scholarly journals Determination of Quantile Range of Optimal Hyperparameters Using Bayesian Estimation

2021 ◽  
Vol 47 (3) ◽  
pp. 988-998
Author(s):  
Ayoade I. Adewole ◽  
Olusoga A. Fasoranbaku
Keyword(s):  
Bayesian Estimation ◽  
Prior Distribution ◽  
Parameter Estimates ◽  
Distributed Data ◽  
Linear Regression Models ◽  
Absolute Deviation ◽  
Data Set ◽  
Empirical Bayesian ◽  
Bayesian Inferences ◽  
Bayesian Estimations

Bayesian estimations have the advantages of taking into account the uncertainty of all parameter estimates which allows virtually the use of vague priors. This study focused on determining the quantile range at which optimal hyperparameter of normally distributed data with vague information could be obtained in Bayesian estimation of linear regression models. A Monte Carlo simulation approach was used to generate a sample size of 200 data-set. Observation precisions and posterior precisions were estimated from the regression output to determine the posterior means estimate for each model to derive the new dependent variables. The variances were divided into 10 equal parts to obtain the hyperparameters of the prior distribution. Average absolute deviation for model selection was used to validate the adequacy of each model. The study revealed the optimal hyperparameters located at 5th and 7th deciles. The research simplified the process of selecting the hyperparameters of prior distribution from the data with vague information in empirical Bayesian inferences. Keywords: Optimal Hyperparameters; Quantile Ranges; Bayesian Estimation; Vague prior

scholarly journals Estimation of Parameters of Two Non-linear Regression Models Using Assumed Values: Reciprocal Power Regression Models

2020 ◽  
pp. 1-19
Author(s):  
Emmanuel O. Biu ◽  
Nduka Wonu
Keyword(s):  
Regression Models ◽  
Nonlinear Models ◽  
Research Work ◽  
Single Step ◽  
Careful Examination ◽  
Parameter Estimates ◽  
Linear Regression Models ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Non Linear

Fitting nonlinear models is not a single-step procedure but it involved a process that requires careful examination of each individual step. Depending on the objective and the application domain, different priorities are set when fitting nonlinear models; these include obtaining acceptable parameter estimates and a good model fit while meeting standard assumptions of statistical models. We propose steps in fitting nonlinear models in this research work. Two reciprocal power regression models were considered with a non-linear data set. Then, the following steps are considered (i) fit the models to the data collected using iterative steps, (ii) to develop a linear model to estimate the parameter β1 and β2 when the initial value (or growth rate β3) lies between -1.0 ≤ β3 ≤1.0 ); using the transform models of the reciprocal power regression model (iii) to find the “best” model between the two models using R2, AIC and BIC. The results show Model B is better than Model A, using the model selection criteria.

Simple Index to Assess the Calibration Quality of Safety Performance Functions Based on Multiple Goodness-of-Fit Metrics

2021 ◽  
pp. 036119812110088
Author(s):  
Raul E. Avelar ◽  
Karen Dixon ◽  
Boniphace Kutela ◽  
Sam Klump ◽  
Beth Wemple ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Synthetic Data ◽  
Calibration Procedure ◽  
Safety Performance ◽  
Absolute Deviation ◽  
Data Set ◽  
Safety Database ◽  
Simple Index ◽  
Safety Performance Functions

The calibration of safety performance functions (SPFs) is a mechanism included in the Highway Safety Manual (HSM) to adjust SPFs in the HSM for use in intended jurisdictions. Critically, the quality of the calibration procedure must be assessed before using the calibrated SPFs. Multiple resources to aid practitioners in calibrating SPFs have been developed in the years following the publication of the HSM 1st edition. Similarly, the literature suggests multiple ways to assess the goodness-of-fit (GOF) of a calibrated SPF to a data set from a given jurisdiction. This paper uses the calibration results of multiple intersection SPFs to a large Mississippi safety database to examine the relations between multiple GOF metrics. The goal is to develop a sensible single index that leverages the joint information from multiple GOF metrics to assess overall quality of calibration. A factor analysis applied to the calibration results revealed three underlying factors explaining 76% of the variability in the data. From these results, the authors developed an index and performed a sensitivity analysis. The key metrics were found to be, in descending order: the deviation of the cumulative residual (CURE) plot from the 95% confidence area, the mean absolute deviation, the modified R-squared, and the value of the calibration factor. This paper also presents comparisons between the index and alternative scoring strategies, as well as an effort to verify the results using synthetic data. The developed index is recommended to comprehensively assess the quality of the calibrated intersection SPFs.

