This paper describes the application of eight statistical and machine-learning methods to derive computer models for predicting mortality of hospital patients with pneumonia from their findings at initial presentation. The eight models were each constructed based on 9847 patient cases and they were each evaluated on 4352 additional cases. The primary evaluation metric was the error in predicted survival as a function of the fraction of patients predicted to survive. This metric is useful in assessing a model’s potential to assist (...) a clinician in deciding whether to treat a given patient in the hospital or at home. We examined the error rates of the models when predicting that a given fraction of patients will survive. We examined survival fractions between 0.1 and 0.6. Over this range, each model’s predictive error rate was within 1% of the error rate of every other model. When predicting that approximately 30°K of the patients will survive, all the models have an error rate of less than 1.5%. The models are distinguished more by the number of variables and parameters that they contain than by their error rates; these differences suggest which models may be the most amenable to future implementation as paper-based guidelines. (shrink)

A reprint of the Prentice-Hall edition of 1992. Prepared by nine distinguished philosophers and historians of science, this thoughtful reader represents a cooperative effort to provide an introduction to the philosophy of science focused on cultivating an understanding of both the workings of science and its historical and social context. Selections range from discussions of topics in general methodology to a sampling of foundational problems in various physical, biological, behavioral, and social sciences. Each chapter contains a list of suggested readings (...) and study questions. (shrink)

is every bit as intelligible and philosophically respectable as many other doctrines currently in favor, e.g., the doctrine that mental events are identical with brain events; the attempt to give a linguistic construal of this latter doctrine meets many of the same sorts of difficulties encountered above (see Hempel, op. cit.). Secondly, I think that evidence for universal determinism may not, as a matter of fact, be so hard to come by as one might imagine. It is a striking fact (...) about our world that we never observe any genuine cases of parallelism; it always seems possible to design some sort of interaction between any two genuine empirical magnitudes. If this is correct, then a true theory T can be deterministic only if universal determinism reigns. (shrink)

A general principle for good pedagogic strategy is this: other things equal, make the essential principles of the subject explicit rather than tacit. We think that this principle is routinely violated in conventional instruction in statistics. Even though most of the early history of probability theory has been driven by causal considerations, the terms “cause” and “causation” have practically disappeared from statistics textbooks. Statistics curricula guide students away from the concept of causality, into remembering perhaps the cliche disclaimer “correlation does (...) not mean causation,” but rarely thinking about what correlation does mean. The treatment of causality is a serious handicap to later studies of such topics as experimental design, where often the main goal is to establish (or disprove) causation. Much of the technical vocabulary of the language used in research design textbooks consists in euphemisms for specific causal relations, e.g, “latent variable,” “intervening variable,” “confounding factor,” etc. The multiplicity of terms used to refer to causation results in confusion and, in effect, may hinder understanding of the basic principles of research design. (shrink)

Measures of algorithmic bias can be roughly classified into four categories, distinguished by the conditional probabilistic dependencies to which they are sensitive. First, measures of "procedural bias" diagnose bias when the score returned by an algorithm is probabilistically dependent on a sensitive class variable (e.g. race or sex). Second, measures of "outcome bias" capture probabilistic dependence between class variables and the outcome for each subject (e.g. parole granted or loan denied). Third, measures of "behavior-relative error bias" capture probabilistic dependence between (...) class variables and the algorithmic score, conditional on target behaviors (e.g. recidivism or loan default). Fourth, measures of "score-relative error bias" capture probabilistic dependence between class variables and behavior, conditional on score. Several recent discussions have demonstrated a tradeoff between these different measures of algorithmic bias, and at least one recent paper has suggested conditions under which tradeoffs may be minimized. -/- In this paper we use the machinery of causal graphical models to show that, under standard assumptions, the underlying causal relations among variables forces some tradeoffs. We delineate a number of normative considerations that are encoded in different measures of bias, with reference to the philosophical literature on the wrongfulness of disparate treatment and disparate impact. While both kinds of error bias are nominally motivated by concern to avoid disparate impact, we argue that consideration of causal structures shows that these measures are better understood as complicated and unreliable measures of procedural biases (i.e. disparate treatment). Moreover, while procedural bias is indicative of disparate treatment, we show that the measure of procedural bias one ought to adopt is dependent on the account of the wrongfulness of disparate treatment one endorses. Finally, given that neither score-relative nor behavior-relative measures of error bias capture the relevant normative considerations, we suggest that error bias proper is best measured by score-based measures of accuracy, such as the Brier score. (shrink)

