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دانلود کتاب Philosophy Of Probability And Statistical Modelling

دانلود کتاب فلسفه احتمال و مدل سازی آماری

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Philosophy Of Probability And Statistical Modelling

دسته بندی: فلسفه
ویرایش:  
نویسندگان: Mauricio Suárez  
سری:  
ISBN (شابک) : 9781108984942 
ناشر: Cambridge University Press 
سال نشر: 2020 
تعداد صفحات: 76 
زبان: English 
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) 
حجم فایل: 2 مگابایت

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توضیحاتی درمورد کتاب به خارجی

Humans have been thinking in probabilistic terms since antiquity. They have been thinking systematically and philosophizing about probability since the seventeenth century. And they have been formalizing probability since the end of the nineteenth century. The twentieth century saw intense philosophical work done on interpreting probability, in a sort of attempt to find out its essence. The twenty-first century, I argue, will bring a focus on more practical endeavours, concerning mainly the methodologies of data analysis and statistical modelling. The essence of probability, it turns out, lies in the diversity of its uses. So, the methodological study of the use of probability is what brings humans closer to a comprehensive understanding of its nature. These and other ideas expounded in this Element developed out of a Marie Curie project on probability and propensities that I carried out at the Institute of Philosophy of the School of Advanced Study at London University during 2013–15. I came out of that project with the distinct impression that the study of practice was of primary importance; and that much philosophy of probability is still to come to terms with it. This Element is my first attempt at the bare bones of a new research programme into the methodology of statistical modelling. Most of the Element is devoted to justifying this methodology – on the grounds of practical involvement with the scientific modelling practice but also, I argue, on account of the limitations of the traditional interpretative approaches to the topic. Thus, the first half of the Element (Sections 1–7) is entirely a state-of-the-art review of the historiography of probability and its ensuing impact upon the interpretative endeavour. This is fitting for a Cambridge Elements volume, which allows for a profuse setting of the stage. And it is anyway needed in order to understand why nothing other than a study of the practice of statistical model building will do for a full understanding of objective probability. I first explore (in Section 1) the dual character of the notion of probability from its inception – the subjective and objective aspects of probability that are essential to any understanding the concept. The twentieth century brought in several interpretations of probability. But one way or another, they all aim to reduce probability to either subjective or objective elements, thus doing away with the duality; and one way or another they all fail, precisely because they do away with the duality. In the remaining sections in this half of the Element, I analyse in detail the many objections against both the main subjective interpretations (the logical and personalist or Bayesian interpretations), and the main objective interpretations (the frequency and propensity interpretations). To make most of these interpretations work, and overcome the objections, demands some Downloaded from https://www.cambridge.org/core. IP address: 181.171.20.59, on 25 Dec 2020 at 13:42:48, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/97811089858262 Philosophy of Probability and Statistical Modelling acknowledgment of the complex duality of probability. This is by now widely accepted, and the Element first reviews the roots and consequences of pluralism about objective probability. The second half of the Element (Sections 8–13) then centres upon the objective aspects of probability, but now without any pretence of a reduction of the whole concept. The discussion is focused entirely on objective probabil- ity, and it contains most of the original material. I advance a number of novel theses, which I defend in various original ways as well as proposing a number of new avenues for research. The starting point is pluralist, and it accepts the duality insofar as it argues that there are important matters of judgement in the selection of crucial aspects of the application of objective probability in prac- tice. Here, the critical distinction, advanced in Sections 8 and 9, is between the traditional project to merely interpret probability and a distinct project to study the application of probability. On the other hand, I go considerably beyond the pluralism defended in the first half of the Element and, in Section 10, I embrace novel forms of pluralism and pragmatism regarding objective probability. The central idea of the second half, which also informs the Element as a whole and looms large through most of its discussions, is what I have elsewhere called the ‘tripartite conception’ of objective probability (Suárez, 2017a). This is the idea that the failure to reduce chance to either propensity or frequency ought to lead to the acceptance of all three concepts as distinct, insufficient yet necessary, parts of the larger notion of ‘objective