Challenging the Link Between Early Childhood Television Exposure and Later Attention Problems: A Multiverse Approach

2021 ◽  
pp. 095679762097165
Author(s):  
Matthew T. McBee ◽  
Rebecca J. Brand ◽  
Wallace E. Dixon
Keyword(s):  
Early Childhood ◽  
Regression Models ◽  
Propensity Score Analysis ◽  
Harmful Effect ◽  
Attention Problems ◽  
Linear Regression Models ◽  
Data Set ◽  
Logistic Regression Models ◽  
Score Analysis ◽  
Television Exposure

In 2004, Christakis and colleagues published an article in which they claimed that early childhood television exposure causes later attention problems, a claim that continues to be frequently promoted by the popular media. Using the same National Longitudinal Survey of Youth 1979 data set ( N = 2,108), we conducted two multiverse analyses to examine whether the finding reported by Christakis and colleagues was robust to different analytic choices. We evaluated 848 models, including logistic regression models, linear regression models, and two forms of propensity-score analysis. If the claim were true, we would expect most of the justifiable analyses to produce significant results in the predicted direction. However, only 166 models (19.6%) yielded a statistically significant relationship, and most of these employed questionable analytic choices. We concluded that these data do not provide compelling evidence of a harmful effect of TV exposure on attention.

scholarly journals Bayesian and E-Bayesian Estimations of Bathtub-Shaped Distribution under Generalized Type-I Hybrid Censoring

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 934
Author(s):  
Yuxuan Zhang ◽  
Kaiwei Liu ◽  
Wenhao Gui
Keyword(s):  
Bayesian Method ◽  
Real Data ◽  
Loss Functions ◽  
Type I ◽  
Statistical Efficiency ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Bayesian Estimations ◽  
Generalized Type

For the purpose of improving the statistical efficiency of estimators in life-testing experiments, generalized Type-I hybrid censoring has lately been implemented by guaranteeing that experiments only terminate after a certain number of failures appear. With the wide applications of bathtub-shaped distribution in engineering areas and the recently introduced generalized Type-I hybrid censoring scheme, considering that there is no work coalescing this certain type of censoring model with a bathtub-shaped distribution, we consider the parameter inference under generalized Type-I hybrid censoring. First, estimations of the unknown scale parameter and the reliability function are obtained under the Bayesian method based on LINEX and squared error loss functions with a conjugate gamma prior. The comparison of estimations under the E-Bayesian method for different prior distributions and loss functions is analyzed. Additionally, Bayesian and E-Bayesian estimations with two unknown parameters are introduced. Furthermore, to verify the robustness of the estimations above, the Monte Carlo method is introduced for the simulation study. Finally, the application of the discussed inference in practice is illustrated by analyzing a real data set.

scholarly journals A Bayesian model for binary Markov chains

2004 ◽  
Vol 2004 (8) ◽  
pp. 421-429 ◽  
Author(s):  
Souad Assoudou ◽  
Belkheir Essebbar
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chains ◽  
Bayesian Estimation ◽  
Bayesian Model ◽  
Transition Probabilities ◽  
Simulated Data ◽  
Bayesian Estimator ◽  
Jeffreys Prior ◽  
Data Set

This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC) techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.

scholarly journals Coupled hydrogeophysical parameter estimation using a sequential Bayesian approach

2010 ◽  
Vol 14 (3) ◽  
pp. 545-556 ◽  
Author(s):  
J. Rings ◽  
J. A. Huisman ◽  
H. Vereecken
Keyword(s):  
Water Content ◽  
Particle Filtering ◽  
Field Data ◽  
Synthetic Data ◽  
Time Domain Reflectometry ◽  
Second Step ◽  
Parameter Estimates ◽  
Posterior Distributions ◽  
Data Set ◽  
Resistivity Tomography

Abstract. Coupled hydrogeophysical methods infer hydrological and petrophysical parameters directly from geophysical measurements. Widespread methods do not explicitly recognize uncertainty in parameter estimates. Therefore, we apply a sequential Bayesian framework that provides updates of state, parameters and their uncertainty whenever measurements become available. We have coupled a hydrological and an electrical resistivity tomography (ERT) forward code in a particle filtering framework. First, we analyze a synthetic data set of lysimeter infiltration monitored with ERT. In a second step, we apply the approach to field data measured during an infiltration event on a full-scale dike model. For the synthetic data, the water content distribution and the hydraulic conductivity are accurately estimated after a few time steps. For the field data, hydraulic parameters are successfully estimated from water content measurements made with spatial time domain reflectometry and ERT, and the development of their posterior distributions is shown.

scholarly journals Efficient Maximum-Likelihood Inference For The Isolation-With-Initial-Migration Model With Potentially Asymmetric Gene Flow

