Statistical Issues in the Analysis of Neuronal Data

Abstract

Kass, Robert E., Valérie Ventura, and Emery N. Brown. Statistical issues in the analysis of neuronal data. J Neurophysiol 94: 8 -25, 2005; doi:10.1152/jn.00648.2004. 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 wellestablished 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. I N T R O D U C T I O NTechnical advances have made available new methods for collecting, storing, and manipulating electrophysiological data. Investigations may now not only characterize neuronal activity in anatomically well defined regions, but they can also examine dynamics of neuronal response and their relationship to behavior. Although elementary methods of data analysis [such as t-tests or visual examination of the peristimulus time histogram (PSTH)] remain useful for many purposes, the growing complexity of neuroscientific experiments, often examining subtle changes on a comparatively fine timescale, requires careful attention to statistical methods for data analysis. In this overview we discuss some of the fundamental data analytical issues that face researchers in neurophysiology, illustrating the general points with the problems of describing the evolution of a neuron's firing rate across time, finding accurate population codes, and assessing time-varying correlation between 2 neurons. In each case recent work has provided a statistical technique that outperforms previous methodology, boosting the scientific information as effectively as if the number of experimental trials, or the number of neurons, had been increased by a substantial factor. We also indicate some of the ways modern statistical procedures can accommodate important complexities, such as dynamic changes in temporal and spatial aspects of hippocampal place cell firing and trial-to-trial variability in cortical neurons recorded from behaving animals. Our review supplements the brief and general guidance offered by Curran-Everett and Benos (2004), and may be regarded as an update to the early work of Perkel et al. (1967a,b).The new field of computational neuroscience uses detailed biophysical models and artificial neural networks to study emergent behavior of neural systems and the way neural systems represent and transmit information (e.g...

Opposite Effects of Stimulant and Antipsychotic Drugs on Striatal Fast-Spiking Interneurons

“…A significant population response to a drug required po0.05 using a paired t-test on saline and drug log firing rates. The distribution of saline and drug firing rates was verified to be log-normal using quantilequantile plots (data not shown), justifying the use of a paired t-test for significance testing of whole population responses (Kass et al, 2005).…”

Statistical Models of Spike Trains

“…History effects may be of the IMI form discussed here, or they may reach back further in time, incoporating effects of many spikes (Kass and Ventura, 2001;Paninski, 2004;Kass et al, 2005;Truccolo et al, 2005;Paninski et al, 2007b), while trial-to-trial variation may be accommodated using slowly-varying, trial-dependent contributions to firing rate Czanner et al, 2008). The advantages of this sort of model become more apparent when one considers multiple simultaneously-recorded spike trains (Brown et al, 2004), where interactions among neurons may be modeled by inclusion of additional terms that define the conditional intensity (Chornoboy et al, 1988;Paninski et al, 2004a;Okatan et al, 2005;Truccolo et al, 2005;Kulkarni and Paninski, 2007;Pillow et al, 2008;Czanner et al, 2008).…”

“…In other words, the pdf fixes the parameter θ and assigns probability to the spike trains that might then occur, while the likelihood function fixes the spike train that was actually observed, and assigns relative likelihood to the parameter values that might have produced it. Because likelihood-based methods use the information in the data as efficiently as possible (see, e.g., Kass et al, 2005) and the references therein), a great deal of effort has been devoted to developing such methods and for carrying out the relevant computations. In the next subsections we discuss three different conceptual approaches for performing statistical inference with the IF model via likelihood-based methods.…”

“…In other words, when performing statistical analysis we are not bound to any one model in particular; instead, we should choose the model which best suits our needs.) A particularly simple framework for analysis of point process data involves likelihood methods based on the conditional intensity function λ(t|H t , θ), the instantaneous firing rate at time t given H t , the complete stimulus and spiking history preceding time t (see Kass et al, 2005) and references therein for further discussion). To be concrete, we define P (spike at time t|H t ) = λ(t|H t , θ)dt or, more precisely,…”

Controversy in statistical analysis of functional magnetic resonance imaging data

“…The ease of analysis afforded by some of the software programs belies the complexity of the methods. This ease of use does not release experimentalists from their responsibility to validate findings using established statistical principles (12,13). Judicious use of nonparametric methods can, as Eklund et al (1) suggest, improve the current analysis paradigm in certain cases.…”