Statistical Significance of Coincident Spikes: Count-Based Versus Rate-Based Statistics

2002 ◽  
Vol 14 (1) ◽  
pp. 121-153 ◽  
Author(s):  
Robert Gütig ◽  
Ad Aertsen ◽  
Stefan Rotter
Keyword(s):  
Neural Coding ◽  
Time Course ◽  
Statistical Significance ◽  
Event Analysis ◽  
Neural Firing ◽  
Test Power ◽  
Firing Rates ◽  
Coding Schemes ◽  
Significance Levels ◽  
Power Curves

Inspired by different conceptualizations of temporal neural coding schemes, there has been recent interest in the search for signs of precisely synchronized neural activity in the cortex. One method developed for this task is unitary-event analysis. This method tests multiple single-neuron recordings for short epochs with significantly more coincident spikes than expected from independent neurons. We reformulated the statistical test underlying this method using a coincidence count distribution based on empirical spike counts rather than on estimated spike probabilities. In the case of two neurons, the requirement of stationary firing rates, originally imposed on both neurons, can be relaxed; only the rate of one neuron needs to be stationary, while the other may follow an arbitrary time course. By analytical calculations of the test power curves of the original and the revised method, we demonstrate that the test power can be increased by a factor of two or more in physiologically realistic regimes. In addition, we analyze the effective significance levels of both methods for neural firing rates ranging between 0.2 Hz and 30 Hz.

scholarly journals Activity in the Barrel Cortex During Active Behavior and Sleep

2010 ◽  
Vol 103 (4) ◽  
pp. 2074-2084 ◽  
Author(s):  
Sujith Vijayan ◽  
Greg J. Hale ◽  
Christopher I. Moore ◽  
Emery N. Brown ◽  
Matthew Wilson
Keyword(s):  
Barrel Cortex ◽  
Slow Wave Sleep ◽  
Neural Firing ◽  
Related Activity ◽  
Firing Rates ◽  
Coding Schemes ◽  
Baseline Activity ◽  
Sensory Cue ◽  
The Individual

The rate at which neurons fire has wide-reaching implications for the coding schemes used by neural systems. Despite the extensive use of the barrel cortex as a model system, relatively few studies have examined the rate of sensory activity in single neurons in freely moving animals. We examined the activity of barrel cortex neurons in behaving animals during sensory cue interaction, during non–stimulus-related activity, during various states of sleep, and during the administration of isoflurane. The activity of regular-spiking units (RSUs: predominantly excitatory neurons) and fast spiking units (FSUs: a subtype of inhibitory interneurons) was examined separately. We characterized activity by calculating neural firing rates, because several reports have emphasized the low firing rates in this system, reporting that both baseline activity and stimulus evoked activity is <1 Hz. We report that, during sensory cue interaction or non–stimulus-related activity, the majority of RSUs in rat barrel cortex fired at rates significantly >1 Hz, with 27.4% showing rates above 10 Hz during cue interaction. Even during slow wave sleep, which had the lowest mean and median firing rates of any nonanesthetized state observed, 80.0% of RSUs fired above 1 Hz. During all of the nonanesthetized states observed 100% of the FSUs fired well above 1 Hz. When rats were administered isoflurane and at a depth of anesthesia used in standard in vivo electrophysiological preparations, all of the RSUs fired below 1 Hz. We also found that >80% of RSUs either upmodulated or downmodulated their firing during cue interaction. These data suggest that low firing rates do not typify the output of the barrel cortex during awake activity and during sleep and indicate that sensory coding at both the individual and population levels may be nonsparse.

Rate Limitations of Unitary Event Analysis

2000 ◽  
Vol 12 (9) ◽  
pp. 2063-2082 ◽  
Author(s):  
A. Roy ◽  
P. N. Steinmetz ◽  
E. Niebur
Keyword(s):  
Firing Rate ◽  
Random Variable ◽  
Event Analysis ◽  
Neural Firing ◽  
Time Intervals ◽  
Relative Variation ◽  
Firing Rates ◽  
Inhomogeneous Poisson Processes ◽  
The Mean ◽  
Unitary Events

Unitary event analysis is a new method for detecting episodes of synchronized neural activity (Riehle, Grüun, Diesmann, & Aertsen, 1997). It detects time intervals that contain coincident firing at higher rates than would be expected if the neurons fired as independent inhomogeneous Poisson processes; all coincidences in such intervals are called unitary events (UEs). Changes in the frequency of UEs that are correlated with behavioral states may indicate synchronization of neural firing that mediates or represents the behavioral state. We show that UE analysis is subject to severe limitations due to the underlying discrete statistics of the number of coincident events. These limitations are particularly stringent for low (0–10 spikes/s) firing rates. Under these conditions, the frequency of UEs is a random variable with a large variation relative to its mean. The relative variation decreases with increasing firing rate, and we compute the lowest firing rate, at which the 95% confidence interval around the mean frequency of UEs excludes zero. This random variation in UE frequency makes interpretation of changes in UEs problematic for neurons with low firing rates. As a typical example, when analyzing 150 trials of an experiment using an averaging window 100 ms wide and a 5ms coincidence window, firing rates should be greater than 7 spikes per second.

