Statistical Issues in the Analysis of Neuronal Data

2005 ◽  
Vol 94 (1) ◽  
pp. 8-25 ◽  
Author(s):  
Robert E. Kass ◽  
Valérie Ventura ◽  
Emery N. Brown
Keyword(s):  
Firing Rate ◽  
Recent Work ◽  
Neuronal Response ◽  
Receptive Fields ◽  
Population Coding ◽  
Time Varying ◽  
New Methods ◽  
Scientific Inference ◽  
Statistical Issues ◽  
Poisson Data

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 well-established 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.

Statistical Assessment of Time-Varying Dependency Between Two Neurons

2005 ◽  
Vol 94 (4) ◽  
pp. 2940-2947 ◽  
Author(s):  
Valérie Ventura ◽  
Can Cai ◽  
Robert E. Kass
Keyword(s):  
Firing Rate ◽  
Statistical Significance ◽  
Companion Paper ◽  
Significance Test ◽  
Spike Timing ◽  
Correct Rejection ◽  
Time Varying ◽  
Adaptive Smoothing ◽  
Correlated Activity ◽  
Poisson Data

The joint peristimulus time histogram (JPSTH) provides a visual representation of the dynamics of correlated activity for a pair of neurons. There are many ways to adjust the JPSTH for the time-varying firing-rate modulation of each neuron, and then to define a suitable measure of time-varying correlated activity. Our approach is to introduce a statistical model for the time-varying joint spiking activity so that the joint firing rate can be estimated more efficiently. We have applied an adaptive smoothing method, which has been shown to be effective in capturing sudden changes in firing rate, to the ratio of joint firing probability to the probability of firing predicted by independence. A bootstrap procedure, applicable to both Poisson and non-Poisson data, was used to define a statistical significance test of whether a large ratio could be attributable to chance alone. A numerical simulation showed that the bootstrap-based significance test has very nearly the correct rejection probability, and can have markedly better power to detect departures from independence than does an approach based on testing contiguous bins in the JPSTH. In a companion paper, we show how this formulation can accommodate latency and time-varying excitability effects, which can confound spike timing effects.

scholarly journals Necessary Conditions for Reliable Propagation of Slowly Time-Varying Firing Rate

2020 ◽  
Vol 14 ◽  
Author(s):  
Navid Hasanzadeh ◽  
Mohammadreza Rezaei ◽  
Sayan Faraz ◽  
Milos R. Popovic ◽  
Milad Lankarany
Keyword(s):  
Firing Rate ◽  
Necessary Conditions ◽  
Time Varying

LES NEURONES DE LA FORMATION RÉTICULAIRE PONTO-BULBAIRE ET LA STIMULATION TRIGÉMINALE

1962 ◽  
Vol 40 (1) ◽  
pp. 261-271
Author(s):  
Guy Lamarche ◽  
J.-M. Langlois
Keyword(s):  
Reticular Formation ◽  
Trigeminal Nerve ◽  
Neuronal Response ◽  
Receptive Fields ◽  
Central Zone ◽  
Painful Stimulus ◽  
Inhibitory Zone ◽  
Sensory Afferents ◽  
Reticular Neurons

A microphysiological study of 209 neurons of the bulbopontine reticular formation was carried out in 80 "encéphales isolés" cats. After physiological stimulations of the trigeminal nerve the following conclusions were arrived at: (1) A functional arrangement exists in the lower recticular formation. Clear differences were found between the medulla and pons. (2) The pontine reticular neurons receive mostly tactile impulses from very large receptive fields. (3) The bulbar neurons receive all modalities of the trigeminal nerve from usually limited and bilateral fields (except proprioception). Pain projects mainly in this part of the reticular core. A central zone of the medulla has all physiological types of cells and is coincidental with Magoun and Rhine's inhibitory zone. (4) There was no neuronal response typical of any sensation. (5) An increase in frequency of a response was obtained in various ways: by changing the origin of the stimulus, by-increasing the intensity of the stimulus or the area of stimulation, or by applying a painful stimulus when the cell also responded to touch. (6) It is suggested that the sensory afferents lose their specificity when they reach the reticular formation but that via this formation they serve to increase awareness and perception of sensation at higher level.

