Through his S–R model of statistical relevance, Wesley Salmon offers a solution to the scientific explanation of objectively improbable events.

Based on Newton’s laws reformulated in the Hamiltonian dynamics combined with statistical mechanics, we formulate a statistical mechanical theory supporting the hypothesis of a closed universe oscillating in phase-space. We find that the behavior of this universe as a whole can be represented by a free entropic oscillator whose lifespan is nonhomogeneous, thus implying that time is shorter or longer according to the state of this universe given through its entropy. We conclude that time reduces to the entropy production of (...) this universe and that a nonzero entropy production means that local fluctuations could exist giving rise to the appearance of masses and to the curvature of the space. (shrink)

The law views with suspicion statistical evidence, even evidence that is probabilistically on a par with direct, individual evidence that the law is in no way suspicious of. But it has proved remarkably hard to either justify this suspicion, or to debunk it. In this paper, we connect the discussion of statistical evidence to broader epistemological discussions of similar phenomena. We highlight Sensitivity – the requirement that a belief be counterfactually sensitive to the truth in a specific way – as (...) a way of epistemically explaining the legal suspicion towards statistical evidence. Still, we do not think of this as a satisfactory vindication of the reluctance to rely on statistical evidence. Knowledge – and Sensitivity, and indeed epistemology in general – are of little, if any, legal value. Instead, we tell an incentive-based story vindicating the suspicion towards statistical evidence. We conclude by showing that the epistemological story and the incentive-based story are closely and interestingly related, and by offering initial thoughts about the role of statistical evidence in morality. (shrink)

Statistical evidence—say, that 95% of your co-workers badmouth each other—can never render resenting your colleague appropriate, in the way that other evidence (say, the testimony of a reliable friend) can. The problem of statistical resentment is to explain why. We put the problem of statistical resentment in several wider contexts: The context of the problem of statistical evidence in legal theory; the epistemological context—with problems like the lottery paradox for knowledge, epistemic impurism and doxastic wrongdoing; and the context of a (...) wider set of examples of responses and attitudes that seem not to be appropriately groundable in statistical evidence. Regrettably, we do not come up with a fully general, fully adequate, fully unified account of all the phenomena discussed. But we give reasons to believe that no such account is forthcoming, and we sketch a somewhat messier account that may be the best that can be had here. (shrink)

Between 1799 and 1806, trials of vaccination to determine its safety and efficacy were undertaken in hospitals in London, Paris, Vienna, and Boston. These trials were among the first instances of formal hospital evaluations of a medical procedure and signal a growing acceptance of a relatively new approach to medical practice. These early evaluations of smallpox vaccination also relied on descriptive and quantitative accounts, as well as probabilistic analyses, and thus occupy a significant, yet hitherto unexamined, place in the history (...) of medical statistics. (shrink)

Researchers in the social and behavioral sciences often have clear expectations about the order/direction of the parameters in their statistical model. For example, a researcher might expect that regression coefficient β 1 is larger than β 2 and β 3. The corresponding hypothesis is H : β 1 > {β 2, β 3 } and this is known as an (order) constrained hypothesis. A major advantage of testing such a hypothesis is that power can be gained and inherently a smaller (...) sample size is needed. This article discusses this gain in sample size reduction, when an increasing number of constraints is included into the hypothesis. The main goal is to present sample-size tables for constrained hypotheses. A sample-size table contains the necessary sample-size at a pre-specified power (say, 0.80) for an increasing number of constraints. To obtain sample-size tables, two Monte Carlo simulations were performed, one for ANOVA and one for multiple regression. Three results are salient. First, in an ANOVA the needed sample-size decreases with 30–50% when complete ordering of the parameters is taken into account. Second, small deviations from the imposed order have only a minor impact on the power. Third, at the maximum number of constraints, the linear regression results are comparable with the ANOVA results. However, in the case of fewer constraints, ordering the parameters (e.g., β 1 > β 2 ) results in a higher power than assigning a positive or a negative sign to the parameters (e.g., β 1 > 0). (shrink)

