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Supervised Machine Learning and Bayesian Regression Kriging with Application to COVID-19 Incidences in Sub-Saharan Africa
Safari Godfrey Lyece,
Samuel Mwalili,
Joseph Kyalo Mung’atu
Issue:
Volume 12, Issue 3, May 2023
Pages:
37-42
Received:
19 April 2023
Accepted:
15 May 2023
Published:
24 May 2023
Abstract: Since COVID-19 invasion of the World, human life has been affected greatly. Several studies have shown a positive correlation between COVID-19 infections and pre-existing conditions such as Diabetes, Cancer, Tuberculosis, and Hypertension. In this study, we would like to determine whether demographic variables have a contribution to the spread of COVID-19 infections. We will apply a machine language method to select the demographic variables which are impactful in the spread of COVID-19 cases in Sub-Saharan Africa. Then we shall determine the nature of COVID-19 cases patterns applying the K-Nearest Neighbor (KNN) in calculating the neighborhood weights between locations/countries. The weights would then be tested for significance to conclude whether the cases patterns are either random, sparsely or clustered. We would then perform simulations to estimate the social demographic/covariates/fixed effects parameters and the random effects parameters. The Bayesian Kriging would be applied to predict Covid-19 cases based on the estimated social demographical variables coefficients/parameters and the random effects parameters in unknown/new locations in Sub Saharan Africa with a known uncertainty. The results showed that Children aged (0-14) years living with HIV AIDS, Prevalence of HIV Total (percentage of population ages 15-49) and Access to electricity (as a percentage of the population) was estimated to contribute to the increase of COVID-19 cases. Prediction of the COVID-19 cases in unknown locations showed that most of the cases were predicted in the elevated locations/areas than in the lower/flatter locations. This could mean that high elevated areas are associated with lower temperatures which increases the spread of COVID-19 cases as opposed to lower/flatter areas which are associated with higher temperatures which reduces the spread of COVID-19 cases.
Abstract: Since COVID-19 invasion of the World, human life has been affected greatly. Several studies have shown a positive correlation between COVID-19 infections and pre-existing conditions such as Diabetes, Cancer, Tuberculosis, and Hypertension. In this study, we would like to determine whether demographic variables have a contribution to the spread of C...
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Bayesian Interval Estimation in a Non-Homogeneous Poisson Process with Delayed S-Shaped Intensity Function
Otieno Collins,
Orawo Luke Akong’o,
Matiri George Munene,
Justin Obwoge Okenye
Issue:
Volume 12, Issue 3, May 2023
Pages:
43-50
Received:
11 April 2023
Accepted:
16 May 2023
Published:
5 June 2023
Abstract: Software reliability assessment has been explored by many researchers over the past decades. With the increasing development of new complex software systems, accurate methods for estimating reliability model parameters are needed. Facilitated by the increasing use of computer systems in various sectors such as air traffic control, banking, industrial processes, and government operations, developing accurate reliability assessment methods is indispensable. The Delayed S-shaped software reliability model is one of the non-homogeneous Poisson process (NHPP) software reliability models proposed for capturing error detection and removal processes in software reliability testing. Many researchers have fitted the model to software failure data and performed estimation using the Maximum Likelihood method and Bayesian approach, however, construction of Bayesian credible sets for the parameters of this model and comparison of their efficiencies with the Wald confidence intervals using simulation have not been explored. The Bayesian interval estimation was conducted with three different joint prior distributions assigned to the parameters α and β of the model, namely the gamma distributed informative prior and, 1/α, and 1/αβ as non-informative priors. The Bayesian credible intervals and Wald confidence intervals for the two parameters were compared on the basis of interval lengths and coverage probabilities. The simulation was assumed to emulate the end-user environment and can generate inter-failure times data for the study. The Delayed S-shaped reliability model variables were simulated with fixed parameters set at (α, β)=(20, 0.5). The hyperparameters for the informative prior were chosen such that they have minimal effect on the results. In other words, the prior information does not swamp the information from the data. The Bayesian method yields superior results, as evidenced by shorter interval lengths and higher coverage probabilities in Table 1.
Abstract: Software reliability assessment has been explored by many researchers over the past decades. With the increasing development of new complex software systems, accurate methods for estimating reliability model parameters are needed. Facilitated by the increasing use of computer systems in various sectors such as air traffic control, banking, industri...
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Monte Carlo Simulation and Derivation of Chi-Square Statistics
Issue:
Volume 12, Issue 3, May 2023
Pages:
51-65
Received:
6 April 2023
Accepted:
22 May 2023
Published:
27 June 2023
Abstract: Computer simulation has become an important tool in teaching statistics. Teaching using computer simulation would enhance the understanding of the concept using visual illustrations. This paper describes how to use simulation in R-programming language to perform a chi-square test. We try to show the distribution of most commonly used chi-square statistics we often found in statistical methods in both derivation and simulation. In statistical methods in such cases as test of independency, test of goodness of fit, test of significance, log likelihood ratio test, significance test and model selection we use chi-square statistic. The approach of the paper will enhance the students’ and researchers’ ability to understand simulation and sampling distribution. The paper contains an expository discussion of chi-square statistic, its derivation and distribution and its derivatives such as t-distribution and F-distribution. We consider two chi-squares, the empirical chi-square statistic and the theoretical chi-square distribution. The empirical distribution of chi-square statistic agrees closely with the theoretical chi-square distribution for large simulations, only the empirical distribution near to zero has lower density compared to the theoretical one for one degree of freedom. This is because the theoretical chi-square distribution at 1 degree of freedom has infinite density near to zero, but for any number of simulation the empirical distribution has finite density near to zero. Chi-square itself turns to normal distribution as the degree of freedom is large.
Abstract: Computer simulation has become an important tool in teaching statistics. Teaching using computer simulation would enhance the understanding of the concept using visual illustrations. This paper describes how to use simulation in R-programming language to perform a chi-square test. We try to show the distribution of most commonly used chi-square sta...
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