Biomedical subjects

Robert E Kass

Publications and source records attributed to Robert E Kass.

12 recordsLinked to original sources

PubMed2005

Testing equality of two functions using BARS.

This article presents two methods of testing the hypothesis of equality of two functions H(0):f(1)(t)=f(2)(t) for all t, in a generalized non-parametric regression framework using a recently developed generalized non-parametric regression method called Bayesian adaptive regression splines (BARS). Of particular interest is the special case of testing equality of two Poisson process intensity functions lambda(1) (t)=lambda(2) (t), which arises frequently in neurophysiological applications. The first method uses Bayes factors, and the second method uses a modified Hotelling T(2) test. Both methods are applied to the analysis of 347 motor cortical neurons and, for certain choices of test criteria, the two methods lead to the same conclusions for all but 7 neurons. A small simulation study of power indicates that the Bayes factor can be somewhat more powerful in small samples. The T(2)-type test should be useful in screening large number of neurons for condition-related activity, while the Bayes factor will be especially helpful in assessing evidence in favour of H(0).

Animals↗

PubMed2005

Spline-based non-parametric regression for periodic functions and its application to directional tuning of neurons.

The activity of neurons in the brain often varies systematically with some quantitative feature of a stimulus or action. A well-known example is the tendency of the firing rates of neurons in the primary motor cortex to vary with the direction of a subject's arm or wrist movement. When this movement is constrained to vary in only two dimensions, the direction of movement may be characterized by an angle, and the neuronal firing rate can be written as a function of this angle. The firing rate function has traditionally been fit with a cosine, but recent evidence suggests that departures from cosine tuning occur frequently. We report here a new non-parametric regression method for fitting periodic functions and demonstrate its application to the fitting of neuronal data. The method is an extension of Bayesian adaptive regression splines (BARS) and applies both to normal and non-normal data, including Poisson data, which commonly arise in neuronal applications. We compare the new method to a periodic version of smoothing splines and some parametric alternatives and find the new method to be especially valuable when the smoothness of the periodic function varies unevenly across its domain.

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PubMed2005

Bayesian tests of extra-Binomial variability.

A simple model for extra-Binomial variability is the Beta-Binomial. A complication in testing the Binomial against the Beta-Binomial alternative is that the Binomial lies on the boundary of the Beta-Binomial, which forces modifications to the usual asymptotic arguments. In this paper, we propose a Bayesian test using a pair of approximate Bayes factors, one for the case in which the maximum likelihood estimator (MLE) of the extra-Binomial variability is zero and one for the case in which it is positive. These approximate Bayes factors are easy to compute. We evaluate the operating characteristics of the Bayes factors and find them to be more powerful than the likelihood ratio test. We then apply the method to three data sets, including one in which the issue is whether a logistic regression intercept should be considered a random effect. In each case, our approximate Bayes factors are close to the exact Bayes factors, which may also be computed with additional effort.

Amputation, Surgical↗

PubMed2005

Trial-to-trial variability and its effect on time-varying dependency between two neurons.

The joint peristimulus time histogram (JPSTH) and cross-correlogram provide a visual representation of correlated activity for a pair of neurons, and the way this activity may increase or decrease over time. In a companion paper we showed how a Bootstrap evaluation of the peaks in the smoothed diagonals of the JPSTH may be used to establish the likely validity of apparent time-varying correlation. As noted in earlier studies by Brody and Ben-Shaul et al., trial-to-trial variation can confound correlation and synchrony effects. In this paper we elaborate on that observation, and present a method of estimating the time-dependent trial-to-trial variation in spike trains that may exceed the natural variation displayed by Poisson and non-Poisson point processes. The statistical problem is somewhat subtle because relatively few spikes per trial are available for estimating a firing-rate function that fluctuates over time. The method developed here decomposes the spike-train variability into a stimulus-related component and a trial-specific component, allowing many degrees of freedom to characterize the former while assuming a small number suffices to characterize the latter. The Bootstrap significance test of the companion paper is then modified to accommodate these general excitability effects. This methodology allows an investigator to assess whether excitability effects are constant or time-varying, and whether they are shared by two neurons. In data from two V1 neurons we find that highly statistically significant evidence of dependency disappears after adjustment for time-varying trial-to-trial variation.

