In repeated games with Nash equilibria in mixed strategies, players optimize by playing randomly. Players are boundedly rational in their randomization efforts. Arguably, they have no internal randomization facility and they fashion external randomization aids from the environment. By conditioning on past play, boundedly rational players exhibit a pattern. The pattern is characterized by cognit...

1. Davey Smith G, Ebrahim S. ‘Mendelian randomization’: can genetic epidemiology contribute to understanding environmental determinants of disease? Int J Epidemiol 2003;32:1–22. 2. Burgess S, Timpson NJ, Ebrahim S, Davey Smith G. Mendelian randomization: where are we now and where are we going? Int J Epidemiol 2015;44:379–88. 3. Glymour MM, Tchetgen EJT, Robins JM. Credible Mendelian randomizat...

BACKGROUND Randomization is considered to be a key feature to protect against bias in randomized clinical trials. Randomization induces comparability with respect to known and unknown covariates, mitigates selection bias, and provides a basis for inference. Although various randomization procedures have been proposed, no single procedure performs uniformly best. In the design phase of a clinica...

Randomization and blocking have the potential to prevent the negative impacts of nonbiologic effects on molecular biomarker discovery. Their use in practice, however, has been scarce. To demonstrate the logistic feasibility and scientific benefits of randomization and blocking, we conducted a microRNA study of endometrial tumors (n = 96) and ovarian tumors (n = 96) using a blocked randomization...

We examine the effect of a parameter λ used to calibrate how responsive randomization probabilities are to observed data in an adaptively randomized clinical trial. We define and motivate the parameter λ and demonstrate how varying this parameter effects the operating characteristics of example clinical trial designs.

• The assumption of independence of errors, i.e., error of an observation is not related to or depends upon that of another. This assumption is usually assured with the use of proper randomization procedure. However, if there is any systematic pattern in the arrangement of treatments from one replication to another, errors may be nonindependent. • The assumption of additive effects can be defin...

We provide a new interpretation of mixed strategy equilibria that incorporates both von Neumann and Morgenstern’s classical concealment role of mixing as well as the more recent Bayesian view originating with Harsanyi. For any two-person game, G, we consider an incomplete information game, IG; in which each player’s type is the probability he assigns to the event that his mixed strategy in G is...

Two-level factorial and fractional factorial designs have played a prominent role in the theory and practice of experimental design. Though commonly used in industrial experiments to identify the significant effects, it is often undesirable to perform the trials of a factorial design (or, fractional factorial design) in a completely random order. Instead, restrictions are imposed on the randomi...

The evolving role of randomization in Bayesian Analysis as well as arguments for and against randomization is discussed. We note that Bayesian Analysis is moving towards a substantially reduced role for randomization, but it is a sample surveys area where more future work of this kind is needed.