… We look at various methods of calibration by initial … level randomness notions going back
to the work of Kurtz [73], Kautz [61], and Solovay [125]; and other calibrations of randomness …

… random variables taking values in [0, 1], while h[x](y) is just a number in [0, 1] (there is no
randomness). This difference will be crucial to distinguishing different notions of calibration. …

… Recently there has been exciting progress in our understanding of algorithmic randomness
for reals, its calibration, and its connection with classical measures of complexity such as …

… ˽ This theory also allows us to calibrate partial randomness. Notions of partial randomness
can … ˽ It also gives us insight into how much and what kinds of randomness are needed for …

… Inspired by this we can calibrate the complexity of ce reals in terms of their Schnorr complexity.
That is, we say that a <sch P iff for all computable machines M, there is a constant c and …

… algorithm is automatically well-calibrated in our sense, there … is: a prediction algorithm is
well-calibrated if any evidence of … calibration and randomness; this will be done following [7]. …

… We seek to explicate the intuitive idea that this outcome sequence exhibits “randomness.”
A minimal requirement for this is generally accepted to be the existence of the limiting relative …

… , calibration and regret, predictiveness and randomness, … calibration dominates all available3
tests used to evaluate forecasts of identifiable properties (Theorem 6.6). Hence, calibration …

… 4], of trying to calibrate the algorithmic randomness of reals1). There are three basic approaches
to algorithmic randomness. They are to characterize randomness in terms of algorithmic …

… study such objects in terms of algorithmic randomness, culminating in some recent work of
the author with Hirschfeldt, Laforte, and Nies concerning methods of calibrating randomness. …