This article focuses on the role of statistical concepts in both experiment and theory in various scientific disciplines, especially physics, including astronomy, and psychology. In Sect. 1 the concept of uncertainty in astronomy is analyzed from Ptolemy to Laplace and Gauss. In Sect. 2 theoretical uses of probability and statistics in science are surveyed. Attention is focused on the historically important example of radioactive decay. In Sect. 3 the use of statistics in biology and the social sciences is examined, with (...) detailed consideration of various Chi-square statistical tests. Such tests are essential for proper evaluation of many different kinds of scientific hypotheses. (shrink)

The advance of science and human knowledge is impeded by misunderstandings of various statistics, insufficient reporting of findings, and the use of numerous standardized and non-standardized presentations of essentially identical information. Communication with journalists and the public is hindered by the failure to present statistics that are easy for non-scientists to interpret as well as by use of the word significant, which in scientific English does not carry the meaning of "important" or "large." This article promotes a new standard method (...) for reporting two-group and two-variable statistics that can enhance the presentation of relevant information, increase understanding of findings, and replace the current presentations of two-group ANOVA, t-tests, correlations, chi-squares, and z-tests of proportions. A brief call to highly restrict the publication of risk ratios, odds ratios, and relative increase in risk percentages is also made, since these statistics appear to provide no useful scientific information regarding the magnitude of findings. (shrink)

The fundamental problem on which Ilya Prigogine and the Brussels–Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of time (...) was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels–Austin Group, is to consider the observed direction of time to be a basic physical phenomenon due to the dynamics of physical systems. This essay focuses mainly on recent developments in the Brussels–Austin Group after the mid-1980s. The fundamental concerns are the same as in their earlier approaches (subdynamics, similarity transformations), but the contemporary approach utilizes rigged Hilbert space (whereas the older approaches used Hilbert space). While the emphasis on nonequilibrium statistical mechanics remains the same, their more recent approach addresses the physical features of large Poincare systems, nonlinear dynamics and the mathematical tools necessary to analyze them. (shrink)

Statistics in public life .................................................................................................... .....5 Things and numbers............................................................................................. ...................8 Representative samples............................................................................................. ..........8 Averages: meaning and relevance .....................................................................................9 Correlations........................................................................................ ................................10 Applied statistics .................................................................................................... ................13 Relative risks .................................................................................................... ..................14 Relative risk versus absolute risk.....................................................................................16 Problems of classification and confounding factors....................................................17 Epidemiological research............................................................................................ ..........19 Publication bias................................................................................................ ..................20 Statistical significance versus scientific relevance................................................................24 Relative risk again............................................................................................... ...............24 P-values............................................................................................ ...................................25 Confidence intervals .................................................................................................... .....26 Correlation is not causation .............................................................................................26 An infamous episode .................................................................................................... ....27 Terror, utopianism and power .............................................................................................29 Faith and science .................................................................................................... ...........29 Fear and power: the precautionary principle.................................................................30 Utopian salvation........................................................................................... ....................32....

This study examined the effect of a prior bout of exercise on implicit cognition. Specifically, we examined whether a prior bout of moderate intensity exercise affected performance on a statistical learning task in healthy adults. A total of 42 participants were allocated to one of three conditions—a control group, a group that exercised for 15 min prior to the statistical learning task, and a group that exercised for 30 min prior to the statistical learning task. The participants in the exercise (...) groups cycled at 60% of their respective V˙O2max. Each group demonstrated significant statistical learning, with similar levels of learning among the three groups. Contrary to previous research that has shown that a prior bout of exercise can affect performance on explicit cognitive tasks, the results of the current study suggest that the physiological stress induced by moderate-intensity exercise does not affect implicit cognition as measured by statistical learning. (shrink)

An examination of topics involved in statistical reasoning with imprecise probabilities. The book discusses assessment and elicitation, extensions, envelopes and decisions, the importance of imprecision, conditional previsions and coherent statistical models.

