https://repository.maseno.ac.ke/handle/123456789/1316 2026-05-15T12:08:40Z https://repository.maseno.ac.ke/handle/123456789/6383 Advancing hierarchical model and variable Selection methods: evaluating performance, Interpretability and implications OPOKU, Seth Larbi Healthcare utilization continues to be a relevant issue for the public health sector in developing situations. However, conventional statistical frameworks tend to understate the contextual and hierarchical nature of the health data. Prior studies have primarily used classical regression approaches that treat observations as autonomous entities, neglecting the relevance of group- or area-context. This disregard for clustering amplifiers limits the health utilization research scope, precision, and interpretability. This research employs a Bayesian hierarchical modeling approach to contextual, socioeconomic, and maternal variables concerning the use of maternal health services in Kenya. The model was applied to hierarchical data using the Least Absolute Shrinkage and Selection Operator (LASSO) technique for variable selection and the Hierarchical Bayesian Information Criterion (HBIC) for model selection. The modified model encompasses fixed effects (population-level predictors), random effects (county heterogeneity), and contextual effects. The HBIC results indicate that Age and Religion were the most influencial predictors. The results highlight the importance of maternal education, health insurance, marital status, household income, religion, and other socioeconomic variables in explaining the inequitable and, at times, regionally differentiated utilization of health services. Incorporating prior information and treating parameter uncertainty are ways the Bayesian approach generates more accurate posterior estimates. This research illustrates the value of Bayesian hierarchical modelling for policy-related inference and small-area estimation in closing the methodological void in public health analytics. The results provide the foundation for more equitable, evidence-based maternal health intervention strategies that account for individual and contextual differences. PhD Thesis 2025-11-06T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/6382 A time-varying covariate model for survival Analysis using longitudinal data BAFFOE, Samuel Statistical methodologies for medical and health science research have changed significantly, bringing out the dynamics of disease progression and treatment outcomes. Methodologies for analyzing survival data help understand the changes in subjects over time, including the assessment of time to event. However, the standard survival models assume only time-invariant relationships, ignoring the changing character of reproductive indicators. This research introduces a modified approach to studying survival analysis, addressing the limitation by developing a time-varying covariate survival analysis model within a longitudinal data modeling framework. A Cox proportional hazards model that incorporates time-varying covariates was developed and validated. A comparison of the predictive accuracy of the modified model with that of the standard model was made. The model was validated using secondary data from Performance Monitoring and Account ability (PMA) data, Kenya. Several key covariates in the traditional model exhibited time-dependent effects, undermining the assumption of constant hazard. The modified model addresses this limitation by incorporating a shared random-effects structure for longitudinal data, which accommodates time-varying effects and yields enhanced and more accurate hazard estimation over time. The modified model proved better than the traditional Cox model at achieving predictive accuracy outcome measures. The modified model increased fitting statistics by reaching new AIC levels of 237,513.6 and BIC levels of 237,573.9 over traditional AIC (238,047.5) and BIC (238,085.2) statistics. Additionally, it displayed a 1.18 percent superior predictive capability through a C-index of 0.858 versus the traditional model’s 0.848 index. The study brings new techniques to survival analysis research while delivering practical recommendations for reproductive health service development through time-varying variable integration. Other than an improvement of methodology in the field of survival analysis, this model produces a more accurate and adaptable framework for clinical forecasting, ultimately leading to improved treatment outcomes. In line with this study, future research might seek to incorporate time series models into the survival analysis approach and dynamic prediction models that merge repeated measures with survival results to obtain more personalized predictions. PhD Thesis 2025-11-06T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/5684 Finite element method solution for steady magnetohydrodynamic flow in a straight horizontal pipe of elliptical cross section KWEYU, David Velocity profile and temperature distribution for Magnetohydrodynamic (MHD) flow in a straight horizontal pipe of elliptical cross section has been investigated. Many researchers have carried out research on pipes of circular, square, rectangular, annular and elliptical cross sections in magnetohydrodynamics because there are many applications. Their studies concentrated on a given cross section as a different entity with fluid being driven by pumps. In this study, investigation is done on a circular pipe as it changes into an elliptical pipe when fluid is propelled by gravitational force. The main purpose of the study is to find out which pipe between one whichhasacircularcrosssectionandanotherofellipticalcrosssectionismorebeneficial. Effects of velocity profile and temperature distribution on the pipe as it changes cross section from circular to elliptical are investigated. Governing equations, partial differential equations (pdes), are formulated, non dimensionalised, expressed in terms of stream function and transformed into ordinary differential equations (odes) using similarity transformation. The odes are solved by Finite Element Method in conjunction with Mathematica version 12.0. The objectives of the study are: To model Finite Element Method solution for steady Magnetohydrodynamic flow in a straight horizontal pipe of elliptical cross section. To formulate governing equations (pdes) in cylindrical coordinates (r,θ,z) comprising Navier-Stokes equations, Ohm’s law of electromagnetism, equation of continuity, cross section of elliptical pipe and heat energy equation. To solve by Finite Element Method the ordinary differential equations (odes) formed when non dimensionalisation and similarity transformation are carried out on the governing equations. To determine the effects of dimensionless numbers of Hartmann number, Reynolds number, Eckert number and Prandtl number as well as other physical quantities of gravitational force and aspect ratio on fluid velocity and temperature. To find out the repercussions of velocity and temperature on a pipe as it transits from circular to elliptical cross section. Finite Element