In her 1996 book, Error and the Growth of Experimental Knowledge, Deborah Mayo argues that use- (or heuristic) novelty is not a criterion we need to consider in assessing the evidential value of observations. Using the notion of a ''severe'' test, Mayo claims that such novelty is valuable only when it leads to severity, and never otherwise. To illustrate her view, she examines the historical case involving the famous 1919 British eclipse expeditions that generated observations supporting Einstein's theory of gravitation (...) over Newton's. My plan here is to defend use-novelty as a valuable methodological principle. I begin by exposing a weakness in Mayo's criticism of use-novelty. Remedying this weakness re-establishes the worth of use-novelty under specific conditions; in particular, heuristically novel data are to be preferred, as I will say, ''prima facie''. Armed with this revised version of use-novelty, I re-examine the history of the eclipse experiments and offer an interpretation of this episode that to an extent-and contrary to Mayo-restores the mildly heretical, Earman/Glymour evaluation of this episode offered in their (1980). I conclude by responding to criticism of my assessment of Mayo's work. (shrink)

Recent discussions of experimental tests of the Sum Rule have been carried out in the context of the special circumstances attending the Cross-Ramsey experiment. A more general analysis of possible tests is presented. A technical mistake of Fine and Glymour concerned with a misunderstanding of the physics of the Cross-Ramsey experiment is explained and a detailed analysis of a thought experiment based on the Einstein-Podolsky-Rosen wave function is given. It is concluded, in agreement with Fine, that scattering experiments do (...) not test the Sum Rule as a principle which supplements standard quantum mechanics. (shrink)

In her 1996 book, Error and the Growth of Experimental Knowledge, Deborah Mayo argues that use- (or heuristic) novelty is not a criterion we need to consider in assessing the evidential value of observations. Using the notion of a “severe” test, Mayo claims that such novelty is valuable only when it leads to severity, and never otherwise. To illustrate her view, she examines the historical case involving the famous 1919 British eclipse expeditions that generated observations supporting Einstein's theory of gravitation (...) over Newton's. My plan here is to defend use-novelty as a valuable methodological principle. I begin by exposing a weakness in Mayo's criticism of use-novelty. Remedying this weakness re-establishes the worth of use-novelty under specific conditions; in particular, heuristically novel data are to be preferred, as I will say, “prima facie”. Armed with this revised version of use-novelty, I re-examine the history of the eclipse experiments and offer an interpretation of this episode that to an extent—and contrary to Mayo—restores the mildly heretical, Earman/Glymour evaluation of this episode offered in their (1980). I conclude by responding to criticism of my assessment of Mayo's work. (shrink)

This anthology presents work on major topics surrounding the concept of evidence as employed in the empirical sciences. Focusing on the "classificatory" concept of evidence rather than the quantitative "degree of confirmation," the selections include Carl G. Hempel's satisfaction definition, R.B. Braithwaite's hypothetic-deductive view, N.R. Hanson's account of retroduction, Nelson Goodman's entrenchment theory, probability definitions discussed by Rudolf Carnap and Wesley Salmon, Clark Glymour's bootstrap theory, and a view of Achinstein's that combines probability and explanation.

The main aim of this paper is to revisit the curve fitting problem using the reliability of inductive inference as a primary criterion for the ‘fittest' curve. Viewed from this perspective, it is argued that a crucial concern with the current framework for addressing the curve fitting problem is, on the one hand, the undue influence of the mathematical approximation perspective, and on the other, the insufficient attention paid to the statistical modeling aspects of the problem. Using goodness-of-fit as the (...) primary criterion for ‘best', the mathematical approximation perspective undermines the reliability of inference objective by giving rise to selection rules which pay insufficient attention to ‘accounting for the regularities in the data'. A more appropriate framework is offered by the error-statistical approach, where (i) statistical adequacy provides the criterion for assessing when a curve captures the regularities in the data adequately, and (ii) the relevant error probabilities can be used to assess the reliability of inductive inference. Broadly speaking, the fittest curve (statistically adequate) is not determined by the smallness if its residuals, tempered by simplicity or other pragmatic criteria, but by the nonsystematic (e.g. white noise) nature of its residuals. The advocated error-statistical arguments are illustrated by comparing the Kepler and Ptolemaic models on empirical grounds. ‡I am grateful to Deborah Mayo and Clark Glymour for many valuable suggestions and comments on an earlier draft of the paper; estimating the Ptolemaic model was the result of Glymour's prompting and encouragement. †To contact the author, please write to: Department of Economics, Virginia Tech 3019 Pamplin Hall (0316), Blacksburg, VA 24061; e-mail: [email protected]. (shrink)