There has long been an impression that reliabilism implies externalism and that frequentist statistics, due to its reliabilist nature, is inherently externalist. I argue, however, that frequentist statistics can plausibly be understood as a form of internalist reliabilism -- internalist in the conventional sense, yet reliabilist in certain unconventional and intriguing ways. Crucially, in developing the thesis that reliabilism does not imply externalism, my aim is not to stretch the meaning of ‘reliabilism’ merely to sever the implication. Instead, it is (...) to gain a deeper understanding of frequentist statistics, which stands as one of the most sustained attempts by scientists to develop an epistemology for their own use. (shrink)

The book explores several open questions in the philosophy of statistical mechanics. Each chapter is written by a leading expert in the field. Here is a list of some questions that are addressed in the book: 1) Boltzmann showed how the phenomenological gas laws of thermodynamics can be derived from statistical mechanics. Since classical mechanics is a deterministic theory there are no probabilities in it. Since statistical mechanics is based on classical mechanics, all the probabilities statistical mechanics talks about cannot (...) be fundamental. However, if probabilities are epistemic, how can they play a role, as they seem to do, in laws, explanation, and prediction? 2) Many physicists use the notion of typicality instead of the one of probability when discussing statistical mechanics. What is the connection between the two notions? 3) How can one extend Boltzmann’s analysis to the quantum domain, where some theories are indeterministic? 4) Boltzmann’s explanation fundamentally involves cosmology: for the explanation to go through the Big Bang needs to have had extremely low entropy. Does the fact that the Big Bang was a low entropy state imply that it was, in some sense, “highly improbable” and requires an explanation? 5) What exactly is the connection between statistical and classical mechanics? Is the one of theory reduction or there is no such thing? 6) Statistical mechanics has two main formulation: one due to Botzmann and the other due to Gibbs. What is the connection between the two formulations . (shrink)

Recently, the practice of deciding legal cases on purely statistical evidence has been widely criticised. Many feel uncomfortable with finding someone guilty on the basis of bare probabilities, even though the chance of error might be stupendously small. This is an important issue: with the rise of DNA profiling, courts are increasingly faced with purely statistical evidence. A prominent line of argument—endorsed by Blome-Tillmann 2017; Smith 2018; and Littlejohn 2018—rejects the use of such evidence by appealing to epistemic norms that (...) apply to individual inquirers. My aim in this paper is to rehabilitate purely statistical evidence by arguing that, given the broader aims of legal systems, there are scenarios in which relying on such evidence is appropriate. Along the way I explain why popular arguments appealing to individual epistemic norms to reject legal reliance on bare statistics are unconvincing, by showing that courts and individuals face different epistemic predicaments (in short, individuals can hedge when confronted with statistical evidence, whilst legal tribunals cannot). I also correct some misconceptions about legal practice that have found their way into the recent literature. (shrink)

In typical statistical learning studies, researchers define sequences in terms of the probability of the next item in the sequence given the current item (or items), and they show that high probability sequences are treated as more familiar than low probability sequences. Existing accounts of these phenomena all assume that participants represent statistical regularities more or less as they are defined by the experimenters—as sequential probabilities of symbols in a string. Here we offer an alternative, or possibly supplementary, hypothesis. Specifically, (...) rather than identifying or labeling individual stimuli discretely in order to predict the next item in a sequence, we need only assume that the participant is able to represent the stimuli as evincing particular similarity relations to one another, with sequences represented as trajectories through this similarity space. We present experiments in which this hypothesis makes sharply different predictions from hypotheses based on the assumption that sequences are learned over discrete, labeled stimuli. We also present a series of simulation models that encode stimuli as positions in a continuous two‐dimensional space, and predict the next location from the current location. Although no model captures all of the data presented here, the results of three critical experiments are more consistent with the view that participants represent trajectories through similarity space rather than sequences of discrete labels under particular conditions. (shrink)

The past two decades have seen a dramatic growth in the use of statisticians and economists for the presentation of expert testimony in legal proceedings. In this paper, we describe a hypothetical case modeled on real ones and involving statistical testimony regarding the causal effect of lead on lowering the IQs of children who ingest lead paint chips. The data we use come from a well-known pioneering study on the topic and the analyses we describe as the expert testimony are (...) similar to ones that can be found in major scientific journals. The battle of the experts in this hypothetical case resembles that which many encounter as expert witnesses. The paper concludes with some observations and advice. (shrink)