2016 ◽  
Author(s):  
Rui J. Costa ◽  
Hilde Wilkinson-Herbots
Keyword(s):  
Gene Flow ◽  
Maximum Likelihood ◽  
Dna Sequences ◽  
Computing Time ◽  
Likelihood Method ◽  
Ancestral Population ◽  
Parameter Estimates ◽  
Fast Method ◽  
Data Set ◽  
Im Model

AbstractThe isolation-with-migration (IM) model is commonly used to make inferences about gene flow during speciation, using polymorphism data. However, Becquet and Przeworski (2009) report that the parameter estimates obtained by fitting the IM model are very sensitive to the model's assumptions (including the assumption of constant gene flow until the present). This paper is concerned with the isolation-with-initial-migration (IIM) model of Wilkinson-Herbots (2012), which drops precisely this assumption. In the IIM model, one ancestral population divides into two descendant subpopulations, between which there is an initial period of gene flow and a subsequent period of isolation. We derive a very fast method of fitting an extended version of the IIM model, which also allows for asymmetric gene flow and unequal population sizes. This is a maximum-likelihood method, applicable to data on the number of segregating sites between pairs of DNA sequences from a large number of independent loci. In addition to obtaining parameter estimates, our method can also be used to distinguish between alternative models representing different evolutionary scenarios, by means of likelihood ratio tests. We illustrate the procedure on pairs of Drosophila sequences from approximately 30,000 loci. The computing time needed to fit the most complex version of the model to this data set is only a couple of minutes. The R code to fit the IIM model can be found in the supplementary files of this paper.

PREDICTION OF DAILY PHOTOVOLTAIC ENERGY PRODUCTION USING WEATHER DATA AND REGRESSION

2021 ◽  
pp. 1-20
Author(s):  
Hüseyin Sarper ◽  
Igor Melnykov ◽  
Lee Anne Martínez
Keyword(s):  
Energy Production ◽  
Weather Prediction ◽  
Model Construction ◽  
Weather Data ◽  
Good Prediction ◽  
Linear Regression Models ◽  
Data Set ◽  
Photovoltaic Energy ◽  
Pv Systems ◽  
Good Prediction Accuracy

Abstract This paper presents linear regression models to predict the daily energy production of three photovoltaic (PV) systems located in southeast Virginia. The prediction is based on daylight duration, sky index, the average relative humidity, and the presence of fog or mist. No other daily weather report components were statistically significant. The proposed method is easy to implement, and it can be used in conjunction with other advanced methods in estimating any given future day’s energy production if weather prediction is available. Data from 2013-2015 was used in the model construction. Model validation was performed using newer (2016, 2017, 2020, and 2021) data not used in the model construction. Results show good prediction accuracy for a simple methodology, free of system parameters, that can be utilized by ordinary photovoltaic energy users. The entire data set can be downloaded using the link provided.

Multilevel Zero-inflated Censored Beta Regression Modeling for Proportions and Rate Data with Extra-zeros

2019 ◽  
Author(s):  
Leili Tapak ◽  
Omid Hamidi ◽  
Majid Sadeghifar ◽  
Hassan Doosti ◽  
Ghobad Moradi
Keyword(s):  
Regression Model ◽  
Simulation Study ◽  
Real Data ◽  
P Value ◽  
Parameter Estimates ◽  
Beta Regression ◽  
Rate Data ◽  
Data Set ◽  
Proposed Model ◽  
Beta Regression Model

Abstract Objectives Zero-inflated proportion or rate data nested in clusters due to the sampling structure can be found in many disciplines. Sometimes, the rate response may not be observed for some study units because of some limitations (false negative) like failure in recording data and the zeros are observed instead of the actual value of the rate/proportions (low incidence). In this study, we proposed a multilevel zero-inflated censored Beta regression model that can address zero-inflation rate data with low incidence.Methods We assumed that the random effects are independent and normally distributed. The performance of the proposed approach was evaluated by application on a three level real data set and a simulation study. We applied the proposed model to analyze brucellosis diagnosis rate data and investigate the effects of climatic and geographical position. For comparison, we also applied the standard zero-inflated censored Beta regression model that does not account for correlation.Results Results showed the proposed model performed better than zero-inflated censored Beta based on AIC criterion. Height (p-value <0.0001), temperature (p-value <0.0001) and precipitation (p-value = 0.0006) significantly affected brucellosis rates. While, precipitation in ZICBETA model was not statistically significant (p-value =0.385). Simulation study also showed that the estimations obtained by maximum likelihood approach had reasonable in terms of mean square error.Conclusions The results showed that the proposed method can capture the correlations in the real data set and yields accurate parameter estimates.

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