Bayesian statistics is an approach to data analysis based on Bayes’ theorem, where available knowledge about parameters in a statistical model is updated with the information in observed data. The background knowledge is expressed as a prior distribution and combined with observational data in the form of a likelihood function to determine the posterior distribution. The posterior can also be used for making predictions about future events. This Primer describes the stages involved in Bayesian analysis, from specifying the prior and data models to deriving inference, model checking and refinement. We discuss the importance of prior and posterior predictive checking, selecting a proper technique for sampling from a posterior distribution, variational inference and variable selection. Examples of successful applications of Bayesian analysis across various research fields are provided, including in social sciences, ecology, genetics, medicine and more. We propose strategies for reproducibility and reporting standards, outlining an updated WAMBS (when to Worry and how to Avoid the Misuse of Bayesian Statistics) checklist. Finally, we outline the impact of Bayesian analysis on artificial intelligence, a major goal in the next decade. This Primer on Bayesian statistics summarizes the most important aspects of determining prior distributions, likelihood functions and posterior distributions, in addition to discussing different applications of the method across disciplines.

Bayesian statistics and modelling

Assessment for learning

Although the statistical tools most often used by researchers in the field of psychology over the last 25 years are based on frequentist statistics, it is often claimed that the alternative Bayesian approach to statistics is gaining in popularity. In the current article, we investigated this claim by performing the very first systematic review of Bayesian psychological articles published between 1990 and 2015 (n = 1,579). We aim to provide a thorough presentation of the role Bayesian statistics plays in psychology. This historical assessment allows us to identify trends and see how Bayesian methods have been integrated into psychological research in the context of different statistical frameworks (e.g., hypothesis testing, cognitive models, IRT, SEM, etc.). We also describe take-home messages and provide "big-picture" recommendations to the field as Bayesian statistics becomes more popular. Our review indicated that Bayesian statistics is used in a variety of contexts across subfields of psychology and related disciplines. There are many different reasons why one might choose to use Bayes (e.g., the use of priors, estimating otherwise intractable models, modeling uncertainty, etc.). We found in this review that the use of Bayes has increased and broadened in the sense that this methodology can be used in a flexible manner to tackle many different forms of questions. We hope this presentation opens the door for a larger discussion regarding the current state of Bayesian statistics, as well as future trends. (PsycINFO Database Record

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A systematic review of Bayesian articles in psychology: The last 25 years.

EXECUTIVE EDITORS Tom Bramley, Cambridge Assessment, UK Jannette Elwood, Queen’s University Belfast, UK Harvey Goldstein, University of Bristol, UK Anthony Green, University of Bedfordshire, UK Sandra Johnson, University of Bristol, UK Joshua McGrane, Oxford University Centre for Educational Assessment, UK Pauline Rea-Dickins, Oxford University Centre for Educational Assessment, UK Gordon Stobart, UCL Institute of Education, UK Sally Thomas, University of Bristol, UK Guoxing Yu, University of Bristol, UK

Assessment in Education: Principles, Policy & Practice

https://ris.utwente.nl/ws/files/6955218/1-s2.0-S1747938X15000652-main.pdf

A systematic review of prerequisites for implementing assessment for learning in classroom practice

Recent research has highlighted the lack of a uniform definition of formative assessment, although its effectiveness is widely acknowledged. This paper addresses the theoretical differences and similarities amongst three approaches to formative assessment that are currently most frequently discussed in educational research literature: data-based decision making (DBDM), Assessment for Learning (AfL) and diagnostic testing (DT). Furthermore, the differences and similarities in the implementation of each approach were explored. This analysis shows that although differences exist amongst the theoretical underpinnings of DBDM, AfL and DT, the combination of these approaches can create more informed learning environments. The thoughtful integration of the three assessment approaches should lead to more valid formative decisions, if a range of evidence about student learning is used to continuously optimise student learning.

Integrating data-based decision making, Assessment for Learning and diagnostic testing in formative assessment

Mainstream teachers about including deaf or hard of hearing students

This paper reports on a survey of the classroom assessment practices of Dutch primary school teachers in mathematics education. We investigated, using an online questionnaire, how teachers collect information on their studentś progress and how teacherś assessment methods, purposes, and beliefs about the usefulness of assessment are related. In total 960 teachers at 557 Dutch primary schools responded to the questionnaire. Observation-based assessment methods of questioning, observing, and correcting written work, were the most frequently - that is weekly applied methods, whereas instrument-based methods, particularly using textbook tests and student monitoring tests were employed several times a year. Teachers used assessment mainly for formative purposes and they considered the assessment methods they used themselves as most relevant.

Teachers' use of classroom assessment in primary school mathematics education in the Netherlands.

There exist diverse approaches that can be used for cognitive diagnostic assessment, such as mastery testing, constrained latent class analysis, rule space methodology, diagnostic cognitive modeling, and person-fit analysis. Each of these approaches can be used within 1 of the 4 psychometric perspectives on diagnostic testing discussed by Borsboom (2008), that is, the dimensional, diagnostic, constructivist, and causal system perspectives. Bayesian evaluation of informative diagnostic hypotheses is an alternative for each of the other approaches that is more flexible in the diagnostic hypotheses that can be evaluated, and it can be used in each of the 4 psychometric perspectives on diagnostic testing. After being formulated, informative diagnostic hypotheses are evaluated by means of the Bayes factor using only the data from the person to be diagnosed. Already, relatively small diagnostic tests render Bayes factors that provide convincing evidence in favor of 1 of the diagnostic hypotheses under consideration

Cognitive Diagnostic Assessment via Bayesian Evaluation of Informative Diagnostic Hypotheses

Linking and equating procedures are used to make the results of different test forms comparable. In the cases where no assumption of random equivalent groups can be made some form of linking design is used. In practice the amount of data available to link the two tests is often very limited due to logistic and security reasons, which affects the precision of linking procedures. This study proposes to enhance the quality of linking procedures based on sparse data by using Bayesian methods which combine the information in the linking data with background information captured in informative prior distributions. We propose two methods for the elicitation of prior knowledge about the difference in difficulty of two tests from subject-matter experts and explain how these results can be used in the specification of priors. To illustrate the proposed methods and evaluate the quality of linking with and without informative priors, an empirical example of linking primary school mathematics tests is presented. The results suggest that informative priors can increase the precision of linking without decreasing the accuracy. (PsycINFO Database Record

Jorine Vermeulen

Papers

Integrating data-based decision making, Assessment for Learning and diagnostic testing in formative assessment

Mainstream teachers about including deaf or hard of hearing students

Teachers' use of classroom assessment in primary school mathematics education in the Netherlands.

Cognitive Diagnostic Assessment via Bayesian Evaluation of Informative Diagnostic Hypotheses

Using expert knowledge for test linking