Fabular: regression formulas as probabilistic programming

Regression formulas are a domain-specific language adopted by several R packages for describing an important and useful class of statistical models: hierarchical linear regressions. Formulas are succinct, expressive, and clearly popular, so are they a useful addition to probabilistic programming languages? And what do they mean? We propose a core calculus of hierarchical linear regression, in which regression coefficients are themselves defined by nested regressions (unlike in R). We explain how our calculus captures the essence of the formula DSL found in R. We describe the design and implementation of Fabular, a version of the Tabular schema-driven probabilistic programming language, enriched with formulas based on our regression calculus. To the best of our knowledge, this is the first formal description of the core ideas of R's formula notation, the first development of a calculus of regression formulas, and the first demonstration of the benefits of composing regression formulas and latent variables in a probabilistic programming language.Adam Ścibior received travel support from the DARPA PPAML programme. Marcin Szymczak was supported by Microsoft Research through its PhD Scholarship Programme.This is the author accepted manuscript. The final version is available from the Association of Computer Machinery via http://dx.doi.org/10.1145/2837614.283765

Reconstruction of the Casting Technology in the Bronze Age on the Basis of Investigations and Visualisation of Casting Moulds

During excavation of the cremation cemetery of urnfield culture in Legnica at Spokojna Street (Lower Silesia, Poland), dated to 1100-700 BC, the largest - so far in Poland – a collection of casting moulds from the Bronze Age was discovered: three moulds for axes casting made out of stone and five moulds for casting sickles, razors, spearhead and chisels, made out of clay. This archaeological find constituted fittings of foundrymen’s graves. In order to perform the complete analysis of moulds in respect of their application in the Bronze Age casting technology analytical methods, as well as, computer aided methods of technological processes were used. Macroscopic investigations were performed and the X-ray fluorescence spectrometry method was used to analyse the chemical composition and metal elements content in mould cavities. Moulds were subjected to three-dimensional scanning and due to the reverse engineering the geometry of castings produced in these moulds were obtained. The gathered data was used to perform design and research works by means of the MAGMA5 software. Various variants of the pouring process and alloys solidification in these archaeological moulds were simulated. The obtained results were utilised in the interpretation of the Bronze Age casting production in stone and clay moulds, with regard to their quality and possibility of casting defects occurrence being the result of these moulds construction. The reverse engineering, modelling and computer simulation allowed the analysis of moulds and castings. Investigations of casting moulds together with their digitalisation and reconstruction of casting technology, confirm the high advancement degree of production processes in the Bronze Age