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Full-Text Articles in Physical Sciences and Mathematics
Fitting A Complex Markov Chain Model For Firm And Market Productivity, Julia Ruth Valder
Fitting A Complex Markov Chain Model For Firm And Market Productivity, Julia Ruth Valder
Theses and Dissertations
This thesis develops a methodology of estimating parameters for a complex Markov chain model for firm productivity. The model consists of two Markov chains, one describing firm-level productivity and the other modeling the productivity of the whole market. If applicable, the model can be used to help with optimal decision making problems for labor demand. The need for such a model is motivated and the economical background of this research is shown. A brief introduction to the concept of Markov chains and their application in this context is given. The simulated data that is being used for the estimation is …
Dimension Reduction For Classification With Many Covariates And Pathway Activity Level Estimation, Seungchul Baek
Dimension Reduction For Classification With Many Covariates And Pathway Activity Level Estimation, Seungchul Baek
Theses and Dissertations
The development of science and technology has enabled the use of more covariates. As a result, it has become more difficult to identify dependencies among many covariates. Dimension reduction provides an efficient way to handle this issue by summarizing the effect of covariates via a few linear combinations of covariates. In this dissertation, two methodologies for real-life problems are provided by using dimension reduction equipped with semiparametric theory. The use of semiparametrics allows maximal flexibility of the model by letting some features of the model completely unspecified, while we still enjoy the interpretability of the model through estimating the parameters …
Semiparametric Statistical Estimation And Inference With Latent Information, Qianqian Wang
Semiparametric Statistical Estimation And Inference With Latent Information, Qianqian Wang
Theses and Dissertations
In Chapter 1, we predicted disease risk by transformation models in the presence of missing subgroup identifiers. When a discrete covariate defining subgroup membership is missing for some of the subjects in a study, the distribution of the outcome follows a mixture distribution of the subgroup-specific distributions. Taking into account the uncertain distribution of the group membership and the covariates, we model the relation between the disease onset time and the covariates through transformation models in each sub-population, and develop a nonparametric maximum likelihood based estimation implemented through EM algorithm along with its inference procedure. We further propose methods to …
Uncertainty Estimation Of Deep Neural Networks, Chao Chen
Uncertainty Estimation Of Deep Neural Networks, Chao Chen
Theses and Dissertations
Normal neural networks trained with gradient descent and back-propagation have received great success in various applications. On one hand, point estimation of the network weights is prone to over-fitting problems and lacks important uncertainty information associated with the estimation. On the other hand, exact Bayesian neural network methods are intractable and non-applicable for real-world applications. To date, approximate methods have been actively under development for Bayesian neural networks, including but not limited to: stochastic variational methods, Monte Carlo dropouts, and expectation propagation. Though these methods are applicable for current large networks, there are limits to these approaches with either underestimation …