A semiparametric Bayesian model for detecting synchrony among multiple neurons.

We propose a scalable semiparametric Bayesian model to capture dependencies among multiple neurons by detecting their cofiring (possibly with some lag time) patterns over time. After discretizing time so there is at most one spike at each interval, the resulting sequence of 1s (spike) and 0s (silence) for each neuron is modeled using the logistic function of a continuous latent variable with a gaussian process prior. For multiple neurons, the corresponding marginal distributions are coupled to their joint probability distribution using a parametric copula model. The advantages of our approach are as follows. The nonparametric component (i.e., the gaussian process model) provides a flexible framework for modeling the underlying firing rates, and the parametric component (i.e., the copula model) allows us to make inferences regarding both contemporaneous and lagged relationships among neurons. Using the copula model, we construct multivariate probabilistic models by separating the modeling of univariate marginal distributions from the modeling of a dependence structure among variables. Our method is easy to implement using a computationally efficient sampling algorithm that can be easily extended to high-dimensional problems. Using simulated data, we show that our approach could correctly capture temporal dependencies in firing rates and identify synchronous neurons. We also apply our model to spike train data obtained from prefrontal cortical areas.

Immune defense in Drosophila melanogaster depends on diet, sex, and mating status.

Immune defense is a complex trait that affects and is affected by many other host factors, including sex, mating, and dietary environment. We used the agriculturally relevant fungal emtomopathogen, Beauveria bassiana, and the model host organism Drosophila melanogaster to examine how the impacts of sex, mating, and dietary environment on immunity are interrelated. We showed that the direction of sexual dimorphism in immune defense depends on mating status and mating frequency. We also showed that post-infection dimorphism in immune defense changes over time and is affected by dietary condition both before and after infection. Supplementing the diet with protein-rich yeast improved post-infection survival but more so when supplementation was done after infection instead of before. The multi-directional impacts among immune defense, sex, mating, and diet are clearly complex, and while our study shines light on some of these relationships, further study is warranted. Such studies have potential downstream applications in agriculture and medicine.

Comparison of two populations of curves with an application in neuronal data analysis.

Often in neurophysiological studies, scientists are interested in testing hypotheses regarding the equality of the overall intensity functions of a group of neurons when recorded under two different experimental conditions. In this paper, we consider such a hypothesis testing problem. We propose two test statistics: a parametric test similar to the modified Hotelling's T2 statistic of Behseta and Kass (Statist. Med. 2005; 24:3523­3534), as well as a nonparametric one similar to the spatial signed-rank test statistic of Möttönen and Oja (J. Nonparametric Statist. 1995; 5:201­213). We implement these tests on smooth curves obtained via fitting Bayesian Adaptive Regression Splines (BARS) to the intensity functions of neuronal Peri-Stimulus Time Histograms. Through simulation, we show that the powers of our proposed tests are extremely high even when the number of sampled neurons and the number of trials per neuron are small. Finally, we apply our methods on a group of motor cortex neurons recorded during a reaching task.

On the effects of signal acuity in a multi-alternative model of decision making.

We consider the effects of signal sharpness or acuity on the performance of neural models of decision making. In these models, a vector of signals is presented, and the subject must decide which of the elements of the vector is the largest. McMillen and Holmes ( 2006 ) derived asymptotically optimal tests under the assumption that the elements of the signal vector were all equal except one. In this letter, we consider the case of signals spread around a peak. The acuity is a measure of how strongly peaked the signal is. We find that the optimal test is one in which the detectors are passed through an output layer that encodes knowledge of the possible shapes of the incoming signals. The incorporation of such an output layer can lead to significant improvements in decision-making tasks.

Bayesian nonparametric modeling for comparison of single-neuron firing intensities.

We propose a fully inferential model-based approach to the problem of comparing the firing patterns of a neuron recorded under two distinct experimental conditions. The methodology is based on nonhomogeneous Poisson process models for the firing times of each condition with flexible nonparametric mixture prior models for the corresponding intensity functions. We demonstrate posterior inferences from a global analysis, which may be used to compare the two conditions over the entire experimental time window, as well as from a pointwise analysis at selected time points to detect local deviations of firing patterns from one condition to another. We apply our method on two neurons recorded from the primary motor cortex area of a monkey's brain while performing a sequence of reaching tasks.

Fluctuations in climate and incidence of coccidioidomycosis in Kern County, California: a review.

Coccidioidomycosis (Valley Fever) is a fungal infection found in the southwestern United States, northern Mexico, and some places in Central and South America. The fungi that cause it (Coccidioides immitis and Coccidioides posadasii) are normally soil dwelling, but, if disturbed, become airborne and infect the host when their spores are inhaled. It is thus natural to surmise that weather conditions, which foster the growth and dispersal of Coccidioides, must have an effect on the number of cases in the endemic areas. This article reviews our attempts to date at quantifying this relationship in Kern County, California (where C. immitis is endemic). We have examined the effect on incidence resulting from precipitation, surface temperature, and wind speed. We have performed our studies by means of a simple linear correlation analysis, and by a generalized autoregressive moving average model. Our first analysis suggests that linear correlations between climatic parameters and incidence are weak; our second analysis indicates that incidence can be predicted largely by considering only the previous history of incidence in the county-the inclusion of climate- or weather-related time sequences improves the model only to a relatively minor extent. Our work therefore suggests that incidence fluctuations (about a seasonally varying background value) are related to biological and/or anthropogenic reasons, and not so much to weather or climate anomalies.

A Dynamic Bayesian Model for Characterizing Cross-Neuronal Interactions During Decision-Making.

