Predicting weather and climate: Uncertainty,ensembles and probability

Simulation-based weather and climate prediction now involves the use of methods that reflect a deep concern with uncertainty. These methods, known as ensemble prediction methods, produce multiple simulations for predictive periods of interest, using different initial conditions, parameter values and/or model structures. This paper provides a non-technical overview of current ensemble methods and considers how the results of studies employing these methods should be interpreted, paying special attention to probabilistic interpretations. A key conclusion is that, while complicated inductive arguments might be given for the trustworthiness of probabilistic weather forecasts obtained from ensemble studies, analogous arguments are out of reach in the case of long-term climate prediction. In light of this, the paper considers how predictive uncertainty should be conveyed to decision makers.     

Acceptance,values, and probability

This essay makes a case for regarding personal probabilities used in Bayesian analyses of confirmation as objects of acceptance and rejection. That in turn entails that personal probabilities are subject to the argument from inductive risk, which aims to show non-epistemic values can legitimately influence scientific decisions about which hypotheses to accept. In a Bayesian context, the argument from inductive risk suggests that value judgments can influence decisions about which probability models to accept for likelihoods and priors. As a consequence, if the argument from inductive risk is sound, then non-epistemic values can affect not only the level of evidence deemed necessary to accept a hypothesis but also degrees of confirmation themselves.     

Non-monotonic probability theory for n-state quantum systems

In previous work, a non-standard theory of probability was formulated and used to systematize interference effects involving the simplest type of quantum systems. The main result here is a self-contained, non-trivial generalization of that theory to capture interference effects involving a much broader range of quantum systems. The discussion also focuses on interpretive matters having to do with the actual/virtual distinction, non-locality, and conditional probabilities.     

Newton and the classical theory of probability

Summary Probabilistic ideas and methods from Newton's writings are discussed in § 1: Newton's ideas pertaining to the definition of probability, his probabilistic method in chronology, his probabilistic ideas and method in the theory of errors and his probabilistic reasonings on the system of the world. Newton's predecessors and his influence upon subsequent scholars are dealt with in §2: beginning with his predecessors the discussion continues with his contemporaries Arbuthnot and De Moiver, then Bentley. The section ends with Laplace, whose determinism is seen as a development of the Newtonian determinism.An addendum is devoted to Lambert's reasoning on randomness and to the influence of Darwin on statistics. A synopsis is attached at the end of the article.Abbreviations PT abridged Philosophical Transactions of the Royal Society 1665–1800 abridged. London, 1809 - Todhunter I. Todhunter, History of the mathematical theory of probability, Cambridge, 1865 To the memory of my mother, Sophia Sheynin (1900–1970)     

An empirical approach to symmetry and probability

We often rely on symmetries to infer outcomes’ probabilities, as when we infer that each side of a fair coin is equally likely to come up on a given toss. Why are these inferences successful? I argue against answering this question with an a priori indifference principle. Reasons to reject such a principle are familiar, yet instructive. They point to a new, empirical explanation for the success of our probabilistic predictions. This has implications for indifference reasoning generally. I argue that a priori symmetries need never constrain our probability attributions, even for initial credences.     

Boltzmann's probability distribution of 1877

Communicated by R. Stuewer     

Measurement outcomes and probability in Everettian quantum mechanics

The decision-theoretic account of probability in the Everett or many-worlds interpretation, advanced by David Deutsch and David Wallace, is shown to be circular. Talk of probability in Everett presumes the existence of a preferred basis to identify measurement outcomes for the probabilities to range over. But the existence of a preferred basis can only be established by the process of decoherence, which is itself probabilistic.     

The branching property of morphactin onPrunus avium seedlings

Riassunto Il trattamento di giovani piantine di ciliegio dolce con la morfattina IT 3456 provoca l'interruzione della dominanza apicale e, quindi, la emissione di germogli laterali. Un successivo trattamento con gibberellina amplifica il fenomeno, ma conduce alla morte dell'apice del germoglio principale.     

A model of calibration for subjective probability distributions and its application to aggregation of judgements

A simple model is proposed of the statistical structure underlying the calibration of auditors' subjective probability distributions for account balances, and potentially for other unknown quantities. The model relates calibration curve shape to two parameters which represent over- or underconfidence and over- or underestimation. It is fitted to data from expert auditors. Different types of account appear to have different calibration characteristics. The model helps predict approximately the effects on calibration of aggregating individual subject distributions. Aggregation improves accuracy, but produces a strong tendency towards underconfidence. One aggregation method, predicting the best judgement in the group and using it as the group judgement, is found to be quite effective, much better than averaging the fractiles of individual distributions.     

Chance,determinism and the classical theory of probability

This paper situates the metaphysical antinomy between chance and determinism in the historical context of some of the earliest developments in the mathematical theory of probability. Since Hacking's seminal work on the subject, it has been a widely held view that the classical theorists of probability were guilty of an unwitting equivocation between a subjective, or epistemic, interpretation of probability, on the one hand, and an objective, or statistical, interpretation, on the other. While there is some truth to this account, I argue that the tension at the heart of the classical theory of probability is not best understood in terms of the duality between subjective and objective interpretations of probability. Rather, the apparent paradox of chance and determinism, when viewed through the lens of the classical theory of probability, manifests itself in a much deeper ambivalence on the part of the classical probabilists as to the rational commensurability of causal and probabilistic reasoning.     