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PubMed2005

Statistical assessment of time-varying dependency between two neurons.

The joint peristimulus time histogram (JPSTH) provides a visual representation of the dynamics of correlated activity for a pair of neurons. There are many ways to adjust the JPSTH for the time-varying firing-rate modulation of each neuron, and then to define a suitable measure of time-varying correlated activity. Our approach is to introduce a statistical model for the time-varying joint spiking activity so that the joint firing rate can be estimated more efficiently. We have applied an adaptive smoothing method, which has been shown to be effective in capturing sudden changes in firing rate, to the ratio of joint firing probability to the probability of firing predicted by independence. A bootstrap procedure, applicable to both Poisson and non-Poisson data, was used to define a statistical significance test of whether a large ratio could be attributable to chance alone. A numerical simulation showed that the bootstrap-based significance test has very nearly the correct rejection probability, and can have markedly better power to detect departures from independence than does an approach based on testing contiguous bins in the JPSTH. In a companion paper, we show how this formulation can accommodate latency and time-varying excitability effects, which can confound spike timing effects.

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PubMed2005

Statistical issues in the analysis of neuronal data.

Analysis of data from neurophysiological investigations can be challenging. Particularly when experiments involve dynamics of neuronal response, scientific inference can become subtle and some statistical methods may make much more efficient use of the data than others. This article reviews well-established statistical principles, which provide useful guidance, and argues that good statistical practice can substantially enhance results. Recent work on estimation of firing rate, population coding, and time-varying correlation provides improvements in experimental sensitivity equivalent to large increases in the number of neurons examined. Modern nonparametric methods are applicable to data from repeated trials. Many within-trial analyses based on a Poisson assumption can be extended to non-Poisson data. New methods have made it possible to track changes in receptive fields, and to study trial-to-trial variation, with modest amounts of data.

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PubMed2004

Automatic correction of ocular artifacts in the EEG: a comparison of regression-based and component-based methods.

A variety of procedures have been proposed to correct ocular artifacts in the electroencephalogram (EEG), including methods based on regression, principal components analysis (PCA) and independent component analysis (ICA). The current study compared these three methods, and it evaluated a modified regression approach using Bayesian adaptive regression splines to filter the electrooculogram (EOG) before computing correction factors. We applied each artifact correction procedure to real and simulated EEG data of varying epoch lengths and then quantified the impact of correction on spectral parameters of the EEG. We found that the adaptive filter improved regression-based artifact correction. An automated PCA method effectively reduced ocular artifacts and resulted in minimal spectral distortion, whereas ICA correction appeared to distort power between 5 and 20 Hz. In general, reducing the epoch length improved the accuracy of estimating spectral power in the alpha (7.5-12.5 Hz) and beta (12.5-19.5 Hz) bands, but it worsened the accuracy for power in the theta (3.5-7.5 Hz) band and distorted time domain features. Results supported the use of regression-based and PCA-based ocular artifact correction and suggested a need for further studies examining possible spectral distortion from ICA-based correction procedures.

Adult↗

PubMed2004

Multiple neural spike train data analysis: state-of-the-art and future challenges.

Multiple electrodes are now a standard tool in neuroscience research that make it possible to study the simultaneous activity of several neurons in a given brain region or across different regions. The data from multi-electrode studies present important analysis challenges that must be resolved for optimal use of these neurophysiological measurements to answer questions about how the brain works. Here we review statistical methods for the analysis of multiple neural spike-train data and discuss future challenges for methodology research.

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PubMed2003

Statistical smoothing of neuronal data.