There is little empirical evidence showing a direct link between a capacity for statistical learning (SL) and proficiency with natural language. Moreover, discussion of the role of SL in language acquisition has seldom focused on literacy development. Our study addressed these issues by investigating the relationship between SL and reading ability in typically developing children and healthy adults. We tested SL using visually presented stimuli within a triplet learning paradigm and examined reading ability by administering the Wide Range Achievement Test (...) (WRAT-4; Wilkinson & Robertson, 2006). A total of 38 typically developing children (mean age of 9;5 years, range 6;4–12;5) and 37 healthy adults (mean age of 21 years, range 18–34) were assessed. In children, SL was significantly related to reading ability. Importantly, this relationship was independent of grade and also age. The adult data, too, revealed that SL was significantly related to reading ability. A regression analysis of the combined child and adult data revealed that SL accounted for a unique amount of variance in reading ability, after age and attention had been taken into consideration. For the first time, this study provides empirical evidence that a capacity for more effective SL is related to higher reading ability in the general population. (shrink)

A naturalistic scheme of primitive conceptual representations is proposed using the statistical measure of mutual information. It is argued that a concept represents, not the class of objects that caused its tokening, but the class of objects that is most likely to have caused it (had it been tokened), as specified by the statistical measure of mutual information. This solves the problem of misrepresentation which plagues causal accounts, by taking the representation relation to be determined via ordinal relationships between conditional (...) probabilities. The scheme can deal with statistical biases and does not rely on arbitrary criteria. Implications for the theory of meaning and semantic content are addressed. (shrink)

Predictive algorithms are playing an increasingly prominent role in society, being used to predict recidivism, loan repayment, job performance, and so on. With this increasing influence has come an increasing concern with the ways in which they might be unfair or biased against individuals in virtue of their race, gender, or, more generally, their group membership. Many purported criteria of algorithmic fairness concern statistical relationships between the algorithm’s predictions and the actual outcomes, for instance requiring that the rate of false (...) positives be equal across the relevant groups. We might seek to ensure that algorithms satisfy all of these purported fairness criteria. But a series of impossibility results shows that this is impossible, unless base rates are equal across the relevant groups. What are we to make of these pessimistic results? I argue that none of the purported criteria, except for a calibration criterion, are necessary conditions for fairness, on the grounds that they can all be simultaneously violated by a manifestly fair and uniquely optimal predictive algorithm, even when base rates are equal. I conclude with some general reflections on algorithmic fairness. (shrink)

A popular informal argument suggests that statistics about the preponderance of criminal involvement among particular demographic groups partially justify others in making defensive mistakes against members of the group. One could worry that evidence-relative accounts of moral rights vindicate this argument. After constructing the strongest form of this objection, I offer several replies: most demographic statistics face an unmet challenge from reference class problems, even those that meet it fail to ground non-negligible conditional probabilities, even if they did, they introduce (...) new costs likely to cancel out any justificatory contribution of the statistic, but even if they didn’t, demographic facts are the wrong sort to make a moral difference to agents’ negative rights. I conclude that the popular argument should be rejected, and evidence-relative theories do not have the worrisome implication. (shrink)

I consider the error-statistical account as both a theory of evidence and as a theory of inference. I seek to show how inferences regarding the truth of hypotheses can be upheld by avoiding a certain kind of alternative hypothesis problem. In addition to the testing of assumptions behind the experimental model, I discuss the role of judgments of implausibility. A benefit of my analysis is that it reveals a continuity in the application of error-statistical assessment to low-level empirical hypotheses and (...) highly general theoretical principles. This last point is illustrated with a brief sketch of the issues involved in the parametric framework analysis of tests of physical theories such as General Relativity and of fundamental physical principles such as the Einstein Equivalence Principle. (shrink)

In this review article, Christiansen provides a historical perspective on the two research traditions, implicit learning and statistical learning, thus nicely setting the scene for this special issue of Topics in Cognitive Science. In this “tale of two literatures”, he first traces the history of both literatures before sketching a framework that provides a basis for understanding implicit learning and statistical learning as a unified phenomenon.