Classical temples in ancient Greece show two deterministic illusionistic principles of architecture, which govern their functional design: geometric proportionalism and a set of illusion-strengthening rules in the proportionalism's stochastic margin. Animal morphology, in its mechanistic-deductive revival, applies just one architectural principle, which is not always satisfactory. Whether a Greek Classical situation occurs in the architecture of living structure is to be investigated by extreme testing with deductive methods.Three deductive methods for explanation of living structure in animal morphology are proposed: the (...) parts, the compromise, and the transformation deduction. The methods are based upon the systems concept for an organism, the flow chart for a functionalistic picture, and the network chart for a structuralistic picture, whereas the optimal design serves as the architectural principle for living structure. These methods show clearly the high explanatory power of deductive methods in morphology, but they also make one open end most explicit: neutral issues do exist. (shrink)

Through the introduction of his ‘common cause principle’ [The Direction of Time, 1956], Hans Reichenbach was the first to formulate a precise link relating causal claims to statements of probability. Despite some criticism, the principle has been hugely influential and successful—a pillar of scientific practice, as well as guiding our reasoning in everyday life. However, Bell’s theorem, taken in conjunction with quantum theory, challenges this principle in a fundamental sense at the microscopic level. For the same reason, the celebrated causal (...) model framework pioneered by Pearl, as well as by Spirtes, Glymour and Scheines, defies satisfactory causal explanations of quantum correlations—the role of the ‘causal Markov condition’ in this framework amounts to a generalisation of Reichenbach’s principle. Much effort has been devoted to the development of quantum causal models to overcome this challenge and to study whether a principled way of causal reasoning, albeit adjusted in its terms, can be maintained when it comes to quantum physics. A clarification of what quantum causal relations are supposed to be is also a much needed step in light of the hotly debated topic of causality in foundations of quantum theory, e.g. in the study of ‘indefinite causal structures’. This paper reports and discusses a framework of quantum causal models and argues that it is promising and interesting for two main reasons. First, it can be seen as a prime example of a recent research programme that took direct and fruitful inspiration from ideas first formulated by Reichenbach—it began by asking, and giving an answer to, how the common cause principle could be generalised appropriately to quantum theoretical terms. Second, the framework did not only facilitate generalisations of the core theorems of the classical framework of causal models, but, above all, it has a theorem at its center that justifies the ‘quantum causal Markov condition’ on the basis of what arguably is a natural definition of causal relations in quantum theory. This provides a conceptually clear grounding of the framework, as well as a proposal for the needed clarification of quantum causal relations in the foundations of quantum theory more generally. (shrink)

Wegner (2002) fails to (1) distinguish conscious will and voluntariness; (2) account for everyday willed acts; and (3) individuate thoughts and acts. Wegner incorrectly implies that (4) we experience acts as willed only when they are caused by unwilled thoughts; (5) thoughts are never true causes of actions; and (6) we experience ourselves as first performing mental acts which then cause our intentional actions.

Henry Leonard and Karel Lambert first introduced so-called presupposition-free (or just simply: free) logics in the 1950’s in order to provide a logical framework allowing for non-denoting singular terms (be they descriptions or constants) such as “the largest prime” or “Pegasus” (see Leonard [1956] and Lambert [1960]). Of course, ever since Russell’s paradigmatic treatment of definite descriptions (Russell [1905]), philosophers have had a way to deal with such terms. A sentence such as “the..

This paper forms an introduction to this issue, the contents of which arose directly or indirectly from a conference in May 2001 on Corruption of scientific integrity? — The commercialisation of academic science. The introduction, in recent decades, of business culture and values into universities and research institutions is incompatible with the openness which scientific and all academic pursuit traditionally require. It has given rise to a web of problems over intellectual property and conflict of interest which has even led (...) to corporate sponsors’ suppressing unfavourable results of clinical trials, to the detriment of patients’ health. Although there are those who see the norms of science developing to recognise the importance of instrumental science aiming at specific goals and of knowledge judged by its value in a context of application, none justifies the covert manipulation of results by vested interest. Public awareness of these problems is growing and creating a climate of opinion where they may be addressed. We suggest a way forward by the introduction of nationally and internationally-accepted guidelines for industrial collaboration which contain proper protections of the core purposes of universities and of the independence of their research. Some codes suggested for this purpose are discussed. We note that some universities are moving to adopt such codes of conduct, but argue the need for strong support from the government through its funding bodies. (shrink)