Spatial determinants of multisensory integration in cat superior colliculus neurons

1996 ◽  
Vol 75 (5) ◽  
pp. 1843-1857 ◽  
Author(s):  
M. A. Meredith ◽  
B. E. Stein
Keyword(s):  
Receptive Field ◽  
Superior Colliculus ◽  
Neuronal Response ◽  
Receptive Fields ◽  
Spatial Relationship ◽  
Physiological Role ◽  
Extracellular Recording ◽  
Average Proportion ◽  
Relationship Of ◽  
High Degree

1. Although a representation of multisensory space is contained in the superior colliculus, little is known about the spatial requirements of multisensory stimuli that influence the activity of neurons here. Critical to this problem is an assessment of the registry of the different receptive fields within individual multisensory neurons. The present study was initiated to determine how closely the receptive fields of individual multisensory neurons are aligned, the physiological role of that alignment, and the possible functional consequences of inducing receptive-field misalignment. 2. Individual multisensory neurons in the superior colliculus of anesthetized, paralyzed cats were studied with the use of standard extracellular recording techniques. The receptive fields of multisensory neurons were large, as reported previously, but exhibited a surprisingly high degree of spatial coincidence. The average proportion of receptive-field overlap was 86% for the population of visual-auditory neurons sampled. 3. Because of this high degree of intersensory receptive-field correspondence, combined-modality stimuli that were coincident in space tended to fall within the excitatory regions of the receptive fields involved. The result was a significantly enhanced neuronal response in 88% of the multisensory neurons studied. If stimuli were spatially disparate, so that one fell outside its receptive field, either a decreased response occurred (56%), or no intersensory effect was apparent (44%). 4. The normal alignment of the different receptive fields of a multisensory neuron could be disrupted by passively displacing the eyes, pinnae, or limbs/body. In no case was a shift in location or size observed in a neuron's other receptive field(s) to compensate for this displacement. The physiological result of receptive-field misalignment was predictable and based on the location of the stimuli relative to the new positions of their respective receptive fields. Now, for example, one component of a spatially coincident pair of stimuli might fall outside its receptive field and inhibit the other's effects. 5. These data underscore the dependence of multisensory integrative responses on the relationship of the different stimuli to their corresponding receptive fields rather than to the spatial relationship of the stimuli to one another. Apparently, the alignment of different receptive fields for individual multisensory neurons ensures that responses to combinations of stimuli derived from the same event are integrated to increase the salience of that event. Therefore the maintenance of receptive-field alignment is critical for the appropriate integration of converging sensory signals and, ultimately, elicitation of adaptive behaviors.

Activity of Primate Subgenual Cingulate Cortex Neurons Is Related to Sleep

2003 ◽  
Vol 90 (1) ◽  
pp. 134-142 ◽  
Author(s):  
Edmund T. Rolls ◽  
Kazuo Inoue ◽  
Andrew Browning
Keyword(s):  
Firing Rate ◽  
Rhesus Macaque ◽  
Neuronal Response ◽  
Visual Stimuli ◽  
Cingulate Cortex ◽  
Awake State ◽  
Cortex Area ◽  
Median Rate ◽  
Subgenual Cingulate ◽  
Resting Behavior

The most frequent type of neuronal response found in the subgenual cingulate cortex (area 25) of the rhesus macaque was a highly significant increase of firing rate when the monkey fell asleep (median rate = 1.6 spikes/s) compared with the awake state (median rate = 0.1 spikes/s). On average, the firing rate of the neurons when awake was 23% of that when the monkeys were asleep. Neurons were not found in this region with responses related to taste, olfactory, and visual stimuli including faces or related to movement. These results are relevant to understanding the function of this region in humans, in which it has been suggested that activation may be related to disengagement from tasks and to induced sadness, both of which we note lead to a more passive or resting behavior. A decrease in the activation of this area in humans has been observed during the recovery from depression, which we note leads to a more active state of behavior.

scholarly journals Optimal Short-Term Population Coding: When Fisher Information Fails

2002 ◽  
Vol 14 (10) ◽  
pp. 2317-2351 ◽  
Author(s):  
M. Bethge ◽  
D. Rotermund ◽  
K. Pawelzik
Keyword(s):  
Fisher Information ◽  
Dynamic Range ◽  
Mean Squared Error ◽  
Average Rate ◽  
Neuronal Response ◽  
Minimum Mean Square Error ◽  
Population Coding ◽  
Neuronal Firing ◽  
Tuning Curves ◽  
Efficient Coding

Efficient coding has been proposed as a first principle explaining neuronal response properties in the central nervous system. The shape of optimal codes, however, strongly depends on the natural limitations of the particular physical system. Here we investigate how optimal neuronal encoding strategies are influenced by the finite number of neurons N (place constraint), the limited decoding time window length T (time constraint), the maximum neuronal firing rate fmax (power constraint), and the maximal average rate fmax (energy constraint). While Fisher information provides a general lower bound for the mean squared error of unbiased signal reconstruction, its use to characterize the coding precision is limited. Analyzing simple examples, we illustrate some typical pitfalls and thereby show that Fisher information provides a valid measure for the precision of a code only if the dynamic range (fmin T, fmax T) is sufficiently large. In particular, we demonstrate that the optimal width of gaussian tuning curves depends on the available decoding time T. Within the broader class of unimodal tuning functions, it turns out that the shape of a Fisher-optimal coding scheme is not unique. We solve this ambiguity by taking the minimum mean square error into account, which leads to flat tuning curves. The tuning width, however, remains to be determined by energy constraints rather than by the principle of efficient coding.

