This thesis focuses on objective Bayesian statistics, by evaluating a number of noninformative priors.
Choosing the prior distribution is the key to Bayesian inference. The probability matching prior for
the product of different powers of k binomial parameters is derived in Chapter 2. In the case of two
and three independently distributed binomial variables, the Jeffreys, uniform and probability matching
priors for the product of the parameters are compared. This research is an extension of the work by
Kim (2006), who derived the probability matching prior for the product of k independent Poisson
rates. In Chapter 3 we derive the probability matching prior for a linear combination of binomial
parameters. The construction of Bayesian credible intervals for the difference of two independent
binomial parameters is discussed.
The probability matching prior for the product of different powers of k Poisson rates is derived in
Chapter 4. This is achieved by using the differential equation procedure of Datta & Ghosh (1995). The
reference prior for the ratio of two Poisson rates is also obtained. Simulation studies are done to com-
pare different methods for constructing Bayesian credible intervals. It seems that if one is interested
in making Bayesian inference on the product of different powers of k Poisson rates, the probability
matching prior is the best. On the other hand, if we want to obtain point estimates, credibility intervals
or do hypothesis testing for the ratio of two Poisson rates, the uniform prior should be used.
In Chapter 5 the probability matching prior for a linear contrast of Poisson parameters is derived,
this prior is extended in such a way that it is also the probability matching prior for the average of
Poisson parameters. This research is an extension of the work done by Stamey & Hamilton (2006). A
comparison is made between the confidence intervals obtained by Stamey & Hamilton (2006) and the
intervals derived by us when using the Jeffreys and probability matching priors. A weighted Monte
Carlo method is used for the computation of the Bayesian credible intervals, in the case of the proba-
bility matching prior. In the last section of this chapter hypothesis testing for two means is considered.
The power and size of the test, using Bayesian methods, are compared to tests used by Krishnamoorthy
& Thomson (2004). For the Bayesian methods the Jeffreys prior, probability matching prior and two
other priors are used.
Bayesian estimation for binomial rates from pooled samples are considered in Chapter 6, where
the Jeffreys prior is used. Bayesian credibility intervals for a single proportion and the difference of
two binomial proportions estimated from pooled samples are considered. The results are compared This thesis focuses on objective Bayesian statistics, by evaluating a number of noninformative priors.
Choosing the prior distribution is the key to Bayesian inference. The probability matching prior for
the product of different powers of k binomial parameters is derived in Chapter 2. In the case of two
and three independently distributed binomial variables, the Jeffreys, uniform and probability matching
priors for the product of the parameters are compared. This research is an extension of the work by
Kim (2006), who derived the probability matching prior for the product of k independent Poisson
rates. In Chapter 3 we derive the probability matching prior for a linear combination of binomial
parameters. The construction of Bayesian credible intervals for the difference of two independent
binomial parameters is discussed.
The probability matching prior for the product of different powers of k Poisson rates is derived in
Chapter 4. This is achieved by using the differential equation procedure of Datta & Ghosh (1995). The
reference prior for the ratio of two Poisson rates is also obtained. Simulation studies are done to com-
pare different methods for constructing Bayesian credible intervals. It seems that if one is interested
in making Bayesian inference on the product of different powers of k Poisson rates, the probability
matching prior is the best. On the other hand, if we want to obtain point estimates, credibility intervals
or do hypothesis testing for the ratio of two Poisson rates, the uniform prior should be used.
In Chapter 5 the probability matching prior for a linear contrast of Poisson parameters is derived,
this prior is extended in such a way that it is also the probability matching prior for the average of
Poisson parameters. This research is an extension of the work done by Stamey & Hamilton (2006). A
comparison is made between the confidence intervals obtained by Stamey & Hamilton (2006) and the
intervals derived by us when using the Jeffreys and probability matching priors. A weighted Monte
Carlo method is used for the computation of the Bayesian credible intervals, in the case of the proba-
bility matching prior. In the last section of this chapter hypothesis testing for two means is considered.
The power and size of the test, using Bayesian methods, are compared to tests used by Krishnamoorthy
& Thomson (2004). For the Bayesian methods the Jeffreys prior, probability matching prior and two
other priors are used.
Bayesian estimation for binomial rates from pooled samples are considered in Chapter 6, where
the Jeffreys prior is used. Bayesian credibility intervals for a single proportion and the difference of
two binomial proportions estimated from pooled samples are considered. The results are compared
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ufs/oai:etd.uovs.ac.za:etd-08162012-091042 |
| Date | 16 August 2012 |
| Creators | Raubenheimer, Lizanne |
| Contributors | Prof AJ van der Merwe |
| Publisher | University of the Free State |
| Source Sets | South African National ETD Portal |
| Language | en-uk |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.uovs.ac.za//theses/available/etd-08162012-091042/restricted/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University Free State or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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