Simply stated, this book bridges the gap between statistics and philosophy. It does this by delineating the conceptual cores of various statistical methodologies (Bayesian/frequentist statistics, model selection, machine learning, causal inference, etc.) and drawing out their philosophical implications. Portraying statistical inference as an epistemic endeavor to justify hypotheses about a probabilistic model of a given empirical problem, the book explains the role of ontological, semantic...

The central role of mathematical modeling in modern evolutionary theory has raised a concern as to why and how abstract formulae can say anything about empirical phenomena of evolution. This Element introduces existing philosophical approaches to this problem and proposes a new account according to which evolutionary models are based on causal, and not just mathematical, assumptions. The novel account features causal models both as the Humean 'uniform nature' underlying evolutionary induct...

What is consciousness? How do physical processes in the brain give rise to the self-aware mind and to feelings as profoundly varied as love or hate aesthetic pleasure or spiritual yearning? These questions today are among the most hotly debated issues among scientists and philosophers and we have seen in recent years superb volumes by such eminent figures as Francis Crick Daniel C. Dennett Gerald Edelman and Roger Penrose all firing volleys in what has come to be called the consciousness w...

Students and instructors alike will benefit from this rigorous, unfussy text, which keeps a clear focus on the basic probabilistic concepts required for an understanding of financial market models, including independence and conditioning. Assuming only some calculus and linear algebra, the text develops key results of measure and integration, which are applied to probability spaces and random variables, culminating in central limit theory. Consequently it provides essential prerequisites t...

This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the cent...

ABSTRACT: Modern linguistic theories are quite diverse and many of them often seem to be incompatible with each other. The theoretical and practical gap between the major linguistic schools may discourage researchers of a school to benefit from a good deal of research done in other linguistic schools. If this theoretical gap is filled, it would be possible to reach a scientific unity among different linguistic trends in order to find greater achievements and prevent loss of time and energy...

Like its predecessor, this book starts from the premise that, rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by a thorough treatment of the three main subjects in probability theory: the law of large numbers, the central limit theorem, and the ...

This book describes the classical axiomatic theories of decision under uncertainty, as well as critiques thereof and alternative theories. It focuses on the meaning of probability, discussing some definitions and surveying their scope of applicability. The behavioral definition of subjective probability serves as a way to present the classical theories, culminating in Savage's theorem. The limitations of this result as a definition of probability lead to two directions - first, similar beh...

The Measure of Mind provides a sustained critique of a widely held representationalist view of propositional attitudes and their role in the production of thought and behaviour. On this view, having a propositional attitude is a matter of having an explicit representation that plays a particular causal/computational role in the production of thought and behaviour. Robert J. Matthews argues that this view does not enjoy the theoretical or the empirical support that proponents claim...

Statisticians and philosophers of science have many common interests but restricted communication with each other. This volume aims to remedy these shortcomings. It provides state-of-the-art research in the area of philosophy of statistics by encouraging numerous experts to communicate with one another without feeling "restricted by their disciplines or thinking "piecemeal in their treatment of issues. A second goal of this book is to present work in the field without bias toward any parti...

Philosophy of Science: A Unified Approach combines a general introduction to philosophy of science with an integrated survey of all its important subfields. As the book’s subtitle suggests, this excellent overview is guided methodologically by "a unified approach" to philosophy of science: behind the diversity of scientific fields one can recognize a methodological unity of the sciences. This unity is worked out in this book, revealing all the while important differences between s...

Stochastic Limit Theory, published in 1994, has become a standard reference in its field. Now reissued in a new edition, offering updated and improved results and an extended range of topics, Davidson surveys asymptotic (large-sample) distribution theory with applications to econometrics, with particular emphasis on the problems of time dependence and heterogeneity. The book is designed to be useful on two levels. First, as a textbook and reference work, giving definitions of the ...