Department of Statistics
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Item Analysis of Investment Returns as Markov Chain Random Walk(International Journal of Mathematics and Mathematical Sciences, 2024) Mettle, F.O.; Agyekum, L.; Aidoo, E.K.; Dowuona, C.O.N.The main objective of this paper is to analyse investment returns using a stochastic model and inform investors about the best stock market to invest in. To this effect, a Markov chain random walk model was successfully developed and implemented on 450 monthly market returns data spanning from January 1976 to December 2020 for Canada, India, Mexico, South Africa, and Switzerland obtained from the Federal Reserves of the Bank of St. Louis. Limiting state probabilities and six-month moving crush probabilities were estimated for each country, and these were used to assess the performance of the markets. Te Mexican market was observed to have the lowest probabilities for all the negative states, while the Indian market recorded the largest limiting probabilities. In the case of positive states, the Mexican market recorded the highest limiting probabilities, while the Indian market recorded the lowest limiting probabilities. The results showed that the Mexican market performed better than the others over the study period, whilst India performed poorly. These findings provide crucial information for market regulators and investors in setting regulations and decision-making in investment.Item Volatility Analysis of Exchange Rate with Correlated Errors: A Sliding Data Matrix Approach(Hindawi, 2022) Mettle, F.O.; Kallah-Dagadu, G.; Aidoo, E.; Debrah, G.; Arku, D.The main objective of this study is to propose a method of analysing the volatility of a seemingly random walk time series with correlated errors without transforming the series as performed traditionally. The proposed method involves the computation of moving volatilities based on sliding and cumulative data matrices. Our method rests on the assumption that the number of subperiods for which the series is available is the same for all periods and on the assumption that the series observations in each subperiod for all the periods under consideration are a random sample from a particular distribution. The method was successfully implemented on a simulated dataset. A paired sample t-test, Wilcoxon signed rank test, repeated measures (ANOVA), and Friedman tests were used to compare the volatilities of the traditional method and the proposed method under both sliding and cumulative data matrices. It was found that the differences among the average volatilities of the traditional method and sliding and cumulative matrix methods were insignificant for the simulated series that follow the random walk theorem. The implementation of the method on exchange rates for Canada, China, South Africa, and Switzerland resulted in adjudging South Africa to have the highest fluctuating exchange rates and hence the most unstable economy.Item Analysis of Exchange Rates as Time-Inhomogeneous Markov Chain with Finite States(Journal of Applied Mathematics, 2022) Mettle, F.O.; Boateng, L.P.; Quaye, E.N.B.; Aidoo, E.K.; Seidu, I.Irrespective of whether the test for homogeneity is significant or not, most researchers assume time-homogeneity in analysing Markov chains due to scanty literature on the analysis of time-inhomogeneous Markov chains. Based on the assumption that, for each point in time in the future, a stochastic process will be subjected to a randomly selected transition matrix from an ergodic set of transition matrices the process was subjected to in the recent past, a methodology was proposed for analysing the long-run behaviours of time-inhomogeneous Markov chains. The proposed model was implemented to historical data consisting of the exchange rate of cedi-dollar, cedi-pound, and cedi-euro spanning over 6 years (January 2012 to December 2017). The results show that under certain “closeness” conditions, the long-run behaviours of the time-inhomogeneous case are almost identical to those of the time-homogeneous case. The paper asserted that even if the Markov chain exhibit time-inhomogeneity, analysing the Markov chain under the assumption of time-homogeneity is a step in the right direction under certain “closeness” conditions; otherwise, the proposed method is recommended. It was also found that investing in dollars yields better returns than the other currencies in Ghana.Item Anomaly Detection in Health Insurance Claims Using Bayesian Quantile Regression(Hindawi, 2021) Nortey, E.N.N.; Pometsey, R.; Asiedu, L.; Iddi, S.; Mettle, F.O.Research has shown that current health expenditure in most countries, especially in sub-Saharan Africa, is inadequate and unsustainable. Yet, fraud, abuse, and waste in health insurance claims by service providers and subscribers threaten the delivery of quality healthcare. It is therefore imperative to analyze health insurance claim data to identify potentially suspicious claims. Typically, anomaly detection can be posited as a classification problem that requires the use of statistical methods such as mixture models and machine learning approaches to classify data points as either normal or anomalous. Additionally, health insurance claim data are mostly associated with problems of sparsity, heteroscedasticity, multicollinearity, and the presence of missing values. The analyses of such data are best addressed by adopting more robust statistical techniques. In this paper, we utilized the Bayesian quantile regression model to establish the relations between claim outcome of interest and subject-level features and further classify claims as either normal or anomalous. An estimated model component is assumed to inherently capture the behaviors of the response variable. A Bayesian mixture model, assuming a normal mixture of two components, is used to label claims as either normal or anomalous. +e model was applied to health insurance data captured on 115 people suffering from various cardiovascular diseases across different states