# Browsing by Subject "Bayesian estimation"

Now showing 1 - 4 of 4

- Results Per Page
1 5 10 20 40 60 80 100

- Sort Options
Ascending Descending

Item Bayesian ridge estimation of age-period-cohort models(2014-08) Xu, Minle; Powers, Daniel A.Show more Age-Period-Cohort models offer a useful framework to study trends of time-specific phenomena in various areas. Yet the perfect linear relationship among age, period, and cohort induces a singular design matrix and brings about the identification issue of age, period, and cohort model due to the identity Cohort = Period -- Age. Over the last few decades, multiple methods have been proposed to cope with the identification issue, e.g., the intrinsic estimator (IE), which may be viewed as a limiting form of ridge regression. This study views the ridge estimator from a Bayesian perspective by introducing a prior distribution(s) for the ridge parameter(s). Data used in this study describe the incidence rate of cervical cancer among Ontario women from 1960 to 1994. Results indicate that a Bayesian ridge model with a common prior for the ridge parameter yields estimates of age, period, and cohort effects similar to those based on the intrinsic estimator and to those based on a ridge estimator. The performance of Bayesian models with distinctive priors for the ridge parameters of age, period, and cohort effects is affected more by the choice of prior distributions. In sum, a Bayesian ridge model is an alternative way to deal with the identification problem of age, period, and cohort model. Future studies should further investigate the influences of different prior choices on Bayesian ridge models.Show more Item Estimating phylogenetic trees from discrete morphological data(2015-05) Wright, April Marie; Hillis, David M., 1958-; Cannatella, David C; Jansen, Robert K; Linder, Craig R; Smith, Martha KShow more Morphological characters have a long history of use in the estimation of phylogenetic trees. Datasets consisting of morphological characters are most often analyzed using the maximum parsimony criterion, which seeks to minimize the amount of character change across a phylogenetic tree. When combined with molecular data, characters are often analyzed using model-based methods, such as maximum likelihood or, more commonly, Bayesian estimation. The efficacy of likelihood and Bayesian methods using a common model for estimating topology from discrete morphological characters, the Mk model, is poorly-explored. In Chapter One, I explore the efficacy of Bayesian estimation of phylogeny, using the Mk model, under conditions that are commonly encountered in paleontological studies. Using simulated data, I describe the relative performances of parsimony and the Mk model under a range of realistic conditions that include common scenarios of missing data and rate heterogeneity. I further examine the use of the Mk model in Chapter Two. Like any model, the Mk model makes a number of assumptions. One is that transition between character states are symmetric (i.e., there is an equal probability of changing from state 0 to state 1 and from state 1 to state 0). Many characters, including alleged Dollo characters and extremely labile characters, may not fit this assumption. I tested methods for relaxing this assumption in a Bayesian context. Using empirical datasets, I performed model fitting to demonstrate cases in which modelling asymmetric transitions among characters is preferred. I used simulated datasets to demonstrate that choosing the best-fit model of transition state symmetry can improve model fit and phylogenetic estimation. In my final chapter, I looked at the use of partitions to model datasets more appropriately. Common in molecular studies, partitioning breaks up the dataset into pieces that evolve according to similar mechanisms. These pieces, called partitions, are then modeled separately. This practice has not been widely adopted in morphological studies. I extended the PartitionFinder software, which is used in molecular studies to score different possible partition schemes to find the one which best models the dataset. I used empirical datasets to demonstrate the effects of partitioning datasets on model likelihoods and on the phylogenetic trees estimated from those datasets.Show more Item Predicting influenza hospitalizations(2012-08) Ramakrishnan, Anurekha; Meyers, Lauren Ancel; Damien, Paul, 1960-Show more Seasonal influenza epidemics are a major public health concern, causing three to five million cases of severe illness and about 250,000 to 500,000 deaths worldwide. Given the unpredictability of these epidemics, hospitals and health authorities are often left unprepared to handle the sudden surge in demand. Hence early detection of disease activity is fundamental to reduce the burden on the healthcare system, to provide the most effective care for infected patients and to optimize the timing of control efforts. Early detection requires reliable forecasting methods that make efficient use of surveillance data. We developed a dynamic Bayesian estimator to predict weekly hospitalizations due to influenza related illnesses in the state of Texas. The prediction of peak hospitalizations using our model is accurate both in terms of number of hospitalizations and the time at which the peak occurs. For 1-to 8 week predictions, the predicted number of hospitalizations was within 8% of actual value and the predicted time of occurrence was within a week of actual peak.Show more Item Using the filter-forward backward sampling algorithm in second-order Bayesian latent growth modeling(2016-12) Bond, Mark Arjun; Beretvas, Susan Natasha; Whittaker, TiffanyShow more In educational and social science research, large-scale testing data are frequently collected longitudinally so that researchers can evaluate change over time. Researchers may then wish to assess the impact of various explanatory variables on student growth in achievement outcomes. Use of structural equation modeling allows for the modeling of item-level measurement error and allows growth trajectories to vary by student. If a Bayesian perspective is adopted, one may use psychometric information known a priori about the test items in the estimation process, which may improve ability estimation. In addition, Bayesian estimation procedures, like the Kalman filter, are able to take advantage of the autoregressive structure of time series data to obtain closed-form solutions for ability distributions. In contrast, a structural equation modeling-based approach using likelihood-based estimation would need to rely on iteratively updating proposed model estimates and checking a discrepancy function, which might achieve a local minimum, or fail to converge. Researchers have previously estimated second-order latent growth models with IRT elements, and this work will expand upon that literature in a number of ways. Bayesian research to date has typically relied on use of the WinBUGS software program to estimate these models which does not allow for certain distributional assumptions. For instance, although certain non-informative priors may be specified, it is not possible to use improper non-informative priors with WinBUGS. Also, WinBUGS does not take advantage of the autoregressive structure of a time series analysis to speed up the estimation process, which is possible using the Kalman filter. Because thousands of iterations of calculation and random-number generation are recommended when using a Bayesian Gibbs sampler, the improved computational efficiency of the Kalman filter may make growth models easier to estimate. When time series data are highly correlated, the Kalman filter, theoretically, should improve the rate of convergence for a Gibbs sampler. Furthermore, research on second-order latent growth modeling has not evaluated the use of informative priors for item parameters. The present work will address these limitations. Parameters based on educational psychology research will be used to simulate a dataset which will be analyzed with and without the Kalman filter. Then, convergence diagnostics, including the traceplot, will be assessed to determine whether the Kalman filter improved the rate of convergence. Additionally, both informative and non-informative priors will be used for item parameters, and parameter recovery will be assessed.Show more