The application of statistical classification to predict sovereign default
- Authors: Vele, Rendani
- Date: 2023-10-13
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/424563 , vital:72164
- Description: When considering sovereign loans, it is imperative for a financial institution to have a good understanding of the sovereign they are transacting with. Defaults can occur if proper evaluation steps are not considered. To aid in the prediction of potential sovereign defaults, financial institutions, together with grading companies, quantify the risk associated with issuing a loan to a sovereign by developing sovereign default early warning systems (EWS). Various classification models are considered in this study to develop sovereign default EWS. These models are the binary logit, probit, Bayesian additive regression trees, and artificial neural networks. This study investigates the predictive performance of the various classification techniques. Sovereign information is not readily available, so missing data techniques are considered in order to counter the data availability issue. Sovereign defaults are rare, which results in an imbalance in the distribution of the binary dependent variable. To assess data sets with such characteristics, metrics for imbalanced data are considered for model performance comparison. From the findings, the Bayesian additive regression technique generated better results than the other techniques when considering a basic data analysis. Moreover when cross-validation was considered, the neural network technique performed best. In addition, regional models had better results than the global model when considering model predictive capability. The significance of this study is to develop sovereign default prediction models using various classification techniques focused on enhancing previous literature and analysis through the application of Bayesian additive regression trees. , Thesis (MSc) -- Faculty of Science, Statistics, 2023
- Full Text:
- Date Issued: 2023-10-13
- Authors: Vele, Rendani
- Date: 2023-10-13
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/424563 , vital:72164
- Description: When considering sovereign loans, it is imperative for a financial institution to have a good understanding of the sovereign they are transacting with. Defaults can occur if proper evaluation steps are not considered. To aid in the prediction of potential sovereign defaults, financial institutions, together with grading companies, quantify the risk associated with issuing a loan to a sovereign by developing sovereign default early warning systems (EWS). Various classification models are considered in this study to develop sovereign default EWS. These models are the binary logit, probit, Bayesian additive regression trees, and artificial neural networks. This study investigates the predictive performance of the various classification techniques. Sovereign information is not readily available, so missing data techniques are considered in order to counter the data availability issue. Sovereign defaults are rare, which results in an imbalance in the distribution of the binary dependent variable. To assess data sets with such characteristics, metrics for imbalanced data are considered for model performance comparison. From the findings, the Bayesian additive regression technique generated better results than the other techniques when considering a basic data analysis. Moreover when cross-validation was considered, the neural network technique performed best. In addition, regional models had better results than the global model when considering model predictive capability. The significance of this study is to develop sovereign default prediction models using various classification techniques focused on enhancing previous literature and analysis through the application of Bayesian additive regression trees. , Thesis (MSc) -- Faculty of Science, Statistics, 2023
- Full Text:
- Date Issued: 2023-10-13
Enhancing the use of large-scale assessment data in South Africa: Multidimensional Item Response Theory
- Authors: Lahoud, Tamlyn Ann
- Date: 2023-03-29
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/422389 , vital:71938
- Description: This research aims to enhance the use of large-scale assessment data in South Africa by evaluating assessment validity by means of multidimensional item response theory and its associated statistical techniques, which have been severely underutilised. Data from the 2014 administration of the grade 6 Mathematics annual national assessment was used in this study and all analyses were conducted using the mirt package in R. A two parameter logistic item response theory model was developed which indicated a clear alignment between the model parameters and difficulty specifications of the test. The test was found to favour learners within the central band on the ability scale. An exploratory five dimensional item response theory model was then developed to investigate the alignment with the test specifications as evidence for construct validity. Significant discrepancies between the factor structure and the specifications of the test were identified. Notably, the results suggest that some items measured an ability that was not purely mathematical, such as reading ability, which would distort the test’s representation of Mathematics ability, disadvantage learners with lower English literacy, and reduce the construct validity of the test. Further validity evidence was obtained by differential item functioning analyses which revealed that fourteen items function differently for learners from different provinces. Although possible reasons for the presence of differential item functioning among provinces were not discussed, its presence provided sufficient evidence against the validity of the test. In conclusion, multidimensional item response theory provided an effective and rigorous approach to establishing the validity of a large-scale assessment. To avoid the pitfalls of the annual national assessments, it is recommended that this multidimensional item and differential item functioning techniques are utilised for the development and evaluation of future national assessment instruments in South Africa. , Thesis (MSc) -- Faculty of Science, Statistics, 2023