scholarly journals GABAA receptors contribute more to rate than temporal coding in the IC of awake mice

2020 ◽  
Vol 123 (1) ◽  
pp. 134-148
Author(s):  
Boris Gourévitch ◽  
Elena J. Mahrt ◽  
Warren Bakay ◽  
Cameron Elde ◽  
Christine V. Portfors
Keyword(s):  
Firing Rate ◽  
Neuronal Response ◽  
Signal Transmission ◽  
Brain Structures ◽  
Temporal Coding ◽  
Model Organisms ◽  
Gabaergic Inhibition ◽  
Response Curves ◽  
Daily Lives ◽  
Complex Sounds

Speech is our most important form of communication, yet we have a poor understanding of how communication sounds are processed by the brain. Mice make great model organisms to study neural processing of communication sounds because of their rich repertoire of social vocalizations and because they have brain structures analogous to humans, such as the auditory midbrain nucleus inferior colliculus (IC). Although the combined roles of GABAergic and glycinergic inhibition on vocalization selectivity in the IC have been studied to a limited degree, the discrete contributions of GABAergic inhibition have only rarely been examined. In this study, we examined how GABAergic inhibition contributes to shaping responses to pure tones as well as selectivity to complex sounds in the IC of awake mice. In our set of long-latency neurons, we found that GABAergic inhibition extends the evoked firing rate range of IC neurons by lowering the baseline firing rate but maintaining the highest probability of firing rate. GABAergic inhibition also prevented IC neurons from bursting in a spontaneous state. Finally, we found that although GABAergic inhibition shaped the spectrotemporal response to vocalizations in a nonlinear fashion, it did not affect the neural code needed to discriminate vocalizations, based either on spiking patterns or on firing rate. Overall, our results emphasize that even if GABAergic inhibition generally decreases the firing rate, it does so while maintaining or extending the abilities of neurons in the IC to code the wide variety of sounds that mammals are exposed to in their daily lives. NEW & NOTEWORTHY GABAergic inhibition adds nonlinearity to neuronal response curves. This increases the neuronal range of evoked firing rate by reducing baseline firing. GABAergic inhibition prevents bursting responses from neurons in a spontaneous state, reducing noise in the temporal coding of the neuron. This could result in improved signal transmission to the cortex.

Interactive effects among several stimulus parameters on the responses of striate cortical complex cells

1991 ◽  
Vol 66 (2) ◽  
pp. 379-389 ◽  
Author(s):  
T. J. Gawne ◽  
B. J. Richmond ◽  
L. M. Optican
Keyword(s):  
Striate Cortex ◽  
Neuronal Response ◽  
Receptive Fields ◽  
Response Strength ◽  
Interactive Effects ◽  
Temporal Modulation ◽  
Complex Cells ◽  
Black And White ◽  
Interaction Terms ◽  
Stimulus Parameters

1. Although neurons within the visual system are often described in terms of their responses to particular patterns such as bars and edges, they are actually sensitive to many different stimulus features, such as the luminances making up the patterns and the duration of presentation. Many different combinations of stimulus parameters can result in the same neuronal response, raising the problem of how the nervous system can extract information about visual stimuli from such inherently ambiguous responses. It has been shown that complex cells transmit significant amounts of information in the temporal modulation of their responses, raising the possibility that different stimulus parameters are encoded in different aspects of the response. To find out how much information is actually available about individual stimulus parameters, we examined the interactions among three stimulus parameters in the temporally modulated responses of striate cortical complex cells. 2. Sixteen black and white patterns were presented to two awake monkeys at each of four luminance-combinations and five durations, giving a total of 320 unique stimuli. Complex cells were recorded in layers 2 and 3 of striate cortex, with the stimuli centered on the receptive fields as determined by mapping with black and white bars. 3. An analysis of variance (ANOVA) was applied to these data with the three stimulus parameters of pattern, the luminance-combinations, and duration as the independent variables. The ANOVA was repeated with the magnitude and three different aspects of the temporal modulation of the response as the dependent variables. For the 19 neurons studied, many of the interactions between the different stimulus parameters were statistically significant. For some response measures the interactions accounted for more than one-half of the total response variance. 4. We also analyzed the stimulus-response relationships with the use of information theoretical techniques. We defined input codes on the basis of each stimulus parameter alone, as well as their combinations, and output codes on the basis of response strength, and on three measures of temporal modulation, also taken individually and together. Transmitted information was greatest when the response of a neuron was interpreted as a temporally modulated message about combinations of all three stimulus parameters. The interaction terms of the ANOVA suggest that the response of a complex cell can only be interpreted as a message about combinations of all three stimulus parameters.(ABSTRACT TRUNCATED AT 400 WORDS)