A modal analysis of luck, due to Duncan Pritchard, has become quite popular in recent years. There are many reasons to like Pritchard’s analysis, but at least two compelling problems have been identified. So I propose an alternative analysis of luck based on the laws of statistical mechanics. The statistical analysis avoids the two problems facing Pritchard’s analysis, and it has many other attractive features.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and (...) made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The computations involved in statistical learning have long been debated. Here, we build on work suggesting that a basic memory process, chunking, may account for the processing of statistical regularities into larger units. Drawing on methods from the memory literature, we developed a novel paradigm to test statistical learning by leveraging a robust phenomenon observed in serial recall tasks: that short‐term memory is fundamentally shaped by long‐term distributional learning. In the statistically induced chunking recall (SICR) task, participants are exposed to (...) an artificial language, using a standard statistical learning exposure phase. Afterward, they recall strings of syllables that either follow the statistics of the artificial language or comprise the same syllables presented in a random order. We hypothesized that if individuals had chunked the artificial language into word‐like units, then the statistically structured items would be more accurately recalled relative to the random controls. Our results demonstrate that SICR effectively captures learning in both the auditory and visual modalities, with participants displaying significantly improved recall of the statistically structured items, and even recall specific trigram chunks from the input. SICR also exhibits greater test–retest reliability in the auditory modality and sensitivity to individual differences in both modalities than the standard two‐alternative forced‐choice task. These results thereby provide key empirical support to the chunking account of statistical learning and contribute a valuable new tool to the literature. (shrink)

A key motivation for Universal Grammar (UG) is developmental: UG can help children acquire the linguistic knowledge that they do as quickly as they do from the data that's available to them. Some of the most fruitful recent work in language acquisition has combined ideas about different hypothesis space building blocks with domain‐general statistical learning. Statistical learning can then provide a way to help navigate the hypothesis space in order to converge on the correct hypothesis. Reinforcement learning is a principled (...) way to update the probability of a categorical option that's in competition with other categorical options. There are two prominent options for linking theory theoretical representations: the Uniformity of Theta Assignment Hypothesis (UTAH) and the relativized form of that theory, relativized UTAH. The learning strategy of Pearl and Sprouse shares the intuition with subjacency that there's a local structural anomaly when syntactic islands occur. (shrink)

Martin Smith has recently proposed, in this journal, a novel and intriguing approach to puzzles and paradoxes in evidence law arising from the evidential standard of the Preponderance of the Evidence. According to Smith, the relation of normic support provides us with an elegant solution to those puzzles. In this paper I develop a counterexample to Smith’s approach and argue that normic support can neither account for our reluctance to base affirmative verdicts on bare statistical evidence nor resolve the pertinent (...) paradoxes. Normic support is, as a consequence, not a successful epistemic anti-luck condition. (shrink)

This study concerns the problem of late complications of antineo-plastic therapy. Reduced parameters of the cardiorespiratory system in childhood may have a tremendous impact on health. In order to assess the selected parameters, to evaluate physical endurance, and compare the results with those obtained for healthy children, a test was carried out on a treadmill, until 80% of maximum pulse rate was reached. To compare the differences between the treatment group and the control group, three approaches were used. The first (...) one was the classical statistical inference, the second consisted in forming a multidimensional normal model and also involved modelling of the correlation between variables. The unstructured type of the working correlation matrix was chosen to obtain the results and correct standard errors. In the last approach, logistic regression was used to model the relationship between binary outcome and covariates, and to differentiate between the groups of patients on the basis of their cardiovascular parameters. (shrink)