- Full Text:
- Date Issued: 2023-03-29
- Authors: Lahoud, Tamlyn Ann
- Date: 2023-03-29
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/422389 , vital:71938
- Description: This research aims to enhance the use of large-scale assessment data in South Africa by evaluating assessment validity by means of multidimensional item response theory and its associated statistical techniques, which have been severely underutilised. Data from the 2014 administration of the grade 6 Mathematics annual national assessment was used in this study and all analyses were conducted using the mirt package in R. A two parameter logistic item response theory model was developed which indicated a clear alignment between the model parameters and difficulty specifications of the test. The test was found to favour learners within the central band on the ability scale. An exploratory five dimensional item response theory model was then developed to investigate the alignment with the test specifications as evidence for construct validity. Significant discrepancies between the factor structure and the specifications of the test were identified. Notably, the results suggest that some items measured an ability that was not purely mathematical, such as reading ability, which would distort the test’s representation of Mathematics ability, disadvantage learners with lower English literacy, and reduce the construct validity of the test. Further validity evidence was obtained by differential item functioning analyses which revealed that fourteen items function differently for learners from different provinces. Although possible reasons for the presence of differential item functioning among provinces were not discussed, its presence provided sufficient evidence against the validity of the test. In conclusion, multidimensional item response theory provided an effective and rigorous approach to establishing the validity of a large-scale assessment. To avoid the pitfalls of the annual national assessments, it is recommended that this multidimensional item and differential item functioning techniques are utilised for the development and evaluation of future national assessment instruments in South Africa. , Thesis (MSc) -- Faculty of Science, Statistics, 2023
- Full Text:
- Date Issued: 2023-03-29
Statistical and Mathematical Learning: an application to fraud detection and prevention
- Authors: Hamlomo, Sisipho
- Date: 2022-04-06
- Subjects: Credit card fraud , Bootstrap (Statistics) , Support vector machines , Neural networks (Computer science) , Decision trees , Machine learning , Cross-validation , Imbalanced data
- Language: English
- Type: Master's thesis , text
- Identifier: http://hdl.handle.net/10962/233795 , vital:50128
- Description: Credit card fraud is an ever-growing problem. There has been a rapid increase in the rate of fraudulent activities in recent years resulting in a considerable loss to several organizations, companies, and government agencies. Many researchers have focused on detecting fraudulent behaviours early using advanced machine learning techniques. However, credit card fraud detection is not a straightforward task since fraudulent behaviours usually differ for each attempt and the dataset is highly imbalanced, that is, the frequency of non-fraudulent cases outnumbers the frequency of fraudulent cases. In the case of the European credit card dataset, we have a ratio of approximately one fraudulent case to five hundred and seventy-eight non-fraudulent cases. Different methods were implemented to overcome this problem, namely random undersampling, one-sided sampling, SMOTE combined with Tomek links and parameter tuning. Predictive classifiers, namely logistic regression, decision trees, k-nearest neighbour, support vector machine and multilayer perceptrons, are applied to predict if a transaction is fraudulent or non-fraudulent. The model's performance is evaluated based on recall, precision, F1-score, the area under receiver operating characteristics curve, geometric mean and Matthew correlation coefficient. The results showed that the logistic regression classifier performed better than other classifiers except when the dataset was oversampled. , Thesis (MSc) -- Faculty of Science, Statistics, 2022
- Full Text:
- Date Issued: 2022-04-06
- Authors: Hamlomo, Sisipho
- Date: 2022-04-06
- Subjects: Credit card fraud , Bootstrap (Statistics) , Support vector machines , Neural networks (Computer science) , Decision trees , Machine learning , Cross-validation , Imbalanced data
- Language: English
- Type: Master's thesis , text
- Identifier: http://hdl.handle.net/10962/233795 , vital:50128
