Maximum Likelihood Estimation for the Negative Binomial Dispersion Parameter

Piegorsch, Walter W.

doi:10.2307/2532104

Cited by 154 publications

(89 citation statements)

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“…Indeed, the estimation of this parameter has been widely studied in different fields (Gourieroux et al 1984;Lawless 1987;McCullagh and Nelder 1989;Dai et al 2013) and several estimation methods were provided such as the maximum likelihood method (Piegorsch 1990), or the method of moment and maximum extended quasilikelihood method (Clark and Perry 1989). A wide range of studies have shown that the estimation of this parameter is very challenging and can be significantly biased, especially when dealing with small data sets.…”

Section: Discussionmentioning

confidence: 99%

Testing the odds of inherent vs. observed overdispersion in neural spike counts

Taouali

Benvenuti

Wallisch

et al. 2016

Journal of Neurophysiology

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The repeated presentation of an identical visual stimulus in the receptive field of a neuron may evoke different spiking patterns at each trial. Probabilistic methods are essential to understand the functional role of this variance within the neural activity. In that case, a Poisson process is the most common model of trial-to-trial variability. For a Poisson process, the variance of the spike count is constrained to be equal to the mean, irrespective of the duration of measurements. Numerous studies have shown that this relationship does not generally hold. Specifically, a majority of electrophysiological recordings show an "overdispersion" effect: responses that exhibit more intertrial variability than expected from a Poisson process alone. A model that is particularly well suited to quantify overdispersion is the Negative-Binomial distribution model. This model is well-studied and widely used but has only recently been applied to neuroscience. In this article, we address three main issues. First, we describe how the Negative-Binomial distribution provides a model apt to account for overdispersed spike counts. Second, we quantify the significance of this model for any neurophysiological data by proposing a statistical test, which quantifies the odds that overdispersion could be due to the limited number of repetitions (trials). We apply this test to three neurophysiological data sets along the visual pathway. Finally, we compare the performance of this model to the Poisson model on a population decoding task. We show that the decoding accuracy is improved when accounting for overdispersion, especially under the hypothesis of tuned overdispersion. spike counts; overdispersion; negative-binomial distribution; decoding; tuning function.

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Section: Discussionmentioning

confidence: 99%

Testing the odds of inherent vs. observed overdispersion in neural spike counts

Taouali

Benvenuti

Wallisch

et al. 2016

Journal of Neurophysiology

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“…Most likely, the phenomenon of excess false positives in methods based strongly on the negative binomial distribution is a consequence of the known downward bias in the MLE for the negative binomial dispersion (Piegorsch, 1990). While this bias is generally small when viewed from the point of view of parameter estimation, it apparently has a large effect on the tail areas of the test statistic.…”

Section: Discussionmentioning

confidence: 99%

Excess False Positive Rates in Methods for Differential Gene Expression Analysis using RNA-Seq Data

Rocke

Ruan

Zhang

et al. 2015

Preprint

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Motivation: An important property of a valid method for testing for differential expression is that the false positive rate should at least roughly correspond to the p-value cutoff, so that if 10,000 genes are tested at a p-value cutoff of 10 −4 , and if all the null hypotheses are true, then there should be only about 1 gene declared to be significantly differentially expressed. We tested this by resampling from existing RNA-Seq data sets and also by matched negative binomial simulations.Results: Methods we examined, which rely strongly on a negative binomial model, such as edgeR, DESeq, and DESeq2, show large numbers of false positives in both the resampled real-data case and in the simulated negative binomial case. This also occurs with a negative binomial generalized linear model function in R. Methods that use only the variance function, such as limma-voom, do not show excessive false positives, as is also the case with a variance stabilizing transformation followed by linear model analysis with limma. The excess false positives are likely caused by apparently small biases in estimation of negative binomial dispersion and, perhaps surprisingly, occur mostly when the mean and/or the dispersion is high, rather than for low-count genes. Contact:dmrocke@ucdavis.edu, lruan@ucdavis.edu, yilzhang@ucdavis.edu, gt4636b@gatech.edu, bpdurbin@ucdavis.edu, saviran@ucdavis.edu.Supplementary Information: The computational tools developed for this study are freely available via our website http://dmrocke.ucdavis.edu/software.html. They can be downloaded as R code or run directly through an interactive web-based shiny application to reproduce the analysis presented here per a user's choice of dataset and the methods to be evaluated.

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“…Please see Maycock and Hall (1984), Piegorsch (1990), Fridstrøm et al (1995), , Wood (2002) and Lord and Bonneson (2005) for further discussion of this problem. Also, showed that the dispersion parameter of the negative binomial model can be incorrectly estimated when data characterized by a small sample size and low sample mean values are used.…”

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confidence: 99%