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Application of survival analysis methods to study under-five child mortality in Uganda.Nasejje, Justine. 12 December 2013 (has links)
Infant and child mortality rates are one of the health indicators in a given community or country. It is the fourth millennium development goal that by 2015, all the united nations member countries are expected to have reduced their infant and child mortality rates by two-thirds. Uganda is one of those countries in sub-Saharan Africa with high infant and child mortality rates and therefore has the need to find out the factors strongly
associated to these high rates in order to provide alternative or maintain the existing interventions. The Uganda Demographic Health Survey (UDHS) funded by USAID, UNFPA, UNICEF, Irish Aid and the United kingdom government provides a data set which is rich in information. This information has attracted many researchers and some of it can be used to help Uganda monitor her infant and child mortality rates to achieve the fourth millennium goal. Survival analysis techniques and frailty modelling
is a well developed statistical tool in analysing time to event data. These methods were adopted in this thesis to examine factors affecting under-five child mortality in Uganda using the UDHS data for 2011 using R and STATA software. Results obtained by fitting the Cox-proportional hazard model and frailty models and drawing inference using both the Frequentists and Bayesian approach showed that, Demographic factors
(sex of the household head, sex of the child and number of births in the past one year) are strongly associated with high under-five child mortality rates. Heterogeneity or unobserved covariates were found to be signifcant at household but insignifcant at community level. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.
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The application of multistate Markov models to HIV disease progression.Reddy, Tarylee. January 2011 (has links)
Survival analysis is a well developed area which explores time to single
event analysis. In some cases, however, such methods may not adequately
capture the disease process as the disease progression may involve intermediate
events of interest. Multistate models incorporate multiple events
or states. This thesis proposes to demystify the theory of multistate models
through an application based approach. We present the key components of
multistate models, relevant derivations, model diagnostics and techniques
for modeling the effect of covariates on transition intensities.
The methods that are developed in the thesis are applied to HIV and
TB data partly sourced from CAPRISA and the HPP programmes in the
University of KwaZulu-Natal. HIV progression is investigated through the
application of a five state Markov model with reversible transitions such
that state 1: CD4 count 500, state 2: 350 CD4 count < 500, state 3:
200 CD4 count < 350, state 4: CD4 count < 200 and state 5: ARV initiation.
The mean sojourn time in each state and transition probabilities
are presented as well as the effect of covariates namely age, gender and
baseline CD4 count on transition rates.
A key finding, consistent with previous research, is that the rate of decline
in CD4 count tends to decrease at lower levels of the marker. Further,
patients enrolling with a CD4 count less than 350 had a far lower chance
of immune recovery and a substantially higher chance of immune deterioration
compared to patients with a higher CD4 count. We noted that older
patients tend to progress more rapidly through the disease than younger
patients. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2011.
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An application of some inventory control techniques.Samuels, Carol Anne. January 1992 (has links)
No abstract available. / Thesis (M.Sc.)-University of Durban-Westville, 1992.
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Applications of Levy processes in finance.Essay, Ahmed Rashid. January 2009 (has links)
The option pricing theory set forth by Black and Scholes assumes that the
underlying asset can be modeled by Geometric Brownian motion, with the
Brownian motion being the driving force of uncertainty. Recent empirical
studies, Dotsis, Psychoyios & Skiadopolous (2007) [17], suggest that the
use of Brownian motion alone is insufficient in accurately describing the
evolution of the underlying asset. A more realistic description of the underlying
asset’s dynamics would be to include random jumps in addition to
that of the Brownian motion.
The concept of including jumps in the asset price model leads us naturally
to the concept of a L'evy process. L'evy processes serve as a building
block for stochastic processes that include jumps in addition to Brownian
motion. In this dissertation we first examine the structure and nature of an
arbitrary L'evy process. We then introduce the stochastic integral for L'evy
processes as well as the extended version of Itˆo’s lemma, we then identify
exponential L'evy processes that can serve as Radon-Nikod'ym derivatives
in defining new probability measures.
Equipped with our knowledge of L'evy processes we then implement
this process in a financial context with the L'evy process serving as driving
source of uncertainty in some stock price model. In particular we look
at jump-diffusion models such as Merton’s(1976) [37] jump-diffusion model
and the jump-diffusion model proposed by Kou and Wang (2004) [30]. As
the L'evy processes we consider have more than one source of randomness
we are faced with the difficulty of pricing options in an incomplete market.
The options that we shall consider shall be mainly European in nature,
where exercise can only occur at maturity. In addition to the vanilla calls
and puts we independently derive a closed form solution for an exchange
option under Merton’s jump-diffusion model making use of conditioning
arguments and stochastic integral representations. We also examine some
exotic options under the Kou and Wang model such as barrier options and
lookback options where the solution to the option price is derived in terms
of Laplace transforms. We then develop the Kou and Wang model to include
only positive jumps, under this revised model we compute the value of a
perpetual put option along with the optimal exercise point.
Keywords
Derivative pricing, L'evy processes, exchange options, stochastic integration. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2009.
