scholarly journals Optimal Binning of Peri-Event Time Histograms Using Akaike Information Criterion

2020 ◽  
Author(s):  
Ali Ghazizadeh ◽  
Frederic Ambroggi
Keyword(s):  
Firing Rate ◽  
Akaike Information Criterion ◽  
Mean Squared Error ◽  
Temporal Dynamics ◽  
Real Data ◽  
Information Criterion ◽  
Neuronal Firing ◽  
Computationally Efficient ◽  
Event Time ◽  
Squared Error

AbstractPeri-event time histograms (PETH) are widely used to study correlations between experimental events and neuronal firing. The accuracy of firing rate estimate using a PETH depends on the choice of binsize. We show that the optimal binsize for a PETH depends on factors such as the number of trials and the temporal dynamics of the firing rate. These factors argue against the use of a one-size-fits-all binsize when making PETHs for an inhomogeneous population of neurons. Here we propose a binsize selection method by adapting the Akaike Information Criterion (AIC). Simulations show that optimal binsizes estimated by AIC closely match the optimal binsizes using mean squared error (MSE). Furthermore, using real data, we find that optimal binning improves detection of responses and their dynamics. Together our analysis strongly supports optimal binning of PETHs and proposes a computationally efficient method for this optimization based on AIC approach to model selection.

scholarly journals A $C_p$ criterion for semiparametric causal inference

Biometrika ◽  
2017 ◽  
Vol 104 (4) ◽  
pp. 845-861 ◽  
Author(s):  
Takamichi Baba ◽  
Takayuki Kanemori ◽  
Yoshiyuki Ninomiya
Keyword(s):  
Causal Inference ◽  
Mean Squared Error ◽  
Real Data ◽  
Information Criterion ◽  
Potential Outcome ◽  
Squared Error ◽  
Doubly Robust Estimation ◽  
Inverse Probability Weighted ◽  
Doubly Robust ◽  
Inverse Probability Weighted Estimation

Summary For marginal structural models, which play an important role in causal inference, we consider a model selection problem within a semiparametric framework using inverse-probability-weighted estimation or doubly robust estimation. In this framework, the modelling target is a potential outcome that may be missing, so there is no classical information criterion. We define a mean squared error for treating the potential outcome and derive an asymptotic unbiased estimator as a $C_{p}$ criterion using an ignorable treatment assignment condition. Simulation shows that the proposed criterion outperforms a conventional one by providing smaller squared errors and higher frequencies of selecting the true model in all the settings considered. Moreover, in a real-data analysis we found a clear difference between the two criteria.

scholarly journals Modelling the growth of rearing cattle

2021 ◽  
Author(s):  
Hanna Unterauer ◽  
Norbert Brunner ◽  
Manfred Kühleitner
Keyword(s):  
Goodness Of Fit ◽  
Linear Growth ◽  
Mean Squared Error ◽  
Least Squares Method ◽  
Information Criterion ◽  
Squared Error ◽  
Akaike Criterion ◽  
Linear Growth Model ◽  
Bp Model ◽  
Scientific Growth

Scientific growth literature often uses the models of Brody, Gompertz, Verhulst, and von Bertalanffy. The versatile five-parameter Bertalanffy-Pütter (BP) model generalizes them. Using the least-squares method, we fitted the BP model to mass-at-age data of 161 calves, cows, bulls, and oxen of cattle breeds that are common in Austria and Southern Germany. We used three measures to assess the goodness of fit: R-squared, normalized root-mean squared error, and the Akaike information criterion together with a correction for sample size. Although the BP model improved the fit of the linear growth model considerably in terms of R-squared, the better fit did not, in general, justify the use of its additional parameters, because most of the data had a non-sigmoidal character. In terms of the Akaike criterion, we could identify only a small core of data (15%) where sigmoidal models were indispensable.    

scholarly journals On the Use of Entropy to Improve Model Selection Criteria

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 394 ◽  
Author(s):  
Andrea Murari ◽  
Emmanuele Peluso ◽  
Francesco Cianfrani ◽  
Pasquale Gaudio ◽  
Michele Lungaroni
Keyword(s):  
Model Selection ◽  
Shannon Entropy ◽  
Selection Criteria ◽  
Mean Squared Error ◽  
Geodesic Distance ◽  
Information Criterion ◽  
Residual Distribution ◽  
Model Selection Criteria ◽  
Synthetic Indicators ◽  
Squared Error

The most widely used forms of model selection criteria, the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC), are expressed in terms of synthetic indicators of the residual distribution: the variance and the mean-squared error of the residuals respectively. In many applications in science, the noise affecting the data can be expected to have a Gaussian distribution. Therefore, at the same level of variance and mean-squared error, models, whose residuals are more uniformly distributed, should be favoured. The degree of uniformity of the residuals can be quantified by the Shannon entropy. Including the Shannon entropy in the BIC and AIC expressions improves significantly these criteria. The better performances have been demonstrated empirically with a series of simulations for various classes of functions and for different levels and statistics of the noise. In presence of outliers, a better treatment of the errors, using the Geodesic Distance, has proved essential.

