<p dir="ltr">Broadly, the focus of this work is on efficient statistical estimation and optimization of data arising from experimental data, particularly motivated by nanomanufacturing experiments on the material tellurene. Tellurene is a novel material for transistors with reliable attributes that enhance the performance of electronics (e.g., nanochip). As a solution-grown product, two-dimensional (2D) tellurene can be manufactured through a scalable process at a low cost. There are three main throughlines to this work, data augmentation, optimization, and equality constraint, and three distinct methodological projects, each of which addresses a subset of these throughlines. For the first project, I apply transfer learning in the analysis of data from a new tellurene experiment (process B) using the established linear regression model from a prior experiment (process A) from a similar study to combine the information from both experiments. The key of this approach is to incorporate the total equivalent amounts (TEA) of a lurking variable (experimental process changes) in terms of an observed (base) factor that appears in both experimental designs into the prespecified linear regression model. The results of the experimental data are presented including the optimal PVP chain length for scaling up production through a larger autoclave size. For the second project, I develop a multi-armed bandit Bayesian optimization (BO) approach to incorporate the equality constraint that comes from a mixture experiment on tellurium nanoproduct and account for factors with categorical levels. A more complex optimization approach was necessitated by the experimenters’ use of a neural network regression model to estimate the response surface. Results are presented on synthetic data to validate the ability of BO to recover the optimal response and its efficiency is compared to Monte Carlo random sampling to understand the level of experimental design complexity at which BO begins to pay off. The third project examines the potential enhancement of parameter estimation by utilizing synthetic data generated through Generative Adversarial Networks (GANs) to augment experimental data coming from a mixture experiment with a small to moderate number of runs. Transfer learning shows high promise for aiding in tellurene experiments, BO’s value increases with the complexity of the experiment, and GANs performed poorly on smaller experiments introducing bias to parameter estimates.</p>