scholarly journals Burst activity plays no role for the field-to-field variability and rate remapping of grid cells

2020 ◽  
Author(s):  
Michaela Poth ◽  
Andreas V.M. Herz
Keyword(s):  
Firing Rate ◽  
Time Scales ◽  
Neural Coding ◽  
Hexagonal Lattice ◽  
Grid Cell ◽  
Grid Cells ◽  
Firing Patterns ◽  
Firing Rates ◽  
Coding Schemes ◽  
Short Time

AbstractGrid cells in rodent medial entorhinal cortex are thought to play a key role for spatial navigation. When the animal is freely moving in an open arena the firing fields of each grid cell tend to form a hexagonal lattice spanning the environment. Firing rates vary from field to field and change under contextual modifications, whereas the field locations do not shift under such “rate remapping”. The observed differences in firing rate could reflect overall activity changes or changes in the detailed spike-train statistics. As these two alternatives imply distinct neural coding schemes, we investigated whether temporal firing patterns vary from field to field and whether they change under rate remapping. Focusing on short time scales, we found that the proportion of bursts compared to all discharge events is similar in all firing fields of a given grid cell and does not change under rate remapping. Mean firing rates with and without bursts are proportional for each cell. However, this ratio varies across cells. Additionally, we looked at how rate remapping relates to entorhinal theta-frequency oscillations. Theta-phase coding was preserved despite firing-rate changes from rate remapping but we did not observe differences between the first and second half of the theta cycle, as had been reported for CA1. Our results indicate that both, the heterogeneity between firing fields and rate remapping, are not due to altered firing patterns on short time scales but reflect location-specific changes at the firing-rate level.

scholarly journals Cavalier Use of Inferential Statistics Is a Major Source of False and Irreproducible Scientific Findings

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 603
Author(s):  
Leonid Hanin
Keyword(s):  
Sample Size ◽  
Gaussian Approximation ◽  
Statistical Significance ◽  
Statistical Analyses ◽  
Random Sample Size ◽  
P Values ◽  
The Central Limit Theorem ◽  
Fixed Sample ◽  
Large Numbers ◽  
Significance Levels

I uncover previously underappreciated systematic sources of false and irreproducible results in natural, biomedical and social sciences that are rooted in statistical methodology. They include the inevitably occurring deviations from basic assumptions behind statistical analyses and the use of various approximations. I show through a number of examples that (a) arbitrarily small deviations from distributional homogeneity can lead to arbitrarily large deviations in the outcomes of statistical analyses; (b) samples of random size may violate the Law of Large Numbers and thus are generally unsuitable for conventional statistical inference; (c) the same is true, in particular, when random sample size and observations are stochastically dependent; and (d) the use of the Gaussian approximation based on the Central Limit Theorem has dramatic implications for p-values and statistical significance essentially making pursuit of small significance levels and p-values for a fixed sample size meaningless. The latter is proven rigorously in the case of one-sided Z test. This article could serve as a cautionary guidance to scientists and practitioners employing statistical methods in their work.

scholarly journals IL-8 and MCP Gene Expression and Production by LPS-Stimulated Human Corneal Stromal Cells

2012 ◽  
Vol 2012 ◽  
pp. 1-4 ◽  
Author(s):  
Roni M. Shtein ◽  
Susan G. Elner ◽  
Zong-Mei Bian ◽  
Victor M. Elner
Keyword(s):  
Gene Expression ◽  
Northern Blot ◽  
Stromal Cells ◽  
Blot Analysis ◽  
Time Course ◽  
Northern Blot Analysis ◽  
Statistical Significance ◽  
Dependent Manner ◽  
Corneal Inflammation ◽  
Chemotactic Protein

Purpose. To determine time course of effect of lipopolysaccharide (LPS) on production of interleukin-8 (IL-8) and monocyte chemotactic protein (MCP) by cultured human corneal stromal cells.Methods. Human corneal stromal cells were harvested from donor corneal specimens, and fourth to sixth passaged cells were used. Cell cultures were stimulated with LPS for 2, 4, 8, and 24 hours. Northern blot analysis of IL-8 and MCP gene expression and ELISA for IL-8 and MCP secretion were performed. ELISA results were analyzed for statistical significance using two-tailed Student'st-test.Results. Northern blot analysis demonstrated significantly increased IL-8 and MCP gene expression after 4 and 8 hours of exposure to LPS. ELISA for secreted IL-8 and MCP demonstrated statistically significant increases (P<0.05) after corneal stromal cell stimulation with LPS.Conclusions. This paper suggests that human corneal stromal cells may participate in corneal inflammation by secreting potent leukocyte chemotactic and activating proteins in a time-dependent manner when exposed to LPS.

