On the Use of Posterior Probabilistic Clustering

Bayesian approach to mixture models makes use of Gibbs sampler, the most common of Markov Chain Monte Carlo (MCMC), for estimation of posterior density and subsequent classification of objects into components of mixture, especially for conjugate priors. In practice conjugacy may not exist and when it does, the time required calculating the posterior density will be far too high for the Bayesian approach to be applied in practice (McLachlan and Peel, 2000). Therefore, we developed a clustering procedure that is a result of using non-conjugate prior distribution of product multinomial to obtain posterior distribution that is hypergeometric, for cross-classifying categorical data. The performance of the scheme was examined through a simulation study of observed tables of counts compared with expected generated by assuming product multinomial to obtain posterior distribution under variety of parameter distributions and loadings. We observed that the approach performed well when the component proportions are properly distinguishable. The approach was illustrated using real life data from social science

Development of a Test Statistic for Testing Equality of Two Means under Unequal Population Variances

In this paper, we propose a test statistic for testing equality of two independent sample means for unequal variances. When group variances differ, the pooled sample variance (  ) is inadequate as a single value for the variances. This problem is commonly known as the Behrens – Fisher problem. Instead, the sample harmonic mean of variances (  ) is proposed, examined and found to better represent the unequal variances. The distribution of  which is known to be generalized Beta is further approximated by the chi – square distribution with the degrees of freedom related to that of degrees of freedom of the chi – square distribution of   . Consequently, it is used to replace the pooled sample variance in the resulting proposed t – test. An example of application is provided. Keywords: Harmonic mean of variances, chi- square distribution, modified t – test statisti

Medicine use among HIV/Aids patients in public hospitals, Kwara State

Background: The prognosis of HIV/AIDS and HIV-related comorbidities has been revolutionized by the use of medicines. However, World Health Organization reported that 50% of patients do not use their medicines as prescribed.Objective: To assess HIV/AIDS patients’ knowledge of the use of medicines dispensed to them.Method: This study was conducted in seven public hospitals in six local government areas, Kwara State. Exit interviews of 780 eligible HIV/AIDS patients were conducted through use of structured questionnaire. Additionally, there were exit observational checks of medicines dispensed to these patients. Descriptive statistics and Fisher Exact test were used for data analyses.Results: Of the 780 study participants, 36.1% had no formal education, 99.9% knew the ‘quantity’ of medicines to be administered, while 99.2% knew the frequency of administration. All the patients knew the route of administration, 96.7% and 94.3% knew the general precautions to avoid concomitant use of dispensed medicines with alcohol or herbal products respectively, while 93.7% of those who received co-trimoxazole knew of the precaution to use “plenty of water” as the vehicle for its administration. There were no significant associations between the patients’ knowledge of these precautions and duration of antiretroviral therapy (P>0.05). However, the patients lacked knowledge of specific precautions of some dispensed medicines.Conclusion: Most of the patients knew of the administration and the general precautions of dispensed medicines. However, lack of knowledge of specific precautions of some dispensed medicines calls for intervention.Keywords: HIV/AIDS patients, Medicine use, Duration of antiretroviral therapy, Public hospitals, Kwara Stat

Investigation of the Mechanical and Microstructural Properties of Masonry Mortar Made with Seashell Particles

In order to study the mechanical and microstructural properties of masonry mortar, combined particles of cockle and scallop seashell wastes were incorporated and analysed through destructive and non-destructive tests. River sand was replaced with the combined seashell particles (SPs) at seven mixes, viz., 0, 5, 10, 15, 20, 25, and 30% with a 0.5 constant water-to-cement ratio (W/C). A mortar mix design of M4-type of BS EN 1996-1-1 was adopted with a target compressive strength of 5.17 MPa at 28 days. The physical, chemical and mineralogy properties of the SPs were analysed through BS standard sieving, X-ray fluorescence (XRF), scanning electron microscopy (SEM), and X-ray diffraction (XRD) methods. The hardened SP-based mortars were subjected to direct compressive strength, rebound hammer, ultrasonic pulse velocity tests, and nonevaporable degree of hydration analysis. The XRF, SEM, and XRD analysis results of the SPs showed over 86% calcium oxide content, irregular and needle-like particles, and hydroxyapatite/calcium silicates, respectively. The direct compressive strength and the non-destructive test results revealed that up to 30% sand replacement with SP in masonry mortar, an improvement of 45% compressive strength could be attained over the control sample. The nonevaporable water method of the degree of hydration analysis showed that after 28 days, hydration increased considerably for the SP-blended mortars over the control, especially the SPM-30 with 30% sand replacement. Therefore, the study concludes that the investigated SPs in blended masonry mortar could benefit an eco-friendly environment and conservation of natural resources