Method (FEM) is embraced instead of other methods like Finite Difference Method (FDM) because FEM is able to handle complicated geometries and boundaries with relative ease while other methods are restricted to handle rectangular shapes. Also many of the real life medical, engineering, astrophysics, etc problems can be solved in weak form, which FEM encompasses compared to strong form, which other methods employ. Results are displayed as tables and graphs and reveal that: Increase in Hartmann number, 1.0≤Ha≤40.0, increases temperature but retards velocity. Rise in Reynolds number, 0.5≤Re≤8.0 and aspect ratio, 1≤α ≤1.6, leads to rise in both velocity and temperature. An upsurge in gravitational force, 0.00002≤λθ ≤0.00008, results in an upsurge in velocity. Temperature increases when Eckert number, 1≤Ec≤40 , increases but decreases when Prandtl number, 0.5≤Pr≤2.0, is raised. In all scenarios, velocity and temperature are maximum at the centre of pipe but diminish to zero at the periphery. Spike in aspect ratio leads to rise in velocity which results in increase in temperature. A pipe of elliptical cross section will be more convenient where there is limited space in the vertical direction due to existing structures yet there is demand in increase in productivity. This is in comparison to circular shape. A pipe of elliptical cross section has greater capacity for the same depth of flow. It is envisaged that the conducting fluid is flowing as a coolant at a nuclear power plant or as molten metal at a metallurgical process. A pipe of elliptical cross section would therefore be moreproductive inindustrialprocessesthanone whichiscircularaccordingto thefindingsofthis dissertation. 2022-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/5571 Arima and vector autoregressive model evaluation in forecasting rainfall: a case of Kisumu Mawora, Thomas Mwakudisa Time Series Analysis has been used over the decades in data analysis and forecast ing. Auto Regressive Integrated Moving Average (ARIMA) models have been fit on economic data and engineering data. The models have also been used in analysis of climate data. Previous studies have focussed on temperature data from National Mete orological Stations where summarized monthly values were used. In this study, we used daily rainfall data from Kenya Meteorological Services Station in Kisumu. The objec tives included univariate time series modelling using ARIMA on long term rainfall data for daily, monthly, seasonal and annual data and forecasting rainfall for the different time periods. The other objective was to compare forecast from univariate ARIMA to Vector Autoregression (VAR) when rainfall, minimum and maximum temperature values are included in model. ARIMA models were fit on the KMS rainfall data, and VAR models were fit on temperature, minimum and maximum rainfall data from KMS. Finally, farm ers’ local rainfall data was compared to that of KMS for independence. Results showed that forecasts under VAR did not give a more precise forecast of future rainfall than ARIMA. Further, that there was not enough statistically significant evidence to suggest that rainfall data from KMS and farmers’ locale were independent. 2022-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/4329 Lie symmetry solutions of the Generalized burgers equation ODUOR, Okoya Edmund Michael Burgers equation: u, + UUx = luxx is a nonlinear partial differential equation which arises in model studies of turbulence and shock wave theory. In physical application of shock waves in fluids, coefficient 1 ,has the meaning of viscosity. For light fluids or gases the solution considers the inviscid limit as 1 tends to zero. The solution of Burgers equation can be classified into two categories: Numerical solutions using both finite difference and finite elements approaches; the analytic solutions found by Cole and Hopf In both cases the solutions have been valid for only 0 ~ 1 ~ 1. In this thesis, we have found a global solution to the Burgers equation with no restriction on 1 i.e. 1 E (- 00 , 00). In pursuit of our objective, we have used, the Lie symmetry analysis. The method includes the development of infinitesimal transformations, generators, prolongations, and the invariant transformations of the Burgers equation. We have managed to determine all the Lie groups admitted by the Burgers equation, and used the symmetry transformations to establish all the solutions corresponding to each Lie group admitted by the equation. These solutions, which are appearing in literature for the first time are more explicit and more general than those previously obtained. This is a big contribution to the mathematical knowledge in the application of Burgers equation. 2005-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/4327 The almost holomophic functional calculus ODHIAMBO, Paul Oleche 2008-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/4320 Unit groups of certain classes of commutative finite rings OWINO, Maurice Oduor 2009-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/4318 Some aspects in the study of invariant subspaces SIMIYU, Achiles Nyongesa 2010-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/4308 Study of non-normal operators in a complex Hilbert Space justus, kitheka 2009-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/4267 The Derivation of a Logistic Nonlinear Black Scholes Merton Partial Differential Equation: European Option NYAKINDA, Joseph Otula \onlinear Black-Scholes equations have been increasingly attracting interest over the last twenty years. This is because they provide more accurate values by taking into account more realistic assumptions, such as transaction costs, illiquid markets, risks from an unprotected portfolio or large investor's preferences, which ruay have an impact on the stock price, the volatility, the drift and the option price itself. Recent models have been developed to take into account the feedback effect of a fund hedging strategy Or of the transaction costs of large traders tv[ost of these models cue represented by nonlinear variations of the well known Black- Scholes Equation.On the other hand, asset security prices may naturally not shoot up indefinitely (exponentially) leading to the use of Verhlusts Logistic equation. The objective of this study was to derive a Logistic Nonlinear Black Scholes f\. lertou Partial Differential equation by considering transaction costs (which \\ere oVBrlooked in the derivation of the classical Black Scholes model) and incorporating the Logistic geometric Brownian motion.The methodology involved, analysis of the geometric Brownian motion, review of logistic models, Ito's process and lemma, stochastic volatility models and the derivation of the linear and nonlinear Black-Scholes-Merton partial differential equation. Illiquid markets have also been analyzed alongside stochastic differential equations. The result of this study may enhance reliable decision making based on a rational prediction of the future asset prices given that in reality the stock market may depict a non linear pattern. 2011-01-01T00:00:00Z