The goal of this paper is to develop a novel statistical model for studying cross-neuronal spike train interactions during decision making. For an individual to successfully complete the task of decision-making, a number of temporally-organized events must occur: stimuli must be detected, potential outcomes must be evaluated, behaviors must be executed or inhibited, and outcomes (such as reward or no-reward) must be experienced. Due to the complexity of this process, it is likely the case that decision-making is encoded by the temporally-precise interactions between large populations of neurons. Most existing statistical models, however, are inadequate for analyzing such a phenomenon because they provide only an aggregated measure of interactions over time. To address this considerable limitation, we propose a dynamic Bayesian model which captures the time-varying nature of neuronal activity (such as the time-varying strength of the interactions between neurons). The proposed method yielded results that reveal new insight into the dynamic nature of population coding in the prefrontal cortex during decision making. In our analysis, we note that while some neurons in the prefrontal cortex do not synchronize their firing activity until the presence of a reward, a different set of neurons synchronize their activity shortly after stimulus onset. These differentially synchronizing sub-populations of neurons suggests a continuum of population representation of the reward-seeking task. Secondly, our analyses also suggest that the degree of synchronization differs between the rewarded and non-rewarded conditions. Moreover, the proposed model is scalable to handle data on many simultaneously-recorded neurons and is applicable to analyzing other types of multivariate time series data with latent structure. Supplementary materials (including computer codes) for our paper are available online.

Bayesian nonparametric analysis of neuronal intensity rates.

We propose a flexible hierarchical Bayesian nonparametric modeling approach to compare the spiking patterns of neurons recorded under multiple experimental conditions. In particular, we showcase the application of our statistical methodology using neurons recorded from the supplementary eye field region of the brains of two macaque monkeys trained to make delayed eye movements to three different types of targets. The proposed Bayesian methodology can be used to perform either a global analysis, allowing for the construction of posterior comparative intervals over the entire experimental time window, or a pointwise analysis for comparing the spiking patterns locally, in a predetermined portion of the experimental time window. By developing our nonparametric Bayesian model we are able to analyze neuronal data from three or more conditions while avoiding the computational expenses typically associated with more traditional analysis of physiological data.

Hebbian learning in linear-nonlinear networks with tuning curves leads to near-optimal, multi-alternative decision making.

Optimal performance and physically plausible mechanisms for achieving it have been completely characterized for a general class of two-alternative, free response decision making tasks, and data suggest that humans can implement the optimal procedure. The situation is more complicated when the number of alternatives is greater than two and subjects are free to respond at any time, partly due to the fact that there is no generally applicable statistical test for deciding optimally in such cases. However, here, too, analytical approximations to optimality that are physically and psychologically plausible have been analyzed. These analyses leave open questions that have begun to be addressed: (1) How are near-optimal model parameterizations learned from experience? (2) What if a continuum of decision alternatives exists? (3) How can neurons' broad tuning curves be incorporated into an optimal-performance theory? We present a possible answer to all of these questions in the form of an extremely simple, reward-modulated Hebbian learning rule by which a neural network learns to approximate the multi-hypothesis sequential probability ratio test.

Bayesian correction for attenuation of correlation in multi-trial spike count data.

When correlation is measured in the presence of noise, its value is decreased. In single-neuron recording experiments, for example, the correlation of selectivity indices in a pair of tasks may be assessed across neurons, but, because the number of trials is limited, the measured index values for each neuron will be noisy. This attenuates the correlation. A correction for such attenuation was proposed by Spearman more than 100 yr ago, and more recent work has shown how confidence intervals may be constructed to supplement the correction. In this paper, we propose an alternative Bayesian correction. A simulation study shows that this approach can be far superior to Spearman's, both in accuracy of the correction and in coverage of the resulting confidence intervals. We demonstrate the usefulness of this technology by applying it to a set of data obtained from the frontal cortex of a macaque monkey while performing serial order and variable reward saccade tasks. There the correction results in a substantial increase in the correlation across neurons in the two tasks.

Statistical modeling of valley fever data in Kern County, California.

Coccidioidomycosis (valley fever) is a fungal infection found in the southwestern US, northern Mexico, and some places in Central and South America. The fungus that causes it (Coccidioides immitis) is normally soil-dwelling but, if disturbed, becomes air-borne and infects the host when its spores are inhaled. It is thus natural to surmise that weather conditions that foster the growth and dispersal of the fungus must have an effect on the number of cases in the endemic areas. We present here an attempt at the modeling of valley fever incidence in Kern County, California, by the implementation of a generalized auto regressive moving average (GARMA) model. We show that the number of valley fever cases can be predicted mainly by considering only the previous history of incidence rates in the county. The inclusion of weather-related time sequences improves the model only to a relatively minor extent. This suggests that fluctuations of incidence rates (about a seasonally varying background value) are related to biological and/or anthropogenic reasons, and not so much to weather anomalies.

Testing equality of several functions: analysis of single-unit firing-rate curves across multiple experimental conditions.

We consider the problem of comparing noisy functions, here trial-averaged neuronal firing-rate curves, across multiple experimental conditions. Of interest are comparisons both within neurons and also among populations of individually recorded neurons. We propose likelihood ratio tests to perform comparisons either pointwise or globally over the entire experimental time. A simulation study of power demonstrates the strength of these tests even for moderate sample sizes. We implement these tests on a group of 233 neurons recorded from primate frontal oculomotor cortex, first, to screen for condition-related differential activity and, second, to search for neurons displaying interesting time-locked features that vary with condition.

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).