Acoustic Echo Cancellation using Computationally Efficient Adaptive Algorithm Techniques

2016 ◽  
Vol 1 (2) ◽  
pp. 57-62
Author(s):  
Mastan Sharif Shaik ◽  
K. Satya Prasad ◽  
Rafi Ahamed Shaik ◽  
D. Venkata Rao
Keyword(s):  
Adaptive Filters ◽  
Mean Squared Error ◽  
Echo Cancellation ◽  
Lms Algorithm ◽  
Acoustic Echo Cancellation ◽  
Computationally Efficient ◽  
Primary Input ◽  
Squared Error ◽  
Acoustic Echo ◽  
The Mean

Several sign based LMS adaptive filters, which are computationally free having multiplier free weight update loops, are proposed for acoustic echo cancellation. The adaptive filters essentially minimizes the mean- squared error between a primary input, which is the echo, and a reference input, which is either echo that is correlated in some way with the echo in the primary input. The results show that the performance of the signed regressor. LMS algorithm is superior than conventional LMS algorithm, the performance of signed LMS and sign- sign LMS based realizations are comparable to that of the LMS based filtering techniques in terms of Average Attenuation and computational complexity.

Using Dense SNPs and Large Families to Reduce Sequencing Costs

2016 ◽  
Vol 2 (11) ◽  
Author(s):  
William Stewart
Keyword(s):  
Confidence Intervals ◽  
Language Impairment ◽  
Specific Language Impairment ◽  
Mean Squared Error ◽  
Real Data ◽  
Gene Location ◽  
Pedigree Structure ◽  
Squared Error ◽  
Snp Data ◽  
Large Families

<p>For modern linkage studies involving many small families, Stewart et al. (2009)[1] introduced an efficient estimator of disease gene location (denoted ) that averages location estimates from random subsamples of the dense SNP data. Their estimator has lower mean squared error than competing estimators and yields narrower confidence intervals (CIs) as well. However, when the number of families is small and the pedigree structure is large (possibly extended), the computational feasibility and statistical properties of  are not known. We use simulation and real data to show that (1) for this extremely important but often overlooked study design, CIs based on  are narrower than CIs based on a single subsample, and (2) the reduction in CI length is proportional to the square root of the expected Monte Carlo error. As a proof of principle, we applied  to the dense SNP data of four large, extended, specific language impairment (SLI) pedigrees, and reduced the single subsample CI by 18%. In summary, confidence intervals based on  should minimize re-sequencing costs beneath linkage peaks, and reduce the number of candidate genes to investigate.</p>

scholarly journals Joint influence of measurement errors and randomized response technique on mean estimation under stratified double sampling

2021 ◽  
Vol 5 (1) ◽  
pp. 192-199
Author(s):  
Ronald Onyango ◽  
◽  
Brian Oduor ◽  
Francis Odundo ◽  
◽  
...  
Keyword(s):  
Measurement Errors ◽  
Mean Squared Error ◽  
Numerical Study ◽  
Real Data ◽  
Auxiliary Variable ◽  
Randomized Response Technique ◽  
Randomized Response ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Joint Influence

The present study proposes a generalized mean estimator for a sensitive variable using a non-sensitive auxiliary variable in the presence of measurement errors based on the Randomized Response Technique (RRT). Expressions for the bias and mean squared error for the proposed estimator are correctly derived up to the first order of approximation. Furthermore, the optimum conditions and minimum mean squared error for the proposed estimator are determined. The efficiency of the proposed estimator is studied both theoretically and numerically using simulated and real data sets. The numerical study reveals that the use of the Randomized Response Technique (RRT) in a survey contaminated with measurement errors increases the variances and mean squared errors of estimators of the finite population mean.

scholarly journals Acoustic Echo Cancellation using Computationally Efficient Adaptive Algorithm Techniques

2016 ◽  
Vol 1 (2) ◽  
pp. 57-62
Author(s):  
Mastan Sharif Shaik ◽  
K. Satya Prasad ◽  
Rafi Ahamed Shaik ◽  
D. Venkata Rao
Keyword(s):  
Adaptive Filters ◽  
Mean Squared Error ◽  
Echo Cancellation ◽  
Lms Algorithm ◽  
Acoustic Echo Cancellation ◽  
Computationally Efficient ◽  
Primary Input ◽  
Squared Error ◽  
Acoustic Echo ◽  
The Mean