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Time series forecasting and model selection in singular spectrum analysisDe Klerk, Jacques 11 1900 (has links)
Dissertation (PhD)--University of Stellenbosch, 2002 / ENGLISH ABSTRACT: Singular spectrum analysis (SSA) originated in the field of Physics. The technique is
non-parametric by nature and inter alia finds application in atmospheric sciences,
signal processing and recently in financial markets. The technique can handle a very
broad class of time series that can contain combinations of complex periodicities,
polynomial or exponential trend. Forecasting techniques are reviewed in this study,
and a new coordinate free joint-horizon k-period-ahead forecasting formulation is
derived. The study also considers model selection in SSA, from which it become
apparent that forward validation results in more stable model selection.
The roots of SSA are outlined and distributional assumptions of signal senes are
considered ab initio. Pitfalls that arise in the multivariate statistical theory are
identified.
Different approaches of recurrent one-period-ahead forecasting are then reviewed.
The forecasting approaches are all supplied in algorithmic form to ensure effortless
adaptation to computer programs. Theoretical considerations, underlying the
forecasting algorithms, are also considered. A new coordinate free joint-horizon kperiod-
ahead forecasting formulation is derived and also adapted for the multichannel
SSA case.
Different model selection techniques are then considered. The use of scree-diagrams,
phase space portraits, percentage variation explained by eigenvectors, cross and
forward validation are considered in detail. The non-parametric nature of SSA
essentially results in the use of non-parametric model selection techniques.
Finally, the study also considers a commercial software package that is available and
compares it with Fortran code, which was developed as part of the study. / AFRIKAANSE OPSOMMING: Singulier spektraalanalise (SSA) het sy oorsprong in die Fisika. Die tegniek is nieparametries
van aard en vind toepassing in velde soos atmosferiese wetenskappe,
seinprossesering en onlangs in finansiële markte. Die tegniek kan 'n wye
verskeidenheid tydreekse hanteer wat kombinasies van komplekse periodisiteite,
polinomiese- en eksponensiële tendense insluit. Vooruitskattingstegnieke word ook in
hierdie studie beskou, en 'n nuwe koërdinaatvrye gesamentlike horison k-periodevooruitskattingformulering
word afgelei. Die studie beskou ook model seleksie in
SSA, waaruit duidelik blyk dat voorwaartse validasie meer stabiele model seleksie tot
gevolg het.
Die agtergrond van SSA word ab initio geskets en verdelingsaannames van seinreekse
beskou. Probleemgevalle wat voorkom in die meervoudige statistiese teorie word
duidelik geïdentifiseer.
Verskeie tegnieke van herhalende toepassing van een-periode-vooruitskatting word
daarna beskou. Die benaderings tot vooruitskatting word in algororitmiese formaat
verskaf wat die aanpassing na rekenaarprogrammering vergemaklik. Teoretiese
vraagstukke, onderliggend aan die vooruitskattings-algortimes, word ook beskou. 'n
Nuwe koërdinaatvrye gesamentlike horison k-periode-vooruitskattingsformulering
word afgelei en aangepas vir die multikanaal SSA geval.
Verskillende model seleksie tegnieke is ook beskou. Die gebruik van "scree"-
diagramme, fase ruimte diagramme, persentasie variasie verklaar deur eievektore,
kruis- en voorwaartse validasie word ook aangespreek. Die nie-parametriese aard van
SSA noop die gebruik van nie-parametriese model seleksie tegnieke.
Die studie vergelyk laastens 'n kommersiële sagtewarepakket met die Fortran
bronkode wat as deel van hierdie studie ontwikkel is.
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Longitudinal analysis of the effect of climatic factors on the wood anatomy of two eucalypt clones.Ayele, Dawit Getnet. 04 February 2014 (has links)
Eucalypt trees are one of tree species used for the manufacturing of papers in
South Africa. The manufacturing of paper consists of cooking the wood with chemicals until
obtaining a pulp. The wood is made of different cells. The shape and structure of these cells, called
wood anatomical characteristics are important for the quality of paper. In addition, the anatomical
characteristics of wood are influenced by environmental factors like climatic factors, soil
compositions etc…. In this study we investigated the effects of the climatic factors (temperature,
rainfall, solar radiation, relative humidity, and wind speed) on wood anatomical characteristics of
two Eucalyptus clones, a GC (Eucalyptus grandis × camuldulensis) and a GU (Eucalyptus grandis ×
urophylla). Nine trees per clone have been selected.
Two sets of data have been collected for this study. The first set of data was eleven anatomical
characteristics of the wood formed daily over a period of five years. The second set of data was the
daily measurement of temperature, rainfall, solar radiation, relative humidity and wind speed in the
experimental area.
Wood is made of two kinds of cell, the fibres and the vessels. The fibres are used for the strength and
support of the tree and the vessels for the nutrition. Eleven characteristics related to those cells have
been measured (diameter, wall thickness, frequency). These characteristics are highly correlated. To
reduce the number of response variables, the principal component analysis was used and the first four
principal components accounts for about 95% of the total variation. Based on the weights associated
with each component the first four principal components were labelled as vessel dimension (VD),
fibre dimension (FD), fibre wall (FW) and vessel frequency (VF).