- Description: Credit card fraud is an ever-growing problem. There has been a rapid increase in the rate of fraudulent activities in recent years resulting in a considerable loss to several organizations, companies, and government agencies. Many researchers have focused on detecting fraudulent behaviours early using advanced machine learning techniques. However, credit card fraud detection is not a straightforward task since fraudulent behaviours usually differ for each attempt and the dataset is highly imbalanced, that is, the frequency of non-fraudulent cases outnumbers the frequency of fraudulent cases. In the case of the European credit card dataset, we have a ratio of approximately one fraudulent case to five hundred and seventy-eight non-fraudulent cases. Different methods were implemented to overcome this problem, namely random undersampling, one-sided sampling, SMOTE combined with Tomek links and parameter tuning. Predictive classifiers, namely logistic regression, decision trees, k-nearest neighbour, support vector machine and multilayer perceptrons, are applied to predict if a transaction is fraudulent or non-fraudulent. The model's performance is evaluated based on recall, precision, F1-score, the area under receiver operating characteristics curve, geometric mean and Matthew correlation coefficient. The results showed that the logistic regression classifier performed better than other classifiers except when the dataset was oversampled. , Thesis (MSc) -- Faculty of Science, Statistics, 2022
- Full Text:
- Date Issued: 2022-04-06
A modelling approach to the analysis of complex survey data
- Authors: Dlangamandla, Olwethu
- Date: 2021-10-29
- Subjects: Sampling (Statistics) , Linear models (Statistics) , Multilevel models (Statistics) , Logistic regression analysis , Complex survey data
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/192955 , vital:45284
- Description: Surveys are an essential tool for collecting data and most surveys use complex sampling designs to collect the data. Complex sampling designs are used mainly to enhance representativeness in the sample by accounting for the underlying structure of the population. This often results in data that are non-independent and clustered. Ignoring complex design features such as clustering, stratification, multistage and unequal probability sampling may result in inaccurate and incorrect inference. An overview of, and difference between, design-based and model-based approaches to inference for complex survey data has been discussed. This study adopts a model-based approach. The objective of this study is to discuss and describe the modelling approach in analysing complex survey data. This is specifically done by introducing the principle inference methods under which data from complex surveys may be analysed. In particular, discussions on the theory and methods of model fitting for the analysis of complex survey data are presented. We begin by discussing unique features of complex survey data and explore appropriate methods of analysis that account for the complexity inherent in the survey data. We also explore the widely applied logistic regression modelling of binary data in a complex sample survey context. In particular, four forms of logistic regression models are fitted. These models are generalized linear models, multilevel models, mixed effects models and generalized linear mixed models. Simulated complex survey data are used to illustrate the methods and models. Various R packages are used for the analysis. The results presented and discussed in this thesis indicate that a logistic mixed model with first and second level predictors has a better fit compared to a logistic mixed model with first level predictors. In addition, a logistic multilevel model with first and second level predictors and nested random effects provides a better fit to the data compared to other logistic multilevel fitted models. Similar results were obtained from fitting a generalized logistic mixed model with first and second level predictor variables and a generalized linear mixed model with first and second level predictors and nested random effects. , Thesis (MSC) -- Faculty of Science, Statistics, 2021
- Full Text:
- Date Issued: 2021-10-29
- Authors: Dlangamandla, Olwethu
- Date: 2021-10-29
- Subjects: Sampling (Statistics) , Linear models (Statistics) , Multilevel models (Statistics) , Logistic regression analysis , Complex survey data
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/192955 , vital:45284
- Description: Surveys are an essential tool for collecting data and most surveys use complex sampling designs to collect the data. Complex sampling designs are used mainly to enhance representativeness in the sample by accounting for the underlying structure of the population. This often results in data that are non-independent and clustered. Ignoring complex design features such as clustering, stratification, multistage and unequal probability sampling may result in inaccurate and incorrect inference. An overview of, and difference between, design-based and model-based approaches to inference for complex survey data has been discussed. This study adopts a model-based approach. The objective of this study is to discuss and describe the modelling approach in analysing complex survey data. This is specifically done by introducing the principle inference methods under which data from complex surveys may be analysed. In particular, discussions on the theory and methods of model fitting for the analysis