Browsing by Subject "Monte Carlo method."
Now showing 1 - 3 of 3
Results Per Page
Sort Options
Item Bayesian and pseudo-likelihood interval estimation for comparing two Poisson rate parameters using under-reported data.(2009-04-01T15:56:04Z) Greer, Brandi A.; Young, Dean M.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.We present interval estimation methods for comparing Poisson rate parameters from two independent populations with under-reported data for the rate difference and the rate ratio. In addition, we apply the Bayesian paradigm to derive credible intervals for both the ratio and the difference of the Poisson rates. We also construct pseudo-likelihood-based confidence intervals for the ratio of the rates. We begin by considering two cases for analyzing under-reported Poisson counts: inference when training data are available and inference when they are not. From these cases we derive two marginal posterior densities for the difference in Poisson rates and corresponding credible sets. First, we perform Monte Carlo simulation analyses to examine the effects of differing model parameters on the posterior density. Then we perform additional simulations to study the robustness of the posterior density to misspecified priors. In addition, we apply the new Bayesian credible intervals for the difference of Poisson rates to an example concerning the mortality rates due to acute lower respiratory infection in two age groups for children in the Upper River Division in Gambia and to an example comparing automobile accident injury rates for male and female drivers. We also use the Bayesian paradigm to derive two closed-form posterior densities and credible intervals for the Poisson rate ratio, again in the presence of training data and without it. We perform a series of Monte Carlo simulation studies to examine the properties of our new posterior densities for the Poisson rate ratio and apply our Bayesian credible intervals for the rate ratio to the same two examples mentioned above. Lastly, we derive three new pseudo-likelihood-based confidence intervals for the ratio of two Poisson rates using the double-sampling paradigm for under-reported data. Specifically, we derive profile likelihood-, integrated likelihood-, and approximate integrated likelihood-based intervals. We compare coverage properties and interval widths of the newly derived confidence intervals via a Monte Carlo simulation. Then we apply our newly derived confidence intervals to an example comparing cervical cancer rates.Item Monte Carlo simulations using infrared improved DGLAP-CS theory.(2009-08-25T16:06:14Z) Joseph, Samuel J.; Ward, Bennie Franklin Leon.; Physics.; Baylor University. Dept. of Physics.A large number of Z and W bosons will be produced at the LHC. A careful study of their properties in the presence of QCD background processes, will be important in studying the Standard Model more rigorously and to uncover new physics which may appear through radiative corrections or through new tree level processes with suppressed couplings. In order to reach the 1% attendant theoretical precision tag on processes such as single Z and W production, more precise Monte Carlos need to be developed. As a step towards this goal a new set of infrared (ir) improved DGLAP-CS kernels was developed by Ward. For this work we implemented these infrared improved kernels in HERWIG6.5 to create a new program HERWIRI1.0. We discuss the phenomological implications of our new Monte Carlo HERWIRI1.0. Specifically we compared pp → 2-jets + X and pp → Z/γ* + X → ℓ⁺ℓ⁻ + X´, with ℓ=e,μ, results obtained by HERWIG6.5 and HERWIRI1.0. The three main quantities that we compared were the pt, energy fraction and rapidity distributions. We made these comparisons at √s=14 TeV, the highest LHC energies. Comparisons were also made for π⁺ production in pp → 2-jets + X at this energy. As expected, the IR-improved spectra were generally softer. As a test of HERWIRI1.0 a comparison of the pt and rapidity distribution data from FNAL at √s=1 96 TeV for the process pp̅ → Z/γ* → e⁺e⁻ + X was made. We found that the softer part of these observed spectra were better described by HERWIRI1.0. This represents a new chapter in precision Monte Carlo simulations for hadron-hadron high energy collisions because the IR-improved kernels do not require an explicit cut-off.Item Normal approximation for Bayesian models with non-sampling bias.(2014-01-28) Yuan, Jiang, 1984-; Stamey, James D.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.Bayesian sample size determination can be computationally intensive for mod- els where Markov chain Monte Carlo (MCMC) methods are commonly used for in- ference. It is also common in a large database where the unmeasured confounding presents. We present a normal theory approximation as an alternative to the time consuming MCMC simulations in sample size determination for a binary regression with unmeasured confounding. Cheng et al. (2009) develop a Bayesian approach to average power calculations in binary regression models. They then apply the model to the common medical scenario where a patient's disease status is not known. In this dissertation, we generate simulations based on their Bayesian model with both binary and normal outcomes. We also use normal theory approximation to speed up such sample size determination and compare power and computational time for both.