Several sign based LMS adaptive filters, which are computationally free having multiplier free weight update loops, are proposed for acoustic echo cancellation. The adaptive filters essentially minimizes the mean-squared error between a primary input, which is the echo, and a reference input, which is either echo that is correlated in some way with the echo in the primary input. The results show that the performance of the signed regressor. LMS algorithm is superior than conventional LMS algorithm, the performance of signed LMS and sign-sign LMS based realizations are comparable to that of the LMS based filtering techniques in terms of Average Attenuation and computational complexity.

scholarly journals The change in estimate method for selecting confounders: A simulation study

2021 ◽  
pp. 096228022110342
Author(s):  
Denis Talbot ◽  
Awa Diop ◽  
Mathilde Lavigne-Robichaud ◽  
Chantal Brisson
Keyword(s):  
Confidence Intervals ◽  
Simulation Study ◽  
Mean Squared Error ◽  
Real Data ◽  
Significance Test ◽  
Simulation Studies ◽  
Squared Error ◽  
Estimate Method ◽  
The Mean ◽  
Work And Health

Background The change in estimate is a popular approach for selecting confounders in epidemiology. It is recommended in epidemiologic textbooks and articles over significance test of coefficients, but concerns have been raised concerning its validity. Few simulation studies have been conducted to investigate its performance. Methods An extensive simulation study was realized to compare different implementations of the change in estimate method. The implementations were also compared when estimating the association of body mass index with diastolic blood pressure in the PROspective Québec Study on Work and Health. Results All methods were susceptible to introduce important bias and to produce confidence intervals that included the true effect much less often than expected in at least some scenarios. Overall mixed results were obtained regarding the accuracy of estimators, as measured by the mean squared error. No implementation adequately differentiated confounders from non-confounders. In the real data analysis, none of the implementation decreased the estimated standard error. Conclusion Based on these results, it is questionable whether change in estimate methods are beneficial in general, considering their low ability to improve the precision of estimates without introducing bias and inability to yield valid confidence intervals or to identify true confounders.

scholarly journals Upgrading Model Selection Criteria with Goodness of Fit Tests for Practical Applications

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 447
Author(s):  
Riccardo Rossi ◽  
Andrea Murari ◽  
Pasquale Gaudio ◽  
Michela Gelfusa
Keyword(s):  
Model Selection ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Information Criterion ◽  
Original Form ◽  
Residual Distribution ◽  
Practical Applications ◽  
Goodness Of Fit Tests ◽  
Squared Error ◽  
The Mean

The Bayesian information criterion (BIC), the Akaike information criterion (AIC), and some other indicators derived from them are widely used for model selection. In their original form, they contain the likelihood of the data given the models. Unfortunately, in many applications, it is practically impossible to calculate the likelihood, and, therefore, the criteria have been reformulated in terms of descriptive statistics of the residual distribution: the variance and the mean-squared error of the residuals. These alternative versions are strictly valid only in the presence of additive noise of Gaussian distribution, not a completely satisfactory assumption in many applications in science and engineering. Moreover, the variance and the mean-squared error are quite crude statistics of the residual distributions. More sophisticated statistical indicators, capable of better quantifying how close the residual distribution is to the noise, can be profitably used. In particular, specific goodness of fit tests have been included in the expressions of the traditional criteria and have proved to be very effective in improving their discriminating capability. These improved performances have been demonstrated with a systematic series of simulations using synthetic data for various classes of functions and different noise statistics.

scholarly journals Wind energy potential assessment based on wind speed, its direction and power data

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Zhiming Wang ◽  
Weimin Liu
Keyword(s):  
Wind Speed ◽  
Wind Energy ◽  
Wind Direction ◽  
Mean Squared Error ◽  
Mixture Distribution ◽  
Information Criterion ◽  
Energy Potential ◽  
Root Mean Squared Error ◽  
Squared Error ◽  
Wind Energy Potential

AbstractBased on wind speed, direction and power data, an assessment method of wind energy potential using finite mixture statistical distributions is proposed. Considering the correlation existing and the effect between wind speed and direction, the angular-linear modeling approach is adopted to construct the joint probability density function of wind speed and direction. For modeling the distribution of wind power density and estimating model parameters of null or low wind speed and multimodal wind speed data, based on expectation–maximization algorithm, a two-component three-parameter Weibull mixture distribution is chosen as wind speed model, and a von Mises mixture distribution with nine components and six components are selected as the models of wind direction and the correlation circular variable between wind speed and direction, respectively. A comprehensive technique of model selection, which includes Akaike information criterion, Bayesian information criterion, the coefficient of determination R2 and root mean squared error, is used to select the optimal model in all candidate models. The proposed method is applied to averaged 10-min field monitoring wind data and compared with the other estimation methods and judged by the values of R2 and root mean squared error, histogram plot and wind rose diagram. The results show that the proposed method is effective and the area under study is not suitable for wide wind turbine applications, and the estimated wind energy potential would be inaccuracy without considering the influence of wind direction.

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