scholarly journals The problem of perfect predictors in statistical spike train models

2020 ◽  
Author(s):  
Sahand Farhoodi ◽  
Uri Eden
Keyword(s):  
Spike Train ◽  
Generalized Linear Models ◽  
Statistical Models ◽  
Linear Models ◽  
Neural Systems ◽  
Advantages And Disadvantages ◽  
Rat Somatosensory Cortex ◽  
Spike Train Data ◽  
Incomplete Sampling ◽  
Single Predictor

Generalized Linear Models (GLMs) have been used extensively in statistical models of spike train data. However, the IRLS algorithm, which is often used to fit such models, can fail to converge in situations where response and non-response can be separated by a single predictor or a linear combination of multiple predictors. Such situations are likely to arise in many neural systems due to properties such as refractoriness and incomplete sampling of the signals that influence spiking. In this paper, we describe multiple classes of approaches to address this problem: Standard IRLS with a fixed iteration limit, computing the maximum likelihood solution in the limit, Bayesian estimation, regularization, change of basis, and modifying the search parameters. We demonstrate a specific application of each of these methods to spiking data from rat somatosensory cortex and discuss the advantages and disadvantages of each. We also provide an example of a roadmap for selecting a method based on the problem’s particular analysis issues and scientific goals.

Capturing Spike Variability in Noisy Izhikevich Neurons Using Point Process Generalized Linear Models

2018 ◽  
Vol 30 (1) ◽  
pp. 125-148 ◽  
Author(s):  
Jacob Østergaard ◽  
Mark A. Kramer ◽  
Uri T. Eden
Keyword(s):  
Spike Train ◽  
Goodness Of Fit ◽  
Linear Models ◽  
Spike Trains ◽  
Noisy Input ◽  
Statistical Sense ◽  
Active Research ◽  
Spike Train Data ◽  
Random Part ◽  
Different Levels

To understand neural activity, two broad categories of models exist: statistical and dynamical. While statistical models possess rigorous methods for parameter estimation and goodness-of-fit assessment, dynamical models provide mechanistic insight. In general, these two categories of models are separately applied; understanding the relationships between these modeling approaches remains an area of active research. In this letter, we examine this relationship using simulation. To do so, we first generate spike train data from a well-known dynamical model, the Izhikevich neuron, with a noisy input current. We then fit these spike train data with a statistical model (a generalized linear model, GLM, with multiplicative influences of past spiking). For different levels of noise, we show how the GLM captures both the deterministic features of the Izhikevich neuron and the variability driven by the noise. We conclude that the GLM captures essential features of the simulated spike trains, but for near-deterministic spike trains, goodness-of-fit analyses reveal that the model does not fit very well in a statistical sense; the essential random part of the GLM is not captured.

Annoyance from Multiple Transportation Noise: Statistical Models and Outlier Detection

2004 ◽  
Vol 43 (05) ◽  
pp. 510-515 ◽  
Author(s):  
C. Schürmann ◽  
B. Griefahn ◽  
S. Kuhnt
Keyword(s):  
Outlier Detection ◽  
Generalized Linear Models ◽  
Statistical Models ◽  
Linear Models ◽  
Good Choice ◽  
Detection Methods ◽  
Noise Levels ◽  
Transportation Noise ◽  
Link Functions ◽  
Exposure Response

Summary Objective: Statistical models for the annoyance from multiple transportation noise are needed to understand and predict the annoyance resulting from specific noise exposures. Methods: Models from the class of generalized linear models are suggested and discussed. Observations which are not well explained by the considered model are regarded as outliers. Outlier detection methods are applied to the data modelled by robust estimates using different link functions. Results: The discussed methods are applied to data from a laboratory experiment using generalized linear models. While considering outliers, a generalized linear model with a complementary log-log link is found to be a good choice in modelling the exposure-response relationship between noise levels and annoyance.

Neural Coding: Higher-Order Temporal Patterns in the Neurostatistics of Cell Assemblies

2000 ◽  
Vol 12 (11) ◽  
pp. 2621-2653 ◽  
Author(s):  
Laura Martignon ◽  
Gustavo Deco ◽  
Kathryn Laskey ◽  
Mathew Diamond ◽  
Winrich Freiwald ◽  
...  
Keyword(s):  
Experimental Data ◽  
Spike Train ◽  
Neural Coding ◽  
Linear Models ◽  
Temporal Patterns ◽  
Higher Order ◽  
Neural Activation ◽  
Spike Train Data ◽  
Behaving Monkeys ◽  
Log Linear

Recent advances in the technology of multiunit recordings make it possible to test Hebb's hypothesis that neurons do not function in isolation but are organized in assemblies. This has created the need for statistical approaches to detecting the presence of spatiotemporal patterns of more than two neurons in neuron spike train data. We mention three possible measures for the presence of higher-order patterns of neural activation—coefficients of log-linear models, connected cumulants, and redundancies—and present arguments in favor of the coefficients of log-linear models. We present test statistics for detecting the presence of higher-order interactions in spike train data by parameterizing these interactions in terms of coefficients of log-linear models. We also present a Bayesian approach for inferring the existence or absence of interactions and estimating their strength. The two methods, the frequentist and the Bayesian one, are shown to be consistent in the sense that interactions that are detected by either method also tend to be detected by the other. A heuristic for the analysis of temporal patterns is also proposed. Finally, a Bayesian test is presented that establishes stochastic differences between recorded segments of data. The methods are applied to experimental data and synthetic data drawn from our statistical models. Our experimental data are drawn from multiunit recordings in the prefrontal cortex of behaving monkeys, the somatosensory cortex of anesthetized rats, and multiunit recordings in the visual cortex of behaving monkeys.