of complex survey data are presented. We begin by discussing unique features of complex survey data and explore appropriate methods of analysis that account for the complexity inherent in the survey data. We also explore the widely applied logistic regression modelling of binary data in a complex sample survey context. In particular, four forms of logistic regression models are fitted. These models are generalized linear models, multilevel models, mixed effects models and generalized linear mixed models. Simulated complex survey data are used to illustrate the methods and models. Various R packages are used for the analysis. The results presented and discussed in this thesis indicate that a logistic mixed model with first and second level predictors has a better fit compared to a logistic mixed model with first level predictors. In addition, a logistic multilevel model with first and second level predictors and nested random effects provides a better fit to the data compared to other logistic multilevel fitted models. Similar results were obtained from fitting a generalized logistic mixed model with first and second level predictor variables and a generalized linear mixed model with first and second level predictors and nested random effects. , Thesis (MSC) -- Faculty of Science, Statistics, 2021
- Full Text:
- Date Issued: 2021-10-29
The application of Classification Trees in the Banking Sector
- Authors: Mtwa, Sithayanda
- Date: 2021-04
- Subjects: To be added
- Language: English
- Type: thesis , text , Masters , MSc
- Identifier: http://hdl.handle.net/10962/178514 , vital:42946
- Description: Access restricted until April 2026. , Thesis (MSc) -- Faculty of Science, Statistics, 2021
- Full Text:
- Date Issued: 2021-04
- Authors: Mtwa, Sithayanda
- Date: 2021-04
- Subjects: To be added
- Language: English
- Type: thesis , text , Masters , MSc
- Identifier: http://hdl.handle.net/10962/178514 , vital:42946
- Description: Access restricted until April 2026. , Thesis (MSc) -- Faculty of Science, Statistics, 2021
- Full Text:
- Date Issued: 2021-04
Bayesian accelerated life tests for the Weibull distribution under non-informative priors
- Authors: Mostert, Philip
- Date: 2020
- Subjects: Accelerated life testing -- Statistical methods , Accelerated life testing -- Mathematical models , Failure time data analysis , Bayesian statistical decision theory , Monte Carlo method , Weibull distribution
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/172181 , vital:42173
- Description: In a competitive world where products are designed to last for long periods of time, obtaining time-to-failure data is both difficult and costly. Hence for products with high reliability, accelerated life testing is required to obtain relevant life-data quickly. This is done by placing the products under higher-than-use stress levels, thereby causing the products to fail prematurely. Part of the analysis of accelerated life-data requires a life distribution that describes the lifetime of a product at a given stress level and a life-stress relationship – which is some function that describes the way in which the life distribution changes across different stress levels. In this thesis it is assumed that the underlying life distribution is the wellknown Weibull distribution, with shape parameter constant over all stress levels and scale parameter as a log-linear function of stress. The primary objective of this thesis is to obtain estimates from Bayesian analysis, and this thesis considers five types of non-informative prior distributions: Jeffreys’ prior, reference priors, maximal data information prior, uniform prior and probability matching priors. Since the associated posterior distribution under all the derived non-informative priors are of an unknown form, the propriety of the posterior distributions is assessed to ensure admissible results. For comparison purposes, estimates obtained via the method of maximum likelihood are also considered. Finding these estimates requires solving non-linear equations, hence the Newton-Raphson algorithm is used to obtain estimates. A simulation study based on the time-to-failure of accelerated data is conducted to compare results between maximum likelihood and Bayesian estimates. As a result of the Bayesian posterior distributions being analytically intractable, two methods to obtain Bayesian estimates are considered: Markov chain Monte Carlo methods and Lindley’s approximation technique. In the simulation study the posterior means and the root mean squared error values of the estimates under the symmetric squared error loss function and the two asymmetric loss functions: the LINEX loss function and general entropy loss function, are considered. Furthermore the coverage rates for the Bayesian Markov chain Monte Carlo and maximum likelihood estimates are found, and are compared by their average interval lengths. A case study using a dataset based on accelerated time-to-failure of an insulating fluid is considered. The fit of these data for the Weibull distribution is studied and is compared to that of other popular life distributions. A full simulation study is conducted to illustrate convergence of the proper posterior distributions. Both maximum likelihood and Bayesian estimates are found for these data. The deviance information criterion is used to compare Bayesian estimates between the prior distributions. The case study is concluded by finding reliability estimates of the data at use-stress levels.