The emergence and interpretation of probability in Bohmian mechanics

A persistent question about the deBroglie–Bohm interpretation of quantum mechanics concerns the understanding of Born's rule in the theory. Where do the quantum mechanical probabilities come from? How are they to be interpreted? These are the problems of emergence and interpretation. In more than 50 years no consensus regarding the answers has been achieved. Indeed, mirroring the foundational disputes in statistical mechanics, the answers to each question are surprisingly diverse. This paper is an opinionated survey of this literature. While acknowledging the pros and cons of various positions, it defends particular answers to how the probabilities emerge from Bohmian mechanics and how they ought to be interpreted.     

The effectiveness of imprecise probability forecasts

In this paper we investigate the feasibility of algorithmically deriving precise probability forecasts from imprecise forecasts. We provide an empirical evaluation of precise probabilities that have been derived from two types of imprecise probability forecasts: probability intervals and probability intervals with second-order probability distributions. The minimum cross-entropy (MCE) principle is applied to the former to derive precise (i.e. additive) probabilities; expectation (EX) is used to derive precise probabilities in the latter case. Probability intervals that were constructed without second-order probabilities tended to be narrower than and contained in those that were amplified by second-order probabilities. Evidence that this narrowness is due to motivational bias is presented. Analysis of forecasters' mean Probability Scores for the derived precise probabilities indicates that it is possible to derive precise forecasts whose external correspondence is as good as directly assessed precise probability forecasts. The forecasts of the EX method, however, are more like the directly assessed precise forecasts than those of the MCE method.     

Understanding Deutsch's probability in a deterministic multiverse

Difficulties over probability have often been considered fatal to the Everett interpretation of quantum mechanics. Here I argue that the Everettian can have everything she needs from ‘probability’ without recourse to indeterminism, ignorance, primitive identity over time or subjective uncertainty: all she needs is a particular rationality principle.The decision-theoretic approach recently developed by Deutsch and Wallace claims to provide just such a principle. But, according to Wallace, decision theory is itself applicable only if the correct attitude to a future Everettian measurement outcome is subjective uncertainty. I argue that subjective uncertainty is not available to the Everettian, but I offer an alternative: we can justify the Everettian application of decision theory on the basis that an Everettian should care about all her future branches. The probabilities appearing in the decision-theoretic representation theorem can then be interpreted as the degrees to which the rational agent cares about each future branch. This reinterpretation, however, reduces the intuitive plausibility of one of the Deutsch–Wallace axioms (measurement neutrality).     

Evaluations of the beta probability integral by bayes and price

Summary The contribution of Bayes to statistical inference has been much discussed, whereas his evaluations of the beta probability integral have received little attention, and Price's improvements of these results have never been analysed in detail. It is the purpose of the present paper to redress this state of affairs and to show that the Bayes-Price approximation to the two-sided beta probability integral is considerably better than the normal approximation, which became popular under the influence of Laplace, although it had been stated by Price.The Bayes-Price results are obtained by approximating the skew beta density by a symmetric beta density times a factor tending to unity for n , the two functions having the same maximum and the same points of inflection. Since the symmetric beta density converges to the normal density, all the results of Laplace based on the normal distribution can be obtained as simple limits of the results of Bayes and Price. This fact was not observed either by Laplace or by Todhunter.     

Chebyshev's lectures on the theory of probability

Communicated by B. Bru     

Retinoic acid regulates avian lung branching through a molecular network

Retinoic acid (RA) is of major importance during vertebrate embryonic development and its levels need to be strictly regulated otherwise congenital malformations will develop. Through the action of specific nuclear receptors, named RAR/RXR, RA regulates the expression of genes that eventually influence proliferation and tissue patterning. RA has been described as crucial for different stages of mammalian lung morphogenesis, and as part of a complex molecular network that contributes to precise organogenesis; nonetheless, nothing is known about its role in avian lung development. The current report characterizes, for the first time, the expression pattern of RA signaling members (stra6, raldh2, raldh3, cyp26a1, rarα, and rarβ) and potential RA downstream targets (sox2, sox9, meis1, meis2, tgfβ2, and id2) by in situ hybridization. In the attempt of unveiling the role of RA in chick lung branching, in vitro lung explants were performed. Supplementation studies revealed that RA stimulates lung branching in a dose-dependent manner. Moreover, the expression levels of cyp26a1, sox2, sox9, rarβ, meis2, hoxb5, tgfβ2, id2, fgf10, fgfr2, and shh were evaluated after RA treatment to disclose a putative molecular network underlying RA effect. In situ hybridization analysis showed that RA is able to alter cyp26a1, sox9, tgfβ2, and id2 spatial distribution; to increase rarβ, meis2, and hoxb5 expression levels; and has a very modest effect on sox2, fgf10, fgfr2, and shh expression levels. Overall, these findings support a role for RA in the proximal–distal patterning and branching morphogenesis of the avian lung and reveal intricate molecular interactions that ultimately orchestrate branching morphogenesis.