural threshold crossings depend on the noise acting upon it? Two models are explored, a binary McCulloch and Pitts (threshold exceedance) model and a model of waiting time to exceedance--a discrete-time version of interspike intervals. If noise grows linearly with the signal, we find the best identification of the signal in terms of the Fisher information is for signals that do not reach the threshold in the absence of noise. Identification attains the same precision under weak and strong signals, but the coding range decreases at both extremes of signal level. We compare the results obtained for Fisher information with those using related first and second moment measures. The maximum obtainable information is plotted as a function of the ratio of noise to signal.

The Annals of Probability, 1986

The Annals of Probability, 1977

... 44 PRISCILLA GREENWOOD AND ITREL MONROE (N > n) so that P(T1(b) < N) = n P(n = min: Xj ... more ... 44 PRISCILLA GREENWOOD AND ITREL MONROE (N > n) so that P(T1(b) < N) = n P(n = min: Xj 0 Al(b), N > n) = S~n?=l P(X, 0 Al(b))P(Xj e Al(b), j < n, N > n) < P(X1 0 Al(b)) 57.- 1 P(N > n) , b-PEN. Also, P(Tl(b) < N) > bP f (P(N > n) - P(Tl(b) < n)) V 0 . The sum converges to EN ...

The Annals of Probability, 1974

ABSTRACT A martintote is a random sequence such that the asymptotic behavior of the process distr... more ABSTRACT A martintote is a random sequence such that the asymptotic behavior of the process distribution, conditioned with respect to the past, remains the same along the sequence. In this respect the conditional distributions of a martintote behave similarly to the conditional expectations of a martingale. We give an optional sampling theorem for martintotes and a class of examples.