scholarly journals Predictive Statistical Representations of Observed and Simulated Rainfall Using Generalized Linear Models

2019 ◽  
Vol 32 (11) ◽  
pp. 3409-3427
Author(s):  
Junho Yang ◽  
Mikyoung Jun ◽  
Courtney Schumacher ◽  
R. Saravanan
Keyword(s):  
Logistic Regression ◽  
Spatial Patterns ◽  
Generalized Linear Models ◽  
Statistical Models ◽  
Large Scale ◽  
Linear Models ◽  
Probability Distributions ◽  
Environmental Parameters ◽  
Radar Observations ◽  
Satellite Radar

Abstract This study explores the feasibility of predicting subdaily variations and the climatological spatial patterns of rain in the tropical Pacific from atmospheric profiles using a set of generalized linear models: logistic regression for rain occurrence and gamma regression for rain amount. The prediction is separated into different rain types from TRMM satellite radar observations (stratiform, deep convective, and shallow convective) and CAM5 simulations (large-scale and convective). Environmental variables from MERRA-2 and CAM5 are used as predictors for TRMM and CAM5 rainfall, respectively. The statistical models are trained using environmental fields at 0000 UTC and rainfall from 0000 to 0600 UTC during 2003. The results are used to predict 2004 rain occurrence and rate for MERRA-2/TRMM and CAM5 separately. The first EOF profile of humidity and the second EOF profile of temperature contribute most to the prediction for both statistical models in each case. The logistic regression generally performs well for all rain types, but does better in the east Pacific compared to the west Pacific. The gamma regression produces reasonable geographical rain amount distributions but rain rate probability distributions are not predicted as well, suggesting the need for a different, higher-order model to predict rain rates. The results of this study suggest that statistical models applied to TRMM radar observations and MERRA-2 environmental parameters can predict the spatial patterns and amplitudes of tropical rainfall in the time-averaged sense. Comparing the observationally trained models to models that are trained using CAM5 simulations points to possible deficiencies in the convection parameterization used in CAM5.

Effect of Different Dentifrices, Bleaching with 35% Hydrogen Peroxide, and Red Wine on Surface Color and Roughness of Bovine Enamel

2020 ◽  
Vol 02 ◽  
Author(s):  
RM Garcia ◽  
WF Vieira-Junior ◽  
JD Theobaldo ◽  
NIP Pini ◽  
GM Ambrosano ◽  
...  
Keyword(s):  
Hydrogen Peroxide ◽  
Generalized Linear Models ◽  
Repeated Measures ◽  
Red Wine ◽  
Linear Models ◽  
Artificial Saliva ◽  
Surface Color ◽  
Dental Bleaching ◽  
Surface Alteration ◽  
Bovine Enamel

Objective: To evaluate color and roughness of bovine enamel exposed to dentifrices, dental bleaching with 35% hydrogen peroxide (HP), and erosion/staining by red wine. Methods: Bovine enamel blocks were exposed to: artificial saliva (control), Oral-B Pro-Health (stannous fluoride with sodium fluoride, SF), Sensodyne Repair & Protect (bioactive glass, BG), Colgate Pro-Relief (arginine and calcium carbonate, AR), or Chitodent (chitosan, CHI). After toothpaste exposure, half (n=12) of the samples were bleached (35% HP), and the other half were not (n=12). The color (CIE L*a* b*, ΔE), surface roughness (Ra), and scanning electron microscopy were evaluated. Color and roughness were assessed at baseline, post-dentifrice and/or -dental bleaching, and after red wine. The data were subjected to analysis of variance (ANOVA) (ΔE) for repeated measures (Ra), followed by Tukey ́s test. The L*, a*, and b* values were analyzed by generalized linear models (a=0.05). Results: The HP promoted an increase in Ra values; however, the SF, BG, and AR did not enable this alteration. After red wine, all groups apart from SF (unbleached) showed increases in Ra values; SF and AR promoted decreases in L* values; AR demonstrated higher ΔE values, differing from the control; and CHI decreased the L* variation in the unbleached group. Conclusion: Dentifrices did not interfere with bleaching efficacy of 35% HP. However, dentifrices acted as a preventive agent against surface alteration from dental bleaching (BG, SF, and AR) or red wine (SF). Dentifrices can decrease (CHI) or increase (AR and SF) staining by red wine.

Economic burden of readmission due to postoperative cerebrospinal fluid leak in Chinese patients

2020 ◽  
Vol 9 (16) ◽  
pp. 1105-1115
Author(s):  
Shuqing Wu ◽  
Xin Cui ◽  
Shaoyu Zhang ◽  
Wenqi Tian ◽  
Jiazhen Liu ◽  
...  
Keyword(s):  
Cerebrospinal Fluid ◽  
Generalized Linear Models ◽  
Economic Burden ◽  
Linear Models ◽  
Chinese Patients ◽  
Cerebrospinal Fluid Leakage ◽  
Index Hospitalization ◽  
Real World Data ◽  
Factors Associated ◽  
Hospitalization Cost

Aim: This real-world data study investigated the economic burden and associated factors of readmissions for cerebrospinal fluid leakage (CSFL) post-cranial, transsphenoidal, or spinal index surgeries. Methods: Costs of CSFL readmissions and index hospitalizations during 2014–2018 were collected. Readmission cost was measured as absolute cost and as percentage of index hospitalization cost. Factors associated with readmission cost were explored using generalized linear models. Results: Readmission cost averaged US$2407–6106, 35–94% of index hospitalization cost. Pharmacy costs were the leading contributor. Generalized linear models showed transsphenoidal index surgery and surgical treatment for CSFL were associated with higher readmission costs. Conclusion: CSFL readmissions are a significant economic burden in China. Factors associated with higher readmission cost should be monitored.

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