- Full Text:
- Date Issued: 2020
- Authors: Mostert, Philip
- Date: 2020
- Subjects: Accelerated life testing -- Statistical methods , Accelerated life testing -- Mathematical models , Failure time data analysis , Bayesian statistical decision theory , Monte Carlo method , Weibull distribution
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/172181 , vital:42173
- Description: In a competitive world where products are designed to last for long periods of time, obtaining time-to-failure data is both difficult and costly. Hence for products with high reliability, accelerated life testing is required to obtain relevant life-data quickly. This is done by placing the products under higher-than-use stress levels, thereby causing the products to fail prematurely. Part of the analysis of accelerated life-data requires a life distribution that describes the lifetime of a product at a given stress level and a life-stress relationship – which is some function that describes the way in which the life distribution changes across different stress levels. In this thesis it is assumed that the underlying life distribution is the wellknown Weibull distribution, with shape parameter constant over all stress levels and scale parameter as a log-linear function of stress. The primary objective of this thesis is to obtain estimates from Bayesian analysis, and this thesis considers five types of non-informative prior distributions: Jeffreys’ prior, reference priors, maximal data information prior, uniform prior and probability matching priors. Since the associated posterior distribution under all the derived non-informative priors are of an unknown form, the propriety of the posterior distributions is assessed to ensure admissible results. For comparison purposes, estimates obtained via the method of maximum likelihood are also considered. Finding these estimates requires solving non-linear equations, hence the Newton-Raphson algorithm is used to obtain estimates. A simulation study based on the time-to-failure of accelerated data is conducted to compare results between maximum likelihood and Bayesian estimates. As a result of the Bayesian posterior distributions being analytically intractable, two methods to obtain Bayesian estimates are considered: Markov chain Monte Carlo methods and Lindley’s approximation technique. In the simulation study the posterior means and the root mean squared error values of the estimates under the symmetric squared error loss function and the two asymmetric loss functions: the LINEX loss function and general entropy loss function, are considered. Furthermore the coverage rates for the Bayesian Markov chain Monte Carlo and maximum likelihood estimates are found, and are compared by their average interval lengths. A case study using a dataset based on accelerated time-to-failure of an insulating fluid is considered. The fit of these data for the Weibull distribution is studied and is compared to that of other popular life distributions. A full simulation study is conducted to illustrate convergence of the proper posterior distributions. Both maximum likelihood and Bayesian estimates are found for these data. The deviance information criterion is used to compare Bayesian estimates between the prior distributions. The case study is concluded by finding reliability estimates of the data at use-stress levels.
- Full Text:
- Date Issued: 2020
Default in payment, an application of statistical learning techniques
- Authors: Gcakasi, Lulama
- Date: 2020
- Subjects: Credit -- South Africa -- Risk assessment , Risk management -- Statistical methods -- South Africa , Credit -- Management -- Statistical methods , Commercial statistics
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/141547 , vital:37984
- Description: The ability of financial institutions to detect whether a customer will default on their credit card payment is essential for its profitability. To that effect, financial institutions have credit scoring systems in place to be able to estimate the credit risk associated with a customer. Various classification models are used to develop credit scoring systems such as k-nearest neighbours, logistic regression and classification trees. This study aims to assess the performance of different classification models on the prediction of credit card payment default. Credit data is usually of high dimension and as a result dimension reduction techniques, namely principal component analysis and linear discriminant analysis, are used in this study as a means to improve model performance. Two classification models are used, namely neural networks and support vector machines. Model performance is evaluated using accuracy and area under the curve (AUC). The neuarl network classifier performed better than the support vector machine classifier as it produced higher accuracy rates and AUC values. Dimension reduction techniques were not effective in improving model performance but did result in less computationally expensive models.