We briefly review Condorcet's and Young's epistemic interpretations of preference aggregation rules as maximum likelihood estimators. We then develop a general framework for interpreting epistemic social choice rules as maximum likelihood estimators, maximum a posteriori estimators, or expected utility maximizers. We illustrate this framework with several examples. Finally, we critique this program.Send article to KindleTo send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage (...) Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.A STATISTICAL APPROACH TO EPISTEMIC DEMOCRACYVolume 9, Issue 2Marcus PivatoDOI: https://doi.org/10.1017/epi.2012.4Your Kindle email address Please provide your Kindle email.@free.kindle.com@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. A STATISTICAL APPROACH TO EPISTEMIC DEMOCRACYVolume 9, Issue 2Marcus PivatoDOI: https://doi.org/10.1017/epi.2012.4Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. A STATISTICAL APPROACH TO EPISTEMIC DEMOCRACYVolume 9, Issue 2Marcus PivatoDOI: https://doi.org/10.1017/epi.2012.4Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by (...) the exponential (“thermal”) distribution, whereas a small fraction of the population in the upper class is characterized by the power-law (“superthermal”) distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium. (shrink)

With his new riddle of induction, Goodman raised a problem for enumerative induction which many have taken to show that only some ‘natural’ properties can be used for making inductive inferences. Arguably, however, (i) enumerative induction is not a method that scientists use for making inductive inferences in the first place. Moreover, it seems at first sight that (ii) Goodman’s problem does not affect the method that scientists actually use for making such inferences—namely, classical statistics. Taken together, this would indicate (...) that (iii) ‘naturalness’ is not such a relevant concept for the problem of induction, after all. I have no objections against (i) and (iii). But, contrary to (ii), I argue that classical statistics does face a version of Goodman’s problem, which I call the statistical riddle of induction. Given that his problem merely is an instance of the more general problem of underdetermination, this is hardly surprising. Perhaps more importantly, I also show how my riddle can be used for exposing a common fallacy in probabilistic reasoning, without relying on Bayesian assumptions. (shrink)

In empirical modeling, an important desiderata for deeming theoretical entities and processes as real is that they can be reproducible in a statistical sense. Current day crises regarding replicability in science intertwines with the question of how statistical methods link data to statistical and substantive theories and models. Different answers to this question have important methodological consequences for inference, which are intertwined with a contrast between the ontological commitments of the two types of models. The key to untangling them is (...) the realization that behind every substantive model there is a statistical model that pertains exclusively to the probabilistic assumptions imposed on the data. It is not that the methodology determines whether to be a realist about entities and processes in a substantive field. It is rather that the substantive and statistical models refer to different entities and processes, and therefore call for different criteria of adequacy. (shrink)

Requiring only a background in elementary calculus and elementary mechanics, this book starts with the basics, introduces the most important developments in classical statistical mechanics over the last thirty years, and guides readers to ...

The recent discovery of a Higgs boson prompted increased attention of statisticians and philosophers of science to the statistical methodology of High Energy Physics. Amidst long-standing debates within the field, HEP has adopted a mixed statistical methodology drawing upon both frequentist and Bayesian methods, but with standard frequentist techniques such as significance testing and confidence interval estimation playing a primary role. Physicists within HEP typically deny that their methodological decisions are guided by philosophical convictions, but are instead based on “pragmatic” (...) considerations, thus distancing themselves from what they perhaps perceive as an ongoing pitched ideological battle between frequentists and Bayesians. Here I argue that there is a philosophical orientation to HEP that is neither exclusively frequentist nor Bayesian, but that lies squarely in the tradition of philosophical pragmatism. I further argue that understanding the statistical methodology of HEP through the perspective of pragmatism clarifies the role of and rationale for significance testing in the search for new phenomena such as the Higgs boson. (shrink)

Statistical significance is almost universally equated with the attribution to some population of nonchance influences as the source of structure in the data. But statistical significance can be divorced from both parameter estimation and probability as, instead, a statement about the atypicality or lack of exchangeability over some distinction of the data relative to some set. From this perspective, the criticisms of significance tests evaporate.