probability’. This tripartite conception is introduced in Section 10, which also assesses the role of judgement and various subjective components. Sections 11, 12, and 13 are then devoted to modelling methodology, and the application of the tripartite conception in statistical modelling practice in particular, in what I call the ‘complex nexus of chance’ (CNC). The thought running through these sections is new and radical: objective probability is constituted by a thick array of interlinked practices in its application; these are practices that essentially involve the three distinct notions pointed to above; and since none of these notions is theoretically reducible to any combination or set of the other two, this means that the overall methodology remains unavoidably ‘complex’. There is no philosophical theory that may explicate fully the concept of objective probability, or chance, by reducing this complexity, and this already sheds light on the limitations of the interpretations reviewed in the Element’s first half. What’s more, the second half of the Element also continues to illustrate the fundamental duality of probability unearthed in the historiographical material reviewed in the first seven sections. It does so in three different yet interrelated ways. First of all, it leaves open that subjective elements may come into the nature of the single-case chances that make up the tripartite conception. Downloaded from https://www.cambridge.org/core. IP address: 181.171.20.59, on 25 Dec 2020 at 13:42:48, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781108985826Philosophy of Science 3 Secondly, confirmation theory comes into the assessment of evidence for and against different models. And, finally, there are irreducible subjective judge- ments involved in the pragmatist methodology advocated in the later sections. For instance, in Section 11 I argue that choosing the appropriate parametrization of the phenomenon to be modelled is a critical part; and there is no algorithm or automatic procedure to do this – the choice of free parameters is subject to some fundamentally ‘subjective’ estimate of what is most appropriate in the context for the purposes of the model at hand. Once again, the ‘subjective’ and the ‘objective’ aspects of probability meet in fundamental ways (see Gelman and Hennig (2017) as well as my response Suárez (2017b) for an account of such a merge in practice). Another related sense of subjectivism in statistical model- ling is sometimes referred to as the ‘art of statistical modelling’ and concerns the choice of a correlative outcome or attribute space. There is nothing arbitrary about this ‘subjectivity’ though, since it answers precisely to specific pragmatic constraints: it is a highly contextual and purpose-driven judgement. On my view, each of the parametrizations of a phenomenon involves a description of its propensities, dispositions, or causal powers. What is relevant about propensities is that they do not fall in the domain of the chance functions that they generate (Suárez, 2018). Rather a propensity is related to a chance function in the way that possibilities are related to probabilities: the propensity sets the range of possible outcomes, the full description of the outcome space, while the chance function defined over this space then determines the precise single-case chance ascribed to each of these outcomes. A different paramet- rization would involve a different description of the system’s propensities, perhaps at a different level of generality or abstraction (and no parametrization is infinitely precise); and focusing on a different set of propensities may well issue in a different set of possible outcomes, hence a different outcome space, over which a different chance function shall lay out its probabilities. Since the parametrizations obey pragmatic constraints that require appropriate judgements within the context of application, it follows that the outcome spaces will corres- pondingly depend on such judgements. In other words, a chance function is not just a description of objective probabilities for objectively possible outcomes; it is one amongst many such descriptions for a particular system, made relevant by appropriate judgements of salience, always within a particular context of inquiry. Here, again, the ‘subjective’ and the ‘objective’ aspects of probability merge.

فهرست مطالب

Cover
Title page
Copyright page
Philosophy of Probability and Statistical Modelling
	Contents
	Introduction
	1 The Archaeology of Probability
	2 The Classical Interpretation: Equipossibility
	3 The Logical Interpretation: Indifference
	4 The Subjective Interpretation: Credence
	5 The Reality of Chance: Empiricism and Pragmatism
	6 The Frequency Interpretation: Actual and Hypothetical Frequencies
	7 The Propensity Interpretation: Single Case and Long Run
	8 Interpreting and Applying Objective Probability
	9 The Explanatory Argument and Ontology
		9.1 The Frequency Interpretation
		9.2 The Propensity Interpretation
		9.3 The Explanatory Argument
	10 Metaphysical Pluralism: The Tripartite Conception
	11 Methodological Pragmatism: The Complex Nexus of Chance
	12 Two Types of Statistical Modelling
		12.1 Pure Probabilism: The Method of Arbitrary Functions
		12.2 Pure Stochasticity: Indeterministic Dynamical Modelling
	13 Towards a Methodology of Chance Explanation
References
Acknowledgements