- Full Text:
- Date Issued: 2020
- Authors: Gcakasi, Lulama
- Date: 2020
- Subjects: Credit -- South Africa -- Risk assessment , Risk management -- Statistical methods -- South Africa , Credit -- Management -- Statistical methods , Commercial statistics
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/141547 , vital:37984
- Description: The ability of financial institutions to detect whether a customer will default on their credit card payment is essential for its profitability. To that effect, financial institutions have credit scoring systems in place to be able to estimate the credit risk associated with a customer. Various classification models are used to develop credit scoring systems such as k-nearest neighbours, logistic regression and classification trees. This study aims to assess the performance of different classification models on the prediction of credit card payment default. Credit data is usually of high dimension and as a result dimension reduction techniques, namely principal component analysis and linear discriminant analysis, are used in this study as a means to improve model performance. Two classification models are used, namely neural networks and support vector machines. Model performance is evaluated using accuracy and area under the curve (AUC). The neuarl network classifier performed better than the support vector machine classifier as it produced higher accuracy rates and AUC values. Dimension reduction techniques were not effective in improving model performance but did result in less computationally expensive models.
- Full Text:
- Date Issued: 2020
Bayesian hierarchical modelling with application in spatial epidemiology
- Authors: Southey, Richard Robert
- Date: 2018
- Subjects: Bayesian statistical decision theory , Spatial analysis (Statistics) , Medical mapping , Pericarditis , Mortality Statistics
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/59489 , vital:27617
- Description: Disease mapping and spatial statistics have become an important part of modern day statistics and have increased in popularity as the methods and techniques have evolved. The application of disease mapping is not only confined to the analysis of diseases as other applications of disease mapping can be found in Econometric and financial disciplines. This thesis will consider two data sets. These are the Georgia oral cancer 2004 data set and the South African acute pericarditis 2014 data set. The Georgia data set will be used to assess the hyperprior sensitivity of the precision for the uncorrelated heterogeneity and correlated heterogeneity components in a convolution model. The correlated heterogeneity will be modelled by a conditional autoregressive prior distribution and the uncorrelated heterogeneity will be modelled with a zero mean Gaussian prior distribution. The sensitivity analysis will be performed using three models with conjugate, Jeffreys' and a fixed parameter prior for the hyperprior distribution of the precision for the uncorrelated heterogeneity component. A simulation study will be done to compare four prior distributions which will be the conjugate, Jeffreys', probability matching and divergence priors. The three models will be fitted in WinBUGS® using a Bayesian approach. The results of the three models will be in the form of disease maps, figures and tables. The results show that the hyperprior of the precision for the uncorrelated heterogeneity and correlated heterogeneity components are sensitive to changes and will result in different results depending on the specification of the hyperprior distribution of the precision for the two components in the model. The South African data set will be used to examine whether there is a difference between the proper conditional autoregressive prior and intrinsic conditional autoregressive prior for the correlated heterogeneity component in a convolution model. Two models will be fitted in WinBUGS® for this comparison. Both the hyperpriors of the precision for the uncorrelated heterogeneity and correlated heterogeneity components will be modelled using a Jeffreys' prior distribution. The results show that there is no significant difference between the results of the model with a proper conditional autoregressive prior and intrinsic conditional autoregressive prior for the South African data, although there are a few disadvantages of using a proper conditional autoregressive prior for the correlated heterogeneity which will be stated in the conclusion.
