In Bayesian analysis, prior elicitation, or the process of facilitating the expression of one’s beliefs to inform statistical modeling, is an essential yet challenging step. Analysts often have beliefs about real-world variables and their relationships. However, existing tools require analysts to translate these beliefs and express them indirectly as probability distributions over model parameters. We present PriorWeaver, an interactive visualization system that facilitates prior elicitation through iterative dataset construction and refinement. Analysts visually express their assumptions about individual variables and their relationships. Under the hood, these assumptions create a dataset used to derive statistical priors. Prior predictive checks then help analysts compare the priors to their assumptions. In a lab study with 17 participants new to Bayesian analysis, we compare PriorWeaver to a baseline incorporating existing techniques. Compared to the baseline, PriorWeaver gave participants greater control, clarity, and confidence, leading to priors that were better aligned with their expectations.

Enabling adaptivity on a uniform Cartesian grid is challenging due to its highly structured grid cells and axis-aligned grid lines. In this paper, we propose a new grid structure - the adaptive staggered-tilted (AST) grid - to conduct adaptive fluid simulations on a regular discretization. The key mechanics underpinning our new grid structure is to allow the emergence of a new set of tilted grid cells from the nodal positions on a background uniform grid. The original axis-aligned cells, in conjunction with the populated axis-tilted cells, jointly function as the geometric primitives to enable adaptivity on a regular spatial discretization. By controlling the states of the tilted cells both temporally and spatially, we can dynamically evolve the adaptive discretizations on an Eulerian domain. Our grid structure preserves almost all the computational merits of a uniform Cartesian grid, including the cache-coherent data layout, the easiness for parallelization, and the existence of high-performance numerical solvers. Further, our grid structure can be integrated into other adaptive grid structures, such as an Octree or a sparsely populated grid, to accommodate the T-junction-free hierarchy. We demonstrate the efficacy of our AST grid by showing examples of large-scale incompressible flow simulation in domains with irregular boundaries.