The longitudinal linear mixed model with age, season, temperature, rainfall, solar radiation, relative
humidity and wind speed as the fixed effects factors and tree as random effect factor was fitted to the
data. From time series modelling result, lagged order of climatic variables were identified and these
lagged climatic variables were included in the model. To account for the physical characteristic of
the trees we included the effect of diameter at breast height, stem radius, daily radial increment, and
the suppression or dominance of the tree in the model. It was found that wood anatomical
characteristics of the two clones were more affected by climatic variables when the tree was on
juvenile stage as compared to mature stage. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2010.
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Nonlinear models for neural networks.Brittain, Susan. January 2000 (has links)
The most commonly used applications of hidden-layer feed forward neural networks are to fit curves to regression data or to provide a surface from which a classification rule can be found. From a statistical viewpoint, the principle underpinning these networks is that of nonparametric regression with sigmoidal curves being located and scaled so that their sum approximates the data well, and the underlying mechanism is that of nonlinear regression, with the weights of the network corresponding to parameters in the regression model, and the objective function implemented in the training of the network defining the error structure. The aim ofthe present study is to use these statistical insights to critically appraise the reliability and the precision of the predicted outputs from a trained hiddenlayer feed forward neural network. / Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 2000.
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Inference from finite population sampling : a unified approach.January 2007 (has links)
In this thesis, we have considered the inference aspects of sampling from a
finite population. There are significant differences between traditional
statistical inference and finite population sampling inference. In the case of
finite population sampling, the statistician is free to choose his own sampling
design and is not confined to independent and identically distributed
observations as is often the case with traditional statistical inference. We look
at the correspondence between the sampling design and the sampling
scheme. We also look at methods used for drawing samples. The non –
existence theorems (Godambe (1955), Hanurav and Basu (1971)) are also
discussed. Since the minimum variance unbiased estimator does not exist for
infinite populations, a number of estimators need to be considered for
estimating the same parameter. We discuss the admissible properties of
estimators and the use of sufficient statistics and the Rao-Blackwell Theorem
for the improvement of inefficient inadmissible estimators. Sampling
strategies using auxiliary information, relating to the population, need to be
used as no sampling strategy can provide an efficient estimator of the
population parameter in all situations. Finally few well known sampling
strategies are studied and compared under a super population model. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2007.
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Aspects of categorical data analysis.Govender, Yogarani. January 1998 (has links)
The purpose of this study is to investigate and understand data which are grouped into categories. At the onset, the study presents a review of early research contributions and controversies surrounding categorical data analysis. The concept of sparseness in a contingency table refers to a table where many
cells have small frequencies. Previous research findings showed that incorrect results were obtained in the analysis of sparse tables. Hence, attention is focussed on the effect of sparseness on modelling and analysis of categorical data in this dissertation.
Cressie and Read (1984) suggested a versatile alternative, the power divergence statistic, to statistics proposed in the past. This study includes a detailed discussion of the power-divergence goodness-of-fit statistic with areas of interest covering a review on the minimum power divergence estimation method and evaluation of model fit. The effects of sparseness are also investigated for the power-divergence statistic. Comparative reviews on the accuracy, efficiency and performance of the power-divergence family of statistics under large and small sample cases are presented. Statistical applications on the power-divergence statistic have been conducted in SAS (Statistical Analysis
Software). Further findings on the effect of small expected frequencies on accuracy of the X2 test are presented from the studies of Tate and Hyer (1973) and Lawal and Upton (1976).
Other goodness-of-fit statistics which bear relevance to the sparse multino-mial case are discussed. They include Zelterman's (1987) D2 goodness-of-fit statistic, Simonoff's (1982, 1983) goodness-of-fit statistics as well as Koehler and Larntz's tests for log-linear models. On addressing contradictions for the
sparse sample case under asymptotic conditions and an increase in sample size, discussions are provided on Simonoff's use of nonparametric techniques to find the variances as well as his adoption of the jackknife and bootstrap technique. / Thesis (M.Sc.)-University of Natal, Durban, 1998.
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Modelling longitudinal counts data with application to recurrent epileptic seizure events.Ngulube, Phathisani. January 2010 (has links)
The objectives of this thesis is to explore different approaches of modelling clustered correlated data in the form of repeated or longitudinal counts data leading to a replicated Poisson process. The specific application is from repeated epileptic seizure time to events data. Two main classes of models will be considered in this thesis. These are the marginal and subject or cluster specific effects models. Under the marginal class of models the generalized estimating equations approach due to Liang and Zeger (1986) is first considered. These models are concerned with population averaged effects as opposed to subject-specific effects which include random subject-specific effects such that multiple or repeated outcomes within a subject or cluster are assumed to be independent conditional on the subject−specific effects.
Finally we consider a distinct class of marginal models which include three common variants namely the approach due to Anderson and Gill (1982), Wei et al (1989) and Prentice et al. (1981) / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2010.
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