Linear integration of convergent visual inputs in an oculomotor reflex pathway

1984 ◽  
Vol 52 (6) ◽  
pp. 1213-1225 ◽  
Author(s):  
R. M. Glantz ◽  
H. B. Nudelman ◽  
B. Waldrop
Keyword(s):  
Motor Neuron ◽  
Firing Rate ◽  
Motor Neurons ◽  
Receptive Fields ◽  
Polarized Light ◽  
Stray Light ◽  
Differential Sensitivity ◽  
Functional Connections ◽  
Cross Correlation Analysis ◽  
Oculomotor Neurons

The functional connectivity between identified visual interneurons [sustaining fibers (SF)] and oculomotor neurons was assessed by simultaneous recording and cross-correlation analysis. A small group of SFs exhibit excitatory functional connections to an identified tonic oculomotor neuron. The excitatory interactions are found exclusively between SFs and oculomotor neurons with similar and/or overlapping excitatory receptive fields. A second group of SFs exhibit inhibitory connections to motor neurons. The excitatory receptive fields of these SFs correspond to the inhibitory receptive fields of the motor neurons. The collective action of the SFs is sufficient to produce all of the steady-state visual behavior of the motor neurons including the increment in firing rate elicited by illumination, unique features of the motor neuron receptive field, and differential sensitivity to blue light and polarized light. Pairs of SFs that converge on the same motor neuron sum their effects linearly. Thus the joint interaction of two SFs on a motor neuron is equal to the sum of the two postsynaptic effects taken separately. Coactivation of excitatory and inhibitory SF inputs to a motor neuron results in a partial cancellation of their postsynaptic effects on the motor neuron's firing rate. The antagonistic interactions protect the system from perturbations by stray light, visual adaptation, and variations in the central excited state. The ensemble information code, at the SF level of the optomotor pathway, is a set of differentially weighted mean firing rates. The weightings reflect differences in the strengths of the several SF-to- motor neuron interactions. One consequence of these differences is a selective weighting of the effects of illumination (in different regions of visual space) on the compensatory eye reflex.

Multisensory Bayesian Inference Depends on Synapse Maturation during Training: Theoretical Analysis and Neural Modeling Implementation

2017 ◽  
Vol 29 (3) ◽  
pp. 735-782 ◽  
Author(s):  
Mauro Ursino ◽  
Cristiano Cuppini ◽  
Elisa Magosso
Keyword(s):  
Bayesian Inference ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimate ◽  
Experimental Studies ◽  
Receptive Fields ◽  
Learning Rule ◽  
Population Coding ◽  
Audiovisual Integration ◽  
Likelihood Estimate ◽  
Bayesian Estimate

Recent theoretical and experimental studies suggest that in multisensory conditions, the brain performs a near-optimal Bayesian estimate of external events, giving more weight to the more reliable stimuli. However, the neural mechanisms responsible for this behavior, and its progressive maturation in a multisensory environment, are still insufficiently understood. The aim of this letter is to analyze this problem with a neural network model of audiovisual integration, based on probabilistic population coding—the idea that a population of neurons can encode probability functions to perform Bayesian inference. The model consists of two chains of unisensory neurons (auditory and visual) topologically organized. They receive the corresponding input through a plastic receptive field and reciprocally exchange plastic cross-modal synapses, which encode the spatial co-occurrence of visual-auditory inputs. A third chain of multisensory neurons performs a simple sum of auditory and visual excitations. The work includes a theoretical part and a computer simulation study. We show how a simple rule for synapse learning (consisting of Hebbian reinforcement and a decay term) can be used during training to shrink the receptive fields and encode the unisensory likelihood functions. Hence, after training, each unisensory area realizes a maximum likelihood estimate of stimulus position (auditory or visual). In cross-modal conditions, the same learning rule can encode information on prior probability into the cross-modal synapses. Computer simulations confirm the theoretical results and show that the proposed network can realize a maximum likelihood estimate of auditory (or visual) positions in unimodal conditions and a Bayesian estimate, with moderate deviations from optimality, in cross-modal conditions. Furthermore, the model explains the ventriloquism illusion and, looking at the activity in the multimodal neurons, explains the automatic reweighting of auditory and visual inputs on a trial-by-trial basis, according to the reliability of the individual cues.

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