Xtrapol8: automatic elucidation of low-occupancy intermediate-states in crystallographic studies

Unstable states studied in kinetic, time-resolved and ligand-based crystallography are often characterized by a low occupancy, hindering structure determination by conventional methods. To automatically extract such structures, we developed Xtrapol8, a program which (i) applies various flavors of Bayesian-statistics weighting to generate the most informative Fourier difference maps; (ii) determines the occupancy of the intermediate state; (iii) calculates various types of extrapolated structure factors, and (iv) refines the corresponding structures.

The Bayesian Inferential Paradigm in Archaeology

Archaeologists often use data and quantitative statistical methods to evaluate their ideas. Although there are various statistical frameworks for decision-making in archaeology and science in general, in this chapter, we provide a simple explanation of Bayesian statistics. To contextualize the Bayesian statistical framework, we briefly compare it to the more widespread null hypothesis significance testing (NHST) approach. We also provide a simple example to illustrate how archaeologists use data and the Bayesian framework to compare hypotheses and evaluate their uncertainty. We then review how archaeologists have applied Bayesian statistics to solve research problems related to radiocarbon dating and chronology, lithic, ceramic, zooarchaeological, bioarchaeological, and spatial analyses. Because recent work has reviewed Bayesian applications in archaeology from the 1990s up to 2017, this work considers the relevant literature published since 2017.

On Johnson’s “Sufficientness” Postulates for Feature-Sampling Models

In the 1920s, the English philosopher W.E. Johnson introduced a characterization of the symmetric Dirichlet prior distribution in terms of its predictive distribution. This is typically referred to as Johnson’s “sufficientness” postulate, and it has been the subject of many contributions in Bayesian statistics, leading to predictive characterization for infinite-dimensional generalizations of the Dirichlet distribution, i.e., species-sampling models. In this paper, we review “sufficientness” postulates for species-sampling models, and then investigate analogous predictive characterizations for the more general feature-sampling models. In particular, we present a “sufficientness” postulate for a class of feature-sampling models referred to as Scaled Processes (SPs), and then discuss analogous characterizations in the general setup of feature-sampling models.

Profit-Driven Methodology for Servo Press Motion Selection under Material Variability

Servo presses enable new types of forming motion profiles that can be used to stamp difficult materials, such as high strength steels. This paper presents an application of Bayesian statistics to intelligently select which motion profile maximizes the expected utility given the properties of the incoming material. Bayesian logistic regression was used in conjunction with expected utility to estimate manufacturing returns, which can be used to make informed process decisions. A use case is presented, which demonstrates that the Smart Forming Algorithm can increase expected returns by more than 20%.

Bayesian Statistics

The chapter “Bayesian Statistics” gives a brief overview of the Bayesian approach to statistical analysis. It starts off by examining the difference between frequentist statistics and Bayesian statistics. Next, it introduces Bayes’ theorem and explains how the theorem is used in statistics and model selection, with the prosecutor’s fallacy given as a practice example. The chapter then goes on to discuss priors and Bayesian parameter estimation. It concludes with some final thoughts on Bayesian approaches. The chapter does not answer the question “Should ecologists become Bayesian?” However, to the extent that alternative models can be posed as alternative values of parameters, Bayesian parameter estimation can help assign probabilities to those hypotheses.