Logic Of Statistical Inference Research Articles

Cosmological Distance Scale. Part 9. Deceleration Parameter

The so-called “unexpected” results of statistical processing of data from increasingly more accurate astrophysical and gravitational measurements are examined. The reasons for the breakdown of the logic of statistical inference, which several leading experts have interpreted as a “metrological and scientific impasse” in cosmology, are pointed out. The data on type SN Ia supernovae used to detect the “accelerating expansion of the universe” are analyzed. It is shown that the errors in the Friedman–Robertson–Walker model as an equation for indirect measurement of distance are multiplicative. Here the hypothesis of a Gaussian form for these errors corresponds to a shift of –2.8% and a mean square deviation of 16.3% for a mean square deviation of the arithmetic mean of 1.8%. It is noted that using the mean square deviation of the arithmetic mean as an indicator of the accuracy of the scale is a crude mistake.

Model Uncertainty and Robustness Tests: Towards a New Logic of Statistical Inference

We augment the increasingly common practice of typically ad hoc robustness tests into a research methodology that allows reliable inferences when researchers do not know the true data-generating process. We identify three principal sources of model uncertainty. First, theories simplify and aim at isolating causal mechanisms under ceteris paribus conditions. Theories thus cannot sufficiently specify the data-generating process. Second, empirical researchers are uncertain about what constitutes the population – the set of cases for which a theory claims validity – from which to draw a representative sample as required for econometric estimation. Finally, model uncertainty also results from the fact that many concepts used in social science theories cannot be observed and therefore can only be measured by proxy variables, which deviate in unknown, but potentially systematic ways from the theoretical concepts. These three causes of model uncertainty result in at least 16 specific aspects of uncertainty about model specification that can be subjected to various robustness tests. Defining robustness as stability of causal inferences, we argue against the misplaced focus on single point estimates from any specific test. Instead, we suggest scholars employ model averaging techniques to assess robustness in terms of the entire set of empirical evidence from the baseline and all robustness test models. This method avoids the type-II error bias of current practice and encourages researchers to undertake a larger set of robustness tests instead of carefully hand-selecting only those tests that do not deviate from their baseline model results. We illustrate our proposal using an example of an existing study by the authors on the political determinants of famine mortality, which contained only two robustness tests and thus begs the question whether the causal inferences are fragile. Subjecting our baseline model to a battery of additional tests, we conclude that our causal inferences are in fact robust: democracies respond more elastically than autocracies to the simultaneous presence of international food aid and a large share of the population being affected, which results in lower famine mortality.

Important areas for future statistical research

It seems to me that statistical science is at a watershed. Accordingly, the editor's initiative in collecting a number of essays on the future of statistics seems timely and of importance. The topic for the essays was, however, given as 'the most important areas of statistical research in the next ten years'. I have some reservations about the restriction to ten years, as that could narrow and bias the focus too much in relation to the most crucial issues for our subject. I shall therefore, briefly, attempt a broader view. Why and in what sense are we at a watershed? Part of the picture is our hugely increased ability to collect and process extensive data sets, with the accompanying problems of sensible and illuminating statistical model-building and inference. The use of powerful computational means for the statistical analysis of such data sets is of course indispensable, but as far as the logic of statistical inference is concerned the computers have, so far, had relatively little

Mathematical statistics and metastatistical analysis

This paper deals with meta-statistical questions concerning frequentist statistics. In Sections 2 to 4 I analyse the dispute between Fisher and Neyman on the so called logic of statistical inference, a polemic that has been concomitant of the development of mathematical statistics. My conclusion is that, whenever mathematical statistics makes it possible to draw inferences, it only uses deductive reasoning. Therefore I reject Fisher's inductive approach to the statistical estimation theory and adhere to Neyman's deductive one. On the other hand, I assert that Neyman-Pearson's testing theory, as well as Fisher's tests of significance, properly belong to decision theory, not to logic, neither deductive nor inductive. I then also disagree with Costantini's view of Fisher's testing model as a theory of hypothetico-deductive inferences.