A central theme in western philosophy was to find formal methods that can reliably discover empirical relationships and their explanations from data assembled from experience. As a philosophical project, that ambition was abandoned in the 20th century and generally dismissed as impossible. It was replaced in philosophy by neo-Kantian efforts at reconstruction and justification, and in professional statistics by the more limited ambition to estimate a small number of parameters in pre-specified hypotheses. The influx of “big data” from climate science, (...) neuropsychology, biology, astronomy and elsewhere implicitly called for a revival of the grander philosophical ambition. Search algorithms are meeting that call, but they pose a problem: how are their accuracies to be assessed in domains where experimentation is limited or impossible? Increasingly, the answer is through simulation of data from models of the kind of process in the domain. In some cases, these innovations require rethinking how the accuracy and informativeness of inference methods can be assessed. Focusing on causal inference, we give an example from neuroscience, but to show that the model/simulation strategy is not confined to causal inference, we also consider two classification problems from astrophysics: identifying exoplanets and identifying dark matter concentrations. (shrink)

It is commonplace to encounter nonstationary or heterogeneous data, of which the underlying generating process changes over time or across data sets. Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper we develop a principled framework for causal discovery from such data, called Constraint-based causal Discovery from Nonstationary/heterogeneous Data, which addresses two important questions. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the (...) causal structure over observed variables. Second, we present a way to determine causal orientations by making use of independence changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. Experimental results on various synthetic and real-world data sets are presented to demonstrate the efficacy of our methods. (shrink)

The ability to identify the mineral composition of rocks and softs is an important tool for the exploration of geological sites. For instance, NASA intends to design robots that are sufficiently autonomous to perform this task on planetary missions. Spectrometer readings provide one important source of data for identifying sites with minerals of interest. Reflectance spectrometers measure intensities of light reflected from surfaces over a range of wavelengths. Spectral intensity patterns may in some cases be sufficiently distinctive for proper identification (...) of minerals or classes of minerals. For some mineral classes, carbonates for example, specific short spectral intervals are known to carry a distinctive signature. Finding similar distinctive spectral ranges for other mineral classes is not an easy problem. We propose and evaluate data-driven techniques that automatically search for spectral ranges optimized for specific minerals. In one set of studies, we partition the whole interval of wavelengths available in our data into sub-intervals, or bins, and use a genetic algorithm to evaluate a candidate selection of subintervals. As alternatives to this computationally expensive search technique, we present an entropy-based heuristic that gives higher scores for wavelengths more likely to distinguish between classes, as well as other greedy search procedures. Results are presented for four different classes, showing reasonable improvements in identifying some, but not all, of the mineral classes tested. (shrink)

We study the identifiability and estimation of functional causal models under selection bias, with a focus on the situation where the selection depends solely on the effect variable, which is known as outcome-dependent selection. We address two questions of identifiability: the identifiability of the causal direction between two variables in the presence of selection bias, and, given the causal direction, the identifiability of the model with outcome-dependent selection. Regarding the first, we show that in the framework of post-nonlinear causal models, (...) once outcome-dependent selection is properly modeled, the causal direction between two variables is generically identifiable; regarding the second, we identify some mild conditions under which an additive noise causal model with outcome-dependent selection is to a large extent identifiable. We also propose two methods for estimating an additive noise model from data that are generated with outcome-dependent selection. (shrink)

In this paper we introduce the notion of a set algebra S satisfying a system E of equations. After defining a notion of freeness for such algebras, we show that, for any system E of equations, set algebras that are free in the class of structures satisfying E exist and are unique up to a bisimulation. Along the way, analogues of classical set-theoretic and algebraic properties are investigated.

Aldo Antonelli offers a novel view on abstraction principles in order to solve a traditional tension between different requirements: that the claims of science be taken at face value, even when involving putative reference to mathematical entities; and that referents of mathematical terms are identified and their possible relations to other objects specified. In his view, abstraction principles provide representatives for equivalence classes of second-order entities that are available provided the first- and second-order domains are in the equilibrium dictated by (...) the abstraction principles, and whose choice is otherwise unconstrained.entities are the referents of abstraction terms: such referents are to an extent indeterminate, but we can still quantify over them, predicate identity or non-identity, etc. Our knowledge of them is limited, but still substantial: we know whatever has to be true no matter how the representatives are chosen, i.e., what is true in all models of the corresponding abstraction principles. This view is backed up by an “austere” conception of universals, according to which these are first-order objects, i.e., ways of collecting first-order objects. Antonelli thus claims that second-order logic does not import any novel ontological commitment beyond ontology of first-order, naturalistically acceptable, objects. Moreover, in the case of arithmetic, even if Hume’s Principle is construed as described above, Frege’s Theorem goes through unaffected, since there is nothing in its proof that depends on an account of the “true nature” of numbers. A viable construal of logicism is then given by the combination of semantic nominalism and a naturalistic conception of abstraction. [Editors note]. (shrink)