- Full Text:
- Date Issued: 2018
- Authors: Southey, Richard Robert
- Date: 2018
- Subjects: Bayesian statistical decision theory , Spatial analysis (Statistics) , Medical mapping , Pericarditis , Mortality Statistics
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/59489 , vital:27617
- Description: Disease mapping and spatial statistics have become an important part of modern day statistics and have increased in popularity as the methods and techniques have evolved. The application of disease mapping is not only confined to the analysis of diseases as other applications of disease mapping can be found in Econometric and financial disciplines. This thesis will consider two data sets. These are the Georgia oral cancer 2004 data set and the South African acute pericarditis 2014 data set. The Georgia data set will be used to assess the hyperprior sensitivity of the precision for the uncorrelated heterogeneity and correlated heterogeneity components in a convolution model. The correlated heterogeneity will be modelled by a conditional autoregressive prior distribution and the uncorrelated heterogeneity will be modelled with a zero mean Gaussian prior distribution. The sensitivity analysis will be performed using three models with conjugate, Jeffreys' and a fixed parameter prior for the hyperprior distribution of the precision for the uncorrelated heterogeneity component. A simulation study will be done to compare four prior distributions which will be the conjugate, Jeffreys', probability matching and divergence priors. The three models will be fitted in WinBUGS® using a Bayesian approach. The results of the three models will be in the form of disease maps, figures and tables. The results show that the hyperprior of the precision for the uncorrelated heterogeneity and correlated heterogeneity components are sensitive to changes and will result in different results depending on the specification of the hyperprior distribution of the precision for the two components in the model. The South African data set will be used to examine whether there is a difference between the proper conditional autoregressive prior and intrinsic conditional autoregressive prior for the correlated heterogeneity component in a convolution model. Two models will be fitted in WinBUGS® for this comparison. Both the hyperpriors of the precision for the uncorrelated heterogeneity and correlated heterogeneity components will be modelled using a Jeffreys' prior distribution. The results show that there is no significant difference between the results of the model with a proper conditional autoregressive prior and intrinsic conditional autoregressive prior for the South African data, although there are a few disadvantages of using a proper conditional autoregressive prior for the correlated heterogeneity which will be stated in the conclusion.
- Full Text:
- Date Issued: 2018
Generalized linear models, with applications in fisheries research
- Authors: Sidumo, Bonelwa
- Date: 2018
- Subjects: Western mosquitofish , Analysis of variance , Fisheries Catch effort South Africa Sundays River (Eastern Cape) , Linear models (Statistics) , Multilevel models (Statistics) , Experimental design
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/61102 , vital:27975
- Description: Gambusia affinis (G. affinis) is an invasive fish species found in the Sundays River Valley of the Eastern Cape, South Africa, The relative abundance and population dynamics of G. affinis were quantified in five interconnected impoundments within the Sundays River Valley, This study utilised a G. affinis data set to demonstrate various, classical ANOVA models. Generalized linear models were used to standardize catch per unit effort (CPUE) estimates and to determine environmental variables which influenced the CPUE, Based on the generalized linear model results dam age, mean temperature, Oreochromis mossambicus abundance and Glossogobius callidus abundance had a significant effect on the G. affinis CPUE. The Albany Angling Association collected data during fishing tag and release events. These data were utilized to demonstrate repeated measures designs. Mixed-effects models provided a powerful and flexible tool for analyzing clustered data such as repeated measures data and nested data, lienee it has become tremendously popular as a framework for the analysis of bio-behavioral experiments. The results show that the mixed-effects methods proposed in this study are more efficient than those based on generalized linear models. These data were better modeled with mixed-effects models due to their flexibility in handling missing data.
- Full Text:
- Date Issued: 2018
- Authors: Sidumo, Bonelwa
- Date: 2018
- Subjects: Western mosquitofish , Analysis of variance , Fisheries Catch effort South Africa Sundays River (Eastern Cape) , Linear models (Statistics) , Multilevel models (Statistics) , Experimental design
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/61102 , vital:27975
- Description: Gambusia affinis (G. affinis) is an invasive fish species found in the Sundays River Valley of the Eastern Cape, South Africa, The relative abundance and population dynamics of G. affinis were quantified in five interconnected impoundments within the Sundays River Valley, This study utilised a G. affinis data set to demonstrate various, classical ANOVA models. Generalized linear models were used to standardize catch per unit effort (CPUE) estimates and to determine environmental variables which influenced the CPUE, Based on the generalized linear model results dam age, mean temperature, Oreochromis mossambicus abundance and Glossogobius callidus abundance had a significant effect on the G. affinis CPUE. The Albany Angling Association collected data during fishing tag and release events. These data were utilized to demonstrate repeated measures designs. Mixed-effects models provided a powerful and flexible tool for analyzing clustered data such as repeated measures data and nested data, lienee it has become tremendously popular as a framework for the analysis of bio-behavioral experiments. The results show that the mixed-effects methods proposed in this study are more efficient than those based on generalized linear models. These data were better modeled with mixed-effects models due to their flexibility in handling missing data.
