The e-posterior Grünwald, Peter D
Philosophical transactions - Royal Society. Mathematical, Physical and engineering sciences/Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences,
05/2023, Volume:
381, Issue:
2247
Journal Article
Peer reviewed
Open access
We develop a representation of a decision maker's uncertainty based on e-variables. Like the Bayesian posterior, this
allows for making predictions against arbitrary loss functions that may not be ...specified ex ante. Unlike the Bayesian posterior, it provides risk bounds that have frequentist validity irrespective of prior adequacy: if the e-collection (which plays a role analogous to the Bayesian prior) is chosen badly, the bounds get loose rather than wrong, making
decision rules safer than Bayesian ones. The resulting quasi-conditional paradigm is illustrated by re-interpreting a previous influential partial Bayes-frequentist unification,
, in terms of e-posteriors. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.
The no-free-lunch theorems promote a skeptical conclusion that all possible machine learning algorithms equally lack justification. But how could this leave room for a learning theory, that shows ...that some algorithms are better than others? Drawing parallels to the philosophy of induction, we point out that the no-free-lunch results presuppose a conception of learning algorithms as purely data-driven. On this conception, every algorithm must have an inherent inductive bias, that wants justification. We argue that many standard learning algorithms should rather be understood as model-dependent: in each application they also require for input a model, representing a bias. Generic algorithms themselves, they can be given a model-relative justification.
Recently, optional stopping has been a subject of debate in the Bayesian psychology community. Rouder (
Psychonomic Bulletin & Review
21
(2), 301–308,
2014
) argues that optional stopping is no ...problem for Bayesians, and even recommends the use of optional stopping in practice, as do (Wagenmakers, Wetzels, Borsboom, van der Maas & Kievit,
Perspectives on Psychological Science
7
, 627–633,
2012
). This article addresses the question of whether optional stopping is problematic for Bayesian methods, and specifies under which circumstances and in which sense it is and is not. By slightly varying and extending Rouder’s (
Psychonomic Bulletin & Review
21
(2), 301–308,
2014
) experiments, we illustrate that, as soon as the parameters of interest are equipped with default or pragmatic priors—which means, in most practical applications of Bayes factor hypothesis testing—resilience to optional stopping can break down. We distinguish between three types of default priors, each having their own specific issues with optional stopping, ranging from no-problem-at-all (type 0 priors) to quite severe (type II priors).
E-variables are tools for retaining type-I error guarantee with optional stopping. We extend E-variables for sequential two-sample tests to general null hypotheses and anytime-valid confidence ...sequences. We provide implementations for estimating risk difference, relative risk and odds-ratios in contingency tables.
•We construct anytime-valid confidence intervals for data streams using E-variables.•Our method can be implemented for arbitrary notions of effect size.•As an example, estimate relative risk, risk difference and odds ratio in 2x2 tables.
Biocatalysts (enzymes and whole cells) catalyze reactions with the advantage of superior chemo-, regio-, and stereo-specificity in mild conditions, thereby avoiding the production of larger amounts ...of waste. The currently great practical importance of immobilized biocatalysts is expressed by the high number of scientific publications together with an ever increasing number of different applications in this area of enzyme technology. This mainly relies on new research results with respect to immobilization techniques and the development of advanced carrier materials designed for this purpose.
The employment of immobilized biocatalysts is one of the most effective and powerful tools used in the modern chemical industry as a prerequisite for an economical and environmentally friendly production process. The book presented here reflects the currently great practical importance of immobilized biocatalysts by means of a variety of actual examples. They comprise the immobilization of enzymes from different enzyme classes and a variety of whole cells with particular importance for the production of compounds for application in the chemical, pharmaceutical and food industry (in part from renewable resources), biohydrogen production, the fabrication of biosensors, and the treatment of waste water. Several articles introduce new research results with respect to immobilization techniques and the development of carrier materials designed for this purpose.
In addition, review articles provide among others an overview of the industrial application of immobilized biocatalysts in various areas including the energy sector, or discuss the many advantages of metal–organic frameworks (MOFs) as platforms for enzyme immobilization. They deal with the pros and cons of many inorganic, organic, hybrid and composite materials, including nano-supports, used for the immobilization of biocatalysts, and with the development of engineered strains applied to the conversion of lignocellulosic biomass to platform chemicals by consolidated bioprocessing.
In summary, the articles meet the state of the art of both scientific and technical standards and the book is indispensable for all those involved in the various aspects of this topic.
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