The purpose of smoothing (filtering) neuronal data is to improve the estimation of the instantaneous firing rate. In some applications, scientific interest centres on functions of the instantaneous firing rate, such as the time at which the maximal firing rate occurs or the rate of increase of firing rate over some experimentally relevant period. In others, the instantaneous firing rate is needed for probability-based calculations. In this paper we point to the very substantial gains in statistical efficiency from smoothing methods compared to using the peristimulus-time histogram (PSTH), and we also demonstrate a new method of adaptive smoothing known as Bayesian adaptive regression splines (DiMatteo 1, Genovese C R and Kass R E 2001 Biometrika 88 1055-71). We briefly review additional applications of smoothing with non-Poisson processes and in the joint PSTH for a pair of neurons.

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PubMed2002

Grammatical morphology and perception of synthetic and natural speech in children with specific language impairments.

Studies investigating the relationship between the use of inflectional morphology and speech-perception abilities in children with SLI traditionally have employed synthetic speech stimuli. The purpose of this study was to replicate the findings reported in Leonard, McGregor, and Allen (1992) with an older group of children with SLI and to determine if the pattern of deficits seen for synthetic speech extends to perception of natural speech stimuli. The speech-perception abilities of 27 children between the ages of 6;11 and 8;11 (15 SLI and 12 NL) were compared using natural and synthetic versions of the [das]-[daS], [dabiba]-[dabuba], and [i]-[u] contrast pairs originally used in Leonard et al. The findings reported by Leonard et al. were replicated with synthetic speech but not for the natural speech. Use of inflectional morphology in obligatory contexts by the children with SLI was not significantly correlated with their perception abilities for any of the natural or synthetic speech-contrast pairs. Further, although both groups' ability to maintain the target contrast in memory declined over the span of the trials for all target contrasts for both natural and synthetic speech, the rate of decline did not differ significantly between the SLI and NL groups. Findings are discussed with respect to possible deficits in linking phonological representations to grammatical representations in children with SLI.

Child↗

PubMed2002

Statistical analysis of temporal evolution in single-neuron firing rates.

A fundamental methodology in neurophysiology involves recording the electrical signals associated with individual neurons within brains of awake behaving animals. Traditional statistical analyses have relied mainly on mean firing rates over some epoch (often several hundred milliseconds) that are compared across experimental conditions by analysis of variance. Often, however, the time course of the neuronal firing patterns is of interest, and a more refined procedure can produce substantial additional information. In this paper we compare neuronal firing in the supplementary eye field of a macaque monkey across two experimental conditions. We take the electrical discharges, or 'spikes', to be arrivals in a inhomogeneous Poisson process and then model the firing intensity function using both a simple parametric form and more flexible splines. Our main interest is in making inferences about certain characteristics of the intensity, including the timing of the maximal firing rate. We examine data from 84 neurons individually and also combine results into a hierarchical model. We use Bayesian estimation methods and frequentist significance tests based on a nonparametric bootstrap procedure. We are thereby able to conclude that a substantial fraction of the neurons exhibit important temporal differences in firing intensity across the two conditions, and we quantify the effect across the population of neurons.

Journal Article↗

PubMed2002

The time-rescaling theorem and its application to neural spike train data analysis.

Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of fit, is crucial for establishing the model's validity prior to using it to make inferences about a particular neural system. Assessing goodness-of-fit is a challenging problem for point process neural spike train models, especially for histogram-based models such as perstimulus time histograms (PSTH) and rate functions estimated by spike train smoothing. The time-rescaling theorem is a well-known result in probability theory, which states that any point process with an integrable conditional intensity function may be transformed into a Poisson process with unit rate. We describe how the theorem may be used to develop goodness-of-fit tests for both parametric and histogram-based point process models of neural spike trains. We apply these tests in two examples: a comparison of PSTH, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the supplementary eye field of a macque monkey and a comparison of temporal and spatial smoothers, inhomogeneous Poisson, inhomogeneous gamma, and inhomogeneous inverse gaussian models of rat hippocampal place cell spiking activity. To help make the logic behind the time-rescaling theorem more accessible to researchers in neuroscience, we present a proof using only elementary probability theory arguments. We also show how the theorem may be used to simulate a general point process model of a spike train. Our paradigm makes it possible to compare parametric and histogram-based neural spike train models directly. These results suggest that the time-rescaling theorem can be a valuable tool for neural spike train data analysis.

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