This paper investigates the conceptual relationship between openness and reproducibility using a model-centric approach, heavily informed by probability theory and statistics. We first clarify the concepts of reliability, auditability, replicability, and reproducibility–each of which denotes a potential scientific objective. Then we advance a conceptual analysis to delineate the relationship between open scientific practices and these objectives. Using the notion of an idealized experiment, we identify which components of an experiment need to be reported and which need to be repeated to achieve the relevant objective. The model-centric framework we propose aims to contribute precision and clarity to the discussions surrounding the so-called reproducibility crisis.

Consistent confirmations obtained independently of each other lend credibility to a scientific result. We refer to results satisfying this consistency as reproducible and assume that reproducibility is a desirable property of scientific discovery. Yet seemingly science also progresses despite irreproducible results, indicating that the relationship between reproducibility and other desirable properties of scientific discovery is not well understood. These properties include early discovery of truth, persistence on truth once it is discovered, and time spent on truth in a long-term scientific inquiry. We build a mathematical model of scientific discovery that presents a viable framework to study its desirable properties including reproducibility. In this framework, we assume that scientists adopt a model-centric approach to discover the true model generating data in a stochastic process of scientific discovery. We analyze the properties of this process using Markov chain theory, Monte Carlo methods, and agent-based modeling. We show that the scientific process may not converge to truth even if scientific results are reproducible and that irreproducible results do not necessarily imply untrue results. The proportion of different research strategies represented in the scientific population, scientists’ choice of methodology, the complexity of truth, and the strength of signal contribute to this counter-intuitive finding. Important insights include that innovative research speeds up the discovery of scientific truth by facilitating the exploration of model space and epistemic diversity optimizes across desirable properties of scientific discovery.

Current attempts at methodological reform in sciences come in response to an overall lack of rigor in methodological and scientific practices in experimental sciences. However, some of these reform attempts suffer from the same mistakes and over-generalizations they purport to address. Considering the costs of allowing false claims to become canonized, we argue for more rigor and nuance in methodological reform. By way of example, we present a formal analysis of three common claims in the metascientific literature: (a) that reproducibility is the cornerstone of science; (b) that data must not be used twice in any analysis; and (c) that exploratory projects are characterized by poor statistical practice. We show that none of these three claims are correct in general and we explore when they do and do not hold.