scholarly journals Chances and risks in the development of the smallest villages in Vysočina Region

2008 ◽  
Vol 56 (3) ◽  
pp. 165-174
Author(s):  
Marie Prášilová ◽  
Tomáš Hlavsa
Keyword(s):  
Community Development ◽  
Statistical Significance ◽  
Contingency Tables ◽  
The Czech Republic ◽  
Increased Risk ◽  
Significance Levels ◽  
Detailed Statistical Analysis ◽  
Area Survey ◽  
Survey Results ◽  
The Village

Vysočina is the region with highest numbers of the smallest villages in the Czech Republic. The current levels of the infrastructure, conditions of living of the inhabitants and chances for development of the communities were examined by means of a questionnaire area survey over the entire number of villages and towns of Vysočina Region in 2007. Survey results were tested as concerns representativity, statistically grouped and ordered in the manner of contingenc tables. For those aspects, where the community representatives felt a degree of deterioration a detailed statistical analysis was carried out. For the groups of villages up to 199 head and up to 499 head significance tests were carried out first and the degree of dependence measured by the Cramer coefficient. Statistical significance was an argument for deeper analyses. Sign sketches for 0,1 %, 1 % and 5 % significance levels were prepared for all the contingency tables. The answers of the conjuncture research were reduced to an alternative statistical variable and association was further studied between the village size and the problem areas of the community development. Probabilities of the separate variants were stated and risks and chances were evaluated for the possibilities for the smallest villages to be threatened as compared with the larger ones. The research results are presented in the shape of risk probabilities, both the relative and absolute ones, using the less applied measures for the risk measurement in two-way contingency tables. The computations are commented verbally and they bring new looks upon the perception of increased risk and chances improvement problems by means of qualitative statistical attributes. The solution is not only practically important but it offers an applicable general methodology instruction, too, for detailed analyses in the empirical research of qualitative phenomena.

Part IV Measurement, 16 Legal Issues with Statistical Evidence

2020 ◽  
Author(s):  
Veljanovski Cento
Keyword(s):  
Statistical Analysis ◽  
European Commission ◽  
Best Practice ◽  
Statistical Significance ◽  
Statistical Evidence ◽  
Legal Issues ◽  
Economic Evidence ◽  
Standard Of Proof ◽  
Significance Levels ◽  
General Concern

This chapter examines some of the legal and evidential issues surrounding statistical evidence. Courts are wary of statistical analysis and treat it as complex and difficult to reconcile with legal methods of determining damages based on documentary evidence. Indeed, the problem of estimated averages can conflict with the court’s approach. Moreover, there are statistical, economic, and legal issues surrounding statistical significance. The general concern is that reliance on conventional statistical significance levels may not reflect the legal standard of proof. The court can be assisted by the Practical Guide and Pass-on Guidelines of the European Commission, but also the best practice guidance of competition authorities for the submission of economic evidence.

scholarly journals Parametric Assessment of Trend Test Power in a Changing Environment

2020 ◽  
Vol 12 (9) ◽  
pp. 3889
Author(s):  
Andrea Gioia ◽  
Maria Francesca Bruno ◽  
Vincenzo Totaro ◽  
Vito Iacobellis
Keyword(s):  
Statistical Tests ◽  
Statistical Significance ◽  
Strong Dependence ◽  
Generalized Extreme Value Distribution ◽  
Monte Carlo Experiment ◽  
Data Series ◽  
Test Power ◽  
Special Cases ◽  
Wide Range ◽  
Position Parameter

In the context of climate and environmental change assessment, the use of probabilistic models in which the parameters of a given distribution may vary in accordance with time has reinforced the need for appropriate procedures to recognize the “statistical significance” of trends in data series arising from stochastic processes. This paper introduces a parametric methodology, which exploits a measure based on the Akaike Information Criterion (AICΔ), and a Rescaled version of the Generalized Extreme Value distribution, in which a linear deterministic trend in the position parameter is accounted for. A Monte Carlo experiment was set up with the generation of nonstationary synthetic series characterized by different sample lengths and covering a wide range of the shape and scale parameters. The performances of statistical tests based on the parametric AICΔ and the non-parametric Mann-Kendall measures were evaluated and compared with reference to observed ranges of annual maxima of precipitation, peak flow, and wind speed. Results allow for sensitivity analysis of the test power and show a strong dependence on the trend coefficient and the L-Coefficient of Variation of the parent distribution from the upper-bounded to the heavy-tailed special cases. An analysis of the sample variability of the position parameter is also presented, based on the same generation sets.

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