Sam Behseta

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

Abstract:  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.

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.

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 Spearmans, 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.

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 Hotellings T2 statistic of Behseta and Kass (Statist. Med. 2005; 24:3523–3534), as well as a nonparametric one similar to the spatial signed-rank test statistic of Möttönen and Oja (J. Nonparametric Statist. 1995; 5:201–213). 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.

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.

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 monkeys brain while performing a sequence of reaching tasks.

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

ABSTRACT The goal of this article 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 that 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 synchronizes their activity shortly after stimulus onset. These differentially synchronizing subpopulations of neurons suggest a continuum of population representation of the reward-seeking task. Second, our analyses also suggest that the degree of synchronization differs between the rewarded and nonrewarded 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 article are available online.

Neuronal Spike Train Analysis Using Gaussian Process Models

Statistical analysis of simultaneously recorded neurons plays an important role in understanding complex behaviors, decision making process, and neurophysiological disorders. Here, we briefly review several statistical methods specifically developed for analysis of neuronal spike trains. We then focus on application of Gaussian process models for estimating time-varying firing rates of neurons and show how this approach can be extended for modeling synchrony among multiple neurons. We finish this chapter by discussing some possible future directions where more advanced nonparametric Bayesian methods can be utilized to improve existing models.

A Bootstrap Attack on Digital Watermarks in the Frequency Domain

In this paper, we propose five simple algorithms to execute a collusion attack given several watermarked documents. Each document considered is a picture represented as a matrix of two dimensional Discrete Cosine Transform (DCT2) coefficients. Our algorithm is independent of media type. Bootstrap methods are used to construct confidence intervals for each DCT2 coefficient and determine its uncertainty. Using simulation studies we show that Bootstrap procedures are highly efficient with respect to the number of iterations and sample size per iteration while maintaining stellar probabilistic coverage, providing results at least as good as averaging or taking the median of signals. Most importantly, a set of simulation studies suggest that the precision of our heuristic methodology increases quickly when the number of watermarked copies are increased, but good probabilistic coverage is achieved with a low number of independently watermarked copies. We conjecture that the Bootstrap methodology will be highly effective in reconstructing the original signal for documents with high redundancy.

A Time Series Intra-Video Collusion Attack on Frame-by-Frame Video Watermarking

Current methods of digital watermarking for video rely on results from digital watermarking for images. However, watermarking each frame using image watermarking techniques is vulnerable to an intra-video collusion attack because it provides grounds to make statistical inference about information within consecutive frames. An algorithm using bootstrapped time series is proposed to exploit this vulnerability. Experimental results demonstrate that this algorithm produces a video with a significantly lower similarity to the given watermarked video using the standard watermark detector.