Some philosphers of science of an empiricist and pragmatist bent have proposed models of statistical explanation, but have then become sceptical of the adequacy of these models. It is argued that general considerations concerning the purpose of function of explanation in science which are usually appealed to by such philosophers show that their scepticism is not well taken; for such considerations provide much the same rationale for the search for statistical explanations, as these philosophers have characterized them, as they do (...) for lawlike explanations. But, it is further argued, a significant piece of what is frequently offered as an explanation of well known phenomena in statistical mechanics, fails to meet this general "pragmatic rationale" for statistical, or indeed any kind of, explanation. The question then arises whether the physicists have misconstrued the value of this piece of physical theorizing, ergodic theory, taking it to be explanatory when it is actually not; or whether, instead, the philosopher's account of just what is genuinely explanatory is too narrow. (shrink)

Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random phenomena are interpreted as classical probabilities, and this interpretation of equally likely chance outcomes is applied to statistical inference using urn models. These are used to address Bayesian criticisms of frequentist methods. Recent descriptions of p-values, confidence intervals, and power are viewed through the lens of classical probability (...) based on a single random sample from the population. (shrink)

Really statistical explanation is a hitherto neglected form of noncausal scientific explanation. Explanations in population biology that appeal to drift are RS explanations. An RS explanation supplies a kind of understanding that a causal explanation of the same result cannot supply. Roughly speaking, an RS explanation shows the result to be mere statistical fallout.

The statistical aspects of quantum explanation are intrinsic to quantum physics; individual quantum events are created in the interactions associated with observation and are not describable by predictive theory. The superposition principle shows the essential difference between quantum and non-quantum physics, and the principle is exemplified in the classic single-photon two-slit interference experiment. Recently Mandel and Pfleegor have done an experiment somewhat similar to the optical single-photon experiment but with two independently operated lasers; interference is obtained even with beam intensity (...) so small that only one photon is in the apparatus at a time. The result can be understood in terms of the superposition of states; or, in terms of the Uncertainty Principle, which is found to forbid the determination of which of the two lasers is the source of a given photon (if conditions for interference are to obtain). The Mandel-Pfleegor experiment gives a physical argument against the continuous localization of a photon that is assumed in the hidden variable theories and therefore gives further support for the generally accepted view that an observed entity (observed state) is created in the observation event. This aspect of quantum physics implies a subjectivism on the level of individual quantum-level occurrences, since there is in quantum theory no basis for asserting the existence of the event independently of observation of it. Extension of this subjectivism to large scale, non-quantum phenomena falls within the principles of quantum theory; counter considerations that argue against such an extension are noted. (shrink)

Tooze provides an interpretation of the dramatic period of statistical innovation between 1900 and the end of World War II. At the turn of the century, virtually none of the economic statistics that we take for granted today were available. By 1944, the entire repertoire of modern economic statistics was being put to work in wartime economic management. As this book reveals, the Weimar Republic and the Third Reich were in the forefront of statistical innovation in the interwar decades. New (...) ways of measuring the economy were inspired both by contemporary developments in macroeconomic theory and the needs of government. The Weimar Republic invested heavily in macroeconomic research. Under the Nazi regime, these statistical tools were to provide the basis for a radical experiment in economic planning. Based on the German example, this book presents the case for a more wide-ranging reconsideration of the history of modern economic knowledge. (shrink)

A statistical mechanical treatment is given of thermal contact between two systems. Reciprocal temperature emerges from this as the relative change in the number of microscopic states a macroscopic system at equilibrium ranges over, at constant volume and chemical composition, with change in internal energy. The significance of this is discussed in detail with reference to a monatomic gas and an Einstein solid.

In their influential paper “Ceteris Paribus, There is No Problem of Provisos”, Earman and Roberts (Synthese 118:439–478, 1999) propose to interpret the non-strict generalizations of the special sciences as statistical generalizations about correlations. I call this view the “statistical account”. Earman and Roberts claim that statistical generalizations are not qualified by “non-lazy” ceteris paribus conditions. The statistical account is an attractive view, since it looks exactly like what everybody wants: it is a simple and intelligible theory of special science laws (...) without the need for mysterious ceteris paribus conditions. I present two challenges to the statistical account. According to the first challenge, the statistical account does not get rid of so-called “non-lazy” ceteris paribus conditions. This result undermines one of the alleged and central advantages of the statistical account. The second challenge is that the statistical account, qua general theory of special science laws, is weakened by the fact that idealized law statements resist a purely statistical interpretation. (shrink)