in the USA. Results show that 25 out of 115 claims (21.7%) were potentially suspicious. +e overall accuracy of the fitted model was assessed to be 92%. +rough the methodological approach and empirical application, we demonstrated that the Bayesian quantile regression is a viable model for anomaly detection.Item Recognition of Augmented Frontal Face Images Using FFT-PCA/ SVD Algorithm(Hindawi, 2021) Ayiah-Mensah, F.; Asiedu, L.; Mettle, F.O.; Minkah, R.In spite of the differences in visual stimulus of human beings such as ageing, changing conditions of a person, and occlusion, recognition can even be done at a glance by the human eye many years after the previous encounter. It has been established that facial differences like the hairstyle changes, growing of one’s beard, wearing of glasses, and other forms of occlusions can hardly hinder the power of the human brain from making a face recognition. However, the same cannot easily be said about automated intelligent systems which have been developed to mimic the skill of the human brain to aid in recognition. There have been growing interests in developing a resilient and efficient recognition system mainly because of its numerous application areas (access control, entertainment/leisure, security system based on biometric data, and user-friendly human-machine interfaces). Although there have been numerous researches on face recognition under varying pose, illumination, expression, and image degradations, problems caused by occlusions are mostly ignored. )is study thus focuses on facial occlusions and proposes an enhancement mechanism through face image augmentation to improve the recognition of occluded face images. This study assessed the performance of Principal Component Analysis with Singular Value Decomposition using Fast Fourier Transform (FFT-PCA/SVD) for preprocessing face recognition algorithm on face images with missingness and augmented face image database. It was found that the average recognition rates for the FFT-PCA/SVD algorithm were the same (90%) when face images with missingness and augmented face images were used as test images, respectively. )e statistical evaluation revealed that there exists a significant difference in the average recognition distances for the face images with missingness and augmented face images when FFT-PCA/SVD is used for recognition. Augmented face images tend to have a relatively lower average recognition distance when used as test images. This finding is contrary to the equal performance assessment by the adopted numerical technique. The MICE algorithm is therefore recommended as a suitable imputation mechanism for enhancing/improving the performance of the face recognition system.Item Evaluation of the DWT-PCA/SVD Recognition Algorithm on Reconstructed Frontal Face Images(Hindawi, 2021) Asiedu, L.; Essah, B.O.; Iddi, S.; Doku-Amponsah, K.; Mettle, F.O.The face is the second most important biometric part of the human body, next to the finger print. Recognition of face image with partial occlusion (half image) is an intractable exercise as occlusions affect the performance of the recognition module. To this end, occluded images are sometimes reconstructed or completed with some imputation mechanism before recognition. This study assessed the performance of the principal component analysis and singular value decomposition algorithm using discrete wavelet transform (DWT-PCA/SVD) as preprocessing mechanism on the reconstructed face image database. The reconstruction of the half face images was done leveraging on the property of bilateral symmetry of frontal faces. Numerical assessment of the performance of the adopted recognition algorithm gave average recognition rates of 95% and 75% when left and right reconstructed face images were used for recognition, respectively. It was evident from the statistical assessment that the DWT-PCA/SVD algorithm gives relatively lower average recognition distance for the left reconstructed face images. DWT-PCA/SVD is therefore recommended as a suitable algorithm for recognizing face images under partial occlusion (half face images). The algorithm performs relatively better on left reconstructed face images.Item Assessing the Effect of Data Augmentation on Occluded Frontal Faces Using DWT-PCA/SVD Recognition Algorithm(Hindawi, 2021) Asiedu, L.; Mensah, J.A.; Ayiah-Mensah, F.; Mettle, F.O.'e drift towards face-based recognition systems can be attributed to recent advances in supportive technology and emerging areas of application including voting systems, access control, human-computer interactions, entertainments, and crime control. Despite the obvious advantages of such systems being less intrusive and requiring minimal cooperation of subjects, the performances of their underlying recognition algorithms are challenged by the quality of face images, usually acquired from uncontrolled environments with poor illuminations, varying head poses, ageing, facial expressions, and occlusions. Although several researchers have leveraged on the property of bilateral symmetry to reconstruct half-occluded face images, their approach becomes deficient in the presence of random occlusions. In this paper, we harnessed the benefits of the multiple imputation by the chained equation technique and image denoising using Discrete Wavelet Transforms (DWTs) to reconstruct degraded face images with random missing pixels. Numerical evaluation of the study algorithm gave a perfect (100%) average recognition rate each for recognition of occluded and augmented face images. 