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Abstract Optimizing the allocation of units into treatment groups can help researchers improve the precision of causal estimators and decrease costs when running factorial experiments. However, existing optimal allocation results typically assume a super-population model and that the outcome data come from a known family of distributions. Instead, we focus on randomization-based causal inference for the finite-population setting, which does not require model specifications for the data or sampling assumptions. We propose exact theoretical solutions for optimal allocation in $2^K${2}^{K}factorial experiments under complete randomization with A-, D-, and E-optimality criteria. We then extend this work to factorial designs with block randomization. We also derive results for optimal allocations when using cost-based constraints. To connect our theory to practice, we provide convenient integer-constrained programming solutions using a greedy optimization approach to find integer optimal allocation solutions for both complete and block randomizations. The proposed methods are demonstrated using two real-life factorial experiments conducted by social scientists. 

Abstract The flexibility and wide applicability of the Fisher randomization test (FRT) make it an attractive tool for assessment of causal effects of interventions from modern-day randomized experiments that are increasing in size and complexity. This paper provides a theoretical inferential framework for FRT by establishing its connection with confidence distributions. Such a connection leads to development’s of (i) an unambiguous procedure for inversion of FRTs to generate confidence intervals with guaranteed coverage, (ii) new insights on the effect of size of the Monte Carlo sample on the estimation of a p-value curve and (iii) generic and specific methods to combine FRTs from multiple independent experiments with theoretical guarantees. Our developments pertain to finite sample settings but have direct extensions to large samples. Simulations and a case example demonstrate the benefit of these new developments. 

Abstract Empirical interatomic potentials require optimization of force field parameters to tune interatomic interactions to mimic ones obtained by quantum chemistry-based methods. The optimization of the parameters is complex and requires the development of new techniques. Here, we propose an INitial-DEsign Enhanced Deep learning-based OPTimization (INDEEDopt) framework to accelerate and improve the quality of the ReaxFF parameterization. The procedure starts with a Latin Hypercube Design (LHD) algorithm that is used to explore the parameter landscape extensively. The LHD passes the information about explored regions to a deep learning model, which finds the minimum discrepancy regions and eliminates unfeasible regions, and constructs a more comprehensive understanding of physically meaningful parameter space. We demonstrate the procedure here for the parameterization of a nickel–chromium binary force field and a tungsten–sulfide–carbon–oxygen–hydrogen quinary force field. We show that INDEEDopt produces improved accuracies in shorter development time compared to the conventional optimization method.