- Full Text:
- Date Issued: 2018
Stochastic models in finance
- Authors: Mazengera, Hassan
- Date: 2017
- Subjects: Finance -- Mathematical models , C++ (Computer program language) , GARCH model , Lebesgue-Radon-Nikodym theorems , Radon measures , Stochastic models , Stochastic processes , Stochastic processes -- Computer programs , Martingales (Mathematics) , Pricing -- Mathematical models
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/162724 , vital:40976
- Description: Stochastic models for pricing financial securities are developed. First, we consider the Black Scholes model, which is a classic example of a complete market model and finally focus on Lévy driven models. Jumps may render the market incomplete and are induced in a model by inclusion of a Poisson process. Lévy driven models are more realistic in modelling of asset price dynamics than the Black Scholes model. Martingales are central in pricing, especially of derivatives and we give them the desired attention in the context of pricing. There are an increasing number of important pricing models where analytical solutions are not available hence computational methods come in handy, see Broadie and Glasserman (1997). It is also important to note that computational methods are also applicable to models with analytical solutions. We computationally value selected stochastic financial models using C++. Computational methods are also used to value or price complex financial instruments such as path dependent derivatives. This pricing procedure is applied in the computational valuation of a stochastic (revenue based) loan contract. Derivatives with simple pay of functions and models with analytical solutions are considered for illustrative purposes. The Black-Scholes P.D.E is complex to solve analytically and finite difference methods are widely used. Explicit finite difference scheme is considered in this thesis for computational valuation of derivatives that are modelled by the Black-Scholes P.D.E. Stochastic modelling of asset prices is important for the valuation of derivatives: Gaussian, exponential and gamma variates are simulated for the valuation purposes.
- Full Text:
- Date Issued: 2017
- Authors: Mazengera, Hassan
- Date: 2017
- Subjects: Finance -- Mathematical models , C++ (Computer program language) , GARCH model , Lebesgue-Radon-Nikodym theorems , Radon measures , Stochastic models , Stochastic processes , Stochastic processes -- Computer programs , Martingales (Mathematics) , Pricing -- Mathematical models
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/162724 , vital:40976
- Description: Stochastic models for pricing financial securities are developed. First, we consider the Black Scholes model, which is a classic example of a complete market model and finally focus on Lévy driven models. Jumps may render the market incomplete and are induced in a model by inclusion of a Poisson process. Lévy driven models are more realistic in modelling of asset price dynamics than the Black Scholes model. Martingales are central in pricing, especially of derivatives and we give them the desired attention in the context of pricing. There are an increasing number of important pricing models where analytical solutions are not available hence computational methods come in handy, see Broadie and Glasserman (1997). It is also important to note that computational methods are also applicable to models with analytical solutions. We computationally value selected stochastic financial models using C++. Computational methods are also used to value or price complex financial instruments such as path dependent derivatives. This pricing procedure is applied in the computational valuation of a stochastic (revenue based) loan contract. Derivatives with simple pay of functions and models with analytical solutions are considered for illustrative purposes. The Black-Scholes P.D.E is complex to solve analytically and finite difference methods are widely used. Explicit finite difference scheme is considered in this thesis for computational valuation of derivatives that are modelled by the Black-Scholes P.D.E. Stochastic modelling of asset prices is important for the valuation of derivatives: Gaussian, exponential and gamma variates are simulated for the valuation purposes.
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- Date Issued: 2017
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