'e study also revealed that the average recognition rate for the augmented face images (75.5811) was significantly lower than the average recognition rate (430.7153) of the occluded face images. MICE augmentation is recommended as a suitable data enhancement mechanism for imputing missing data/pixel of occluded face images.Item Modeling the Amount of Waste Generated by Households in the Greater Accra Region Using Artificial Neural Networks(Hindawi, 2021) Chapman-Wardy, C.; Asiedu, L; Doku-Amponsah, K.; Mettle, F.O.Waste can be defined as solids or liquids unwanted by members of the society and meant to be disposed. In developing countries such as Ghana, the management of waste is the responsibility of the metropolitan authorities. These authorities do not seem to have effective management of the waste situation, and therefore, it is not unusual to see waste clog the drains and litter the streets of the capital city, Accra. )e impact of waste on the environment, along with its associated health-related problems, cannot be overemphasized. )e Joint Monitoring Programme report in 2015 ranked Ghana as the seventh dirtiest country in the world. )e lack of effective waste management planning is evident in the large amount of waste dumped in open areas and gutters that remains uncollected. In planning for solid waste management, reliable data concerning waste generation, influencing factors on waste generation, and a reliable forecast of waste quantities are required. )is study used two algorithms, namely, Lev enberg–Marquardt and the Bayesian regularization, to estimate the parameters of an artificial neural network model fitted to predict the average monthly waste generated and critically assess the factors that influence solid waste generation in some selected districts of the Greater Accra region. )e study found Bayesian regularization algorithm to be suitable with the minimum mean square error of 104.78559 on training data and 217.12465 on test data and higher correlation coefficients (0.99801 on training data, 0.99570 on test data, and 0.99767 on the overall data) between the target variables (average monthly waste generated) and the predicted outputs. House size, districts, employment category, dominant religion, and house type with respective importance of 0.56, 0.172, 0.061, 0.027, and 0.026 were found to be the top five important input variables required for forecasting household waste. It is recommended that efforts of the government and its stakeholders to reduce the amount of waste generated by households be directed at providing bins, increasing the frequency of waste collection (especially in highly populated areas), and managing the economic activities in the top five selected districts (Ledzekuku Krowor, Tema West, Asheidu Keteke, Ashaiman, and Ayawaso West), amongst others.Item Assessing the Performance of DWT-PCA/SVD Face Recognition Algorithm under Multiple Constraints(Hindawi, 2021) Mensah, J.A.; Asiedu, L.; Mettle, F.O.; Iddi, S.Many architectures of face recognition modules have been developed to tackle the challenges posed by varying environmental constraints such as illumination, occlusions, pose, and expressions. These recognition systems have mainly focused on a single constraint at a time and have achieved remarkable successes. However, the presence of multiple constraints may deteriorate the performance of these face recognition systems. In this study, we assessed the performance of Principal Component Analysis and Singular Value Decomposition using Discrete Wavelet Transform (DWT-PCA/SVD) for preprocessing face recognition algorithm on multiple constraints (partially occluded face images acquired with varying expressions). Numerical evaluation of the study algorithm gave reasonably average recognition rates of 77.31% and 76.85% for left and right reconstructed face images with varying expressions, respectively. A statistically significant difference was established between the average recognition distance of the left and right reconstructed face images acquired with varying expressions using pairwise comparison test. The post hoc analysis using the Bonferroni simultaneous confidence interval revealed that the significant difference established through the pairwise comparison test was mainly due to the sad expressions. Although the performance of the DWT-PCA/SVD algorithm declined as compared to its performance on single constraints, the algorithm attained appreciable performance level under multiple constraints. The DWT-PCA/SVD recognition algorithm performs reasonably well for recognition when partial occlusion with varying expressions is the underlying constraint.Item Modelling the Transmission Dynamics of Tuberculosis in the Ashanti Region of Ghana(Interdisciplinary Perspectives on Infectious Diseases, 2020-03-31) Mettle, F.O.; Affi, P.O.; Twumasi, C.Mathematical models can aid in elucidating the spread of infectious disease dynamics within a given population over time. In an attempt to model tuberculosis (TB) dynamics among high-burden districts in the Ashanti Region of Ghana, the SEIR epidemic model with demography was employed within both deterministic and stochastic settings for comparison purposes. /e deterministic model showed success in modelling TB infection in the region to the transmission dynamics of the stochastic SEIR model over time. It predicted tuberculosis dying out in ten of twelve high-burden districts in the Ashanti Region, but an outbreak in Obuasi municipal and Amansie West district. /e effect of introducing treatment at the incubation stage of TB transmission was also investigated, and it was discovered that treatment introduced at the exposed stage decreased the spread of TB. Branching process approximation was used to derive explicit forms of relevant epidemiological quantities of the deterministic SEIR model for stability analysis of equilibrium points. Numerical simulations were performed to validate the overall infection rate, basic reproductive number, herd immunity threshold, and Malthusian parameter based on bootstrapping, jackknife, and Latin Hypercube sampling schemes. It was recommended that the Ghana Health Service should find a good mechanism to detect TB in the early stages of infection in the region. Public health attention must also be given to districts with a potentially higher risk of experiencing endemic TB even though the estimates of the overall epidemic thresholds from our SEIR model suggested that the Ashanti Region as a whole had herd immunity against TB infection.