Probabilism in Geological Data Analysis

AbstractThe way in which probability can enter the interpretation of geological data is outlined. Probabilistic models are introduced in data synopses to allow statistical inferences about samples and population parameters. Inferences of this type are a special application of mathematical theory and have little to do with testing scientific generalizations. The logic of statistical inference, as used in operations research, is contrasted with that of geological inference. Geology is a cumulative science; its methodology is not that of experimentation with formal replication; inferences are developed from observations and tested and refined against new data, often by different investigators at different times and in different places. Because of the way in which inferences are drawn, sampling in geology is purposive. Random sampling, necessary for inferences based on sampling theory, is unattainable in most geological contexts. Different classes of geological measurements require careful consideration as to their appropriate form of synopsis, and, particularly, as to whether a parametric probability model is applicable.

On Models and theories of inference; structural or pivotal analysis

Recent material is surveyed concerning the foundations of statistical models, the definition and logic of statistical inference, and the additives used in various applications of theories of inference. This background is then used to compare structural/structured models [Fraser 1966, 1968, 1979] and pivotal models [Barnard 1974, 1981]; the models are found to be identical except for nomencalture and basic justification which supports the structural format. An outline is given of the development of the structural/structured model and of the corresponding mode of inference. The recent pivotal methods of analysis are assessed with this development as background.

Progesterone levels and psychological state in normal women

Abstract The possibility of a relationship between progesterone level and psychological state was studied. Three groups of 10 women each were administered psychological tests during menstruation to obtain a common base line. Groups were tested again so as to obtain data during progessively higher progesterone peaks (one group during normal-cycle calculated peak, one during the height of Enovid therapy, one during the third trimester of pregnancy). Of 57 variables analyzed, only 2 varied significantly and progressively among the three groups. These 2 could be indicative of increasing emotional vulnerability with increasing progesterone level. The logic of statistical inference, however, renders even these findings dubious, since one would expect approximately three variables (of 57) to reach the 0.05 probability level by chance. It was concluded that serious psychological disturbances are unlikely hazards secondary to increased progesterone levels in normal women.

Progesterone levels and psychological state in normal women

The possibility of a relationship between progesterone level and psychological state was studied. Three groups of 10 women each were administered psychological tests during menstruation to obtain a common base line. Groups were tested again so as to obtain data during progessively higher progesterone peaks (one group during normal-cycle calculated peak, one during the height of Enovid therapy, one during the third trimester of pregnancy). Of 57 variables analyzed, only 2 varied significantly and progressively among the three groups. These 2 could be indicative of increasing emotional vulnerability with increasing progesterone level. The logic of statistical inference, however, renders even these findings dubious, since one would expect approximately three variables (of 57) to reach the 0.05 probability level by chance. It was concluded that serious psychological disturbances are unlikely hazards secondary to increased progesterone levels in normal women.

BOOK REVIEWS

Book reviewed in this article:Logic of Statistical Inference. By Ian Hacking.Mathematical Epistemology and Psychology. By Evert W. Beth and Jean Piaget.Test Theory. By D. Magnusson.Elementary Statistical Theory for Behaviour Scientists. By J. W. Cotton.Fundamentals of Behavioural Statistics. By R. Runyon and A. Haber.

Logic of Statistical Inference. By Ian Hacking. Pp. ix, 232. 40s. 1965. (Cambridge University Press)

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Logic of Statistical Inference.

Logic of Statistical Inference.

Logic of Statistical Inference.

Logic of Statistical Inference.

Logic of Statistical Inference.

Preface 1. Long run frequencies 2. The chance set-up 3. Support 4. The long run 5. The law of likelihood 6. Statistical tests 7. Theories of testing 8. Random sampling 9. The fiducial argument 10. Estimation 11. Point estimation 12. Bayes' theory 13. The subjective theory.

Logic of Statistical Inference.

Logic of Statistical Inference.

Logic of Statistical Inference.

Logic of Statistical Inference.