Positivity yield of HIV index testing services from selected healthcare facilities in Ondo State, southwest Nigeria

Background: Index testing is a voluntary process whereby HIV seropositive clients are counselled and, after obtaining consent, their sexual and needle sharing partners are offered HIV testing services. Index testing has been associated with high HIV positivity yield. The aim of this study is to determine the positivity yield and identify factors influencing the yield from index testing strategy in selected healthcare facilities in Ondo State, southwest Nigeria. Methodology: Six public hospitals in Ondo State with the highest HIV clients currently on treatment were selected. Records of all clients newly diagnosed to be HIV positive at the selected facilities from June 2018 to September 2019, and who had an outcome for index testing services were reviewed. Data were collected using a chart abstraction template from the index testing registers. Information collected included age and gender of the index clients and their partners, method of referral and notification of partners, HIV test results of partners and linkage status of new HIVpositive partners. Data analyses were done using the Statistical Package for the Social Sciences (SPSS) software version 24.0. Chi-square was used to test association between variables at a significance level of p<0.01. Results: The records of a total of 904 index clients and their partners were reviewed with partner elicitation ratio of 1:1. The mean ages of index clients and their partners were 38.52±10.96 and 38.98±10.79 years respectively, and majority of the index clients (34.6%) and partners (35.5%) were in the 35-44 years age group. A total of 548 index clients were females (60.6%) while 528 of their partners were males (58.4%), indicating  predominantly heterosexual (96.4%) and few homosexual (lesbian) relationships (3.6%). One-fifth (20%) of partners tested positive for HIV andwere all (100%) linked to antiretroviral therapy (ART). The HIV positivity rate in partners of male index clients (26.9%) was significantly higher than in partners of female index clients (15.5%) (p<0.01). Partner referral method was mostly through assisted referral (56%) and most (82%) were contacted by the index clients through phone. Conclusion: Due to its high positivity yield, index testing is a veritable strategy to increase HIV case detection and linkage to ART. Hence, proper deployment of index testing will be critical to improving ART coverage and achieving epidemiological control. Keywords: HIV, client; partner; index testing; ART; southwest Nigeri

Modelling language extinction using Susceptible-Infectious-Removed (SIR) model

The study presents a stochastic epidemic model applied to the model of indigenous language extinction. The Susceptible-Infectious-Removed (SIR) categorization of an endemic disease has been reformulated to capture the dynamics of indigenous language decline, based on the assumption of non-homogeneous mixing. The time in which an indigenous language is expected to be extinct was derived using a modified SIR model with the population segmented into several sub-communities of small sizes representing family units. The data obtained from the 2016 indigenous language survey conducted in several parts of Nigeria and from the 2013 Nigeria Demographic Health Survey (NDHS) were used to estimate the key parameters of the model for Nigeria’s several indigenous languages. The parameters of interest included the basic reproduction number, the threshold of endemicity, and the time in which a language is expected to be extinct, starting from the endemic level. On the basis of the time in which a language is expected to be extinct, several of the surveyed languages appeared to be in a precarious condition, while others seemed virile, thanks to a high language transfer quotient within families

On Hypothesis Testing Under Unequal Group Variances: The Use of the Harmonic Variance

The assumptions of equality of group variances required for ANOVA often fail for real life data. However, because the major aim is to test equality of group means, a single summary value for these group variances is a necessity. Previous works in literature have zeroed in on the choice of either the Harmonic or Geometric mean as a proper mean especially when extreme observation(s) are present which renders a simple mean inappropriate. In this work, the asymptotic sample distribution of harmonic mean of group variances is established to be a chi- square distribution though the degrees of freedom need not be an integer. Keywords:  Harmonic mean of group variances, three - parameter Beta distribution, chi – square distribution

Use Of Linear Programming For Optimal Production In A Production Line In Coca –Cola Bottling Company, Ilorin

Many companies were and are still established to derive financial profit. In this regard the main aim of such establishments is to maximize (optimize) profit. This research is on using Linear programming Technique to derive the maximum profit from production of soft drink for Nigeria Bottling Company Nigeria, Ilorin plant. Linear Programming of the operations of the company was formulated and optimum results derived using Software that employed Simplex method. The result shows that two particular items should be produced even when the company should satisfy demands of the other- not- so profitable items in the surrounding of the plants