LitArk » Books » Romance novel

Vallverdú - Bayesians Versus Frequentists: a Philosophical Debate on Statistical Reasoning

Here you can read online Vallverdú - Bayesians Versus Frequentists: a Philosophical Debate on Statistical Reasoning full text of the book (entire story) in english for free. Download pdf and epub, get meaning, cover and reviews about this ebook. City: Berlin;Heidelberg, year: 2016, publisher: Springer, genre: Romance novel. Description of the work, (preface) as well as reviews are available. Best literature library LitArk.com created for fans of good reading and offers a wide selection of genres:

Romance novel Science fiction Adventure Detective Science History Home and family Prose Art Politics Computer Non-fiction Religion Business Children Humor

Choose a favorite category and find really read worthwhile books. Enjoy immersion in the world of imagination, feel the emotions of the characters or learn something new for yourself, make an fascinating discovery.

Book:
Bayesians Versus Frequentists: a Philosophical Debate on Statistical Reasoning
Author:
Vallverd / Jordi
Publisher:
Springer
Genre:
Books / Romance novel
Year:
2016
City:
Berlin;Heidelberg
Rating:
5 / 5
Favourites:
Add to favourites
Your mark:
- 100
- 1
- 2
- 3
- 4
- 5

Description
Author's other books
Similar books

Bayesians Versus Frequentists: a Philosophical Debate on Statistical Reasoning: summary, description and annotation

We offer to read an annotation, description, summary or preface (depends on what the author of the book "Bayesians Versus Frequentists: a Philosophical Debate on Statistical Reasoning" wrote himself). If you haven't found the necessary information about the book — write in the comments, we will try to find it.

Vallverdú: author's other books

Who wrote Bayesians Versus Frequentists: a Philosophical Debate on Statistical Reasoning? Find out the surname, the name of the author of the book and a list of all author's works by series.

Bayesians Versus Frequentists: a Philosophical Debate on Statistical Reasoning — read online for free the complete book (whole text) full work

Below is the text of the book, divided by pages. System saving the place of the last page read, allows you to conveniently read the book "Bayesians Versus Frequentists: a Philosophical Debate on Statistical Reasoning" online for free, without having to search again every time where you left off. Put a bookmark, and you can go to the page where you finished reading at any time.

Light

Font size:

↓

↑

Reset

Interval:

↓

↑

Bookmark:

Make

The Author(s) 2016

Jordi Vallverd Bayesians Versus Frequentists SpringerBriefs in Statistics 10.1007/978-3-662-48638-2_1

1. Some Questions to Begin with

Jordi Vallverd 1

(1)

Faculty of Philosophy and Arts, Universitat Autnoma de Barcelona, Bellaterra (Cerdanyola del Valls), Spain

Jordi Vallverd

Email:

Abstract

First chapter analyzes how living systems such as amoebae, insects, fishes, chicks, or dolphins are able to deal with numbers without any symbolic system, explaining the notions of subitization or numerosity, among others. At the same time, the cognitive limits for humans in relation to number processing are explored, especially those expressed by kids. Once provided this basic naturalistic framework for minds and numbers, the concepts of ignorance, chance, and statistics are introduced as well as their related basic philosophical debates.

Keywords

Subitization Numerosity Animal cognition Cognition Natural statistics Ignorance Chance Determinism

A book about statistics is, at the end, a book about numbers and how we establish relationships between these numbers and some events in the world. Perhaps, it is a problem of my background as philosopher, but I think that before we study the schools of statistics with more or less detail, we should reconsider what we know about numbers, minds, and chance.

1.1 Numbers and/or Neurons

Our knowledge comes from two different sources:

On the one hand, from experiential data (from own observations, experiments, prerecorded first- or second-hand data stored in books/computers/oral tales,) and on the other, from mental mechanisms to obtain connections, regularities, patterns, or relationships among data. It is a dynamic feedback process in which the emphasis into one or another side of both prominent sources marks the classification as realist/idealist or similar categories. In some cases, this knowledge is expressed linguistically, but in some special cases by numbers. And the laws and semantics of numbers are not the same as that of words.

From our common sense and natural understanding, we can infer that human minds are not naturally designed to deal with numbers and let me explain why. The maximum amount of elements we can visually identify as an exact number is 4. As I have written elsewhere (Vallverd

Beyond the body constraints at the beginning of counting tools (in this case), there are several pending conceptual aspects about numbers and counting:

(a)

Ostensive definition and mimics: It generally expressed as defining by finger pointing, an ostensive definition implies the definition or identity of a concept through the finger pointing at the object itself. According to Wittgenstein (, 6):

I will call it ostensive teaching of words. I say that it will form an important part of the training, because it is so with human beings; not because it could not be imagined otherwise.) This ostensive teaching of words can be said to establish an association between the word and the thing.

In the identity between one mark into a bone and one day or between one object and one finger, it is a highly symbolic process, something close to a friendly extension of imitation. We learn looking at the place where the others eyes gaze or fingers/hands/arms point to. We know then the intentions and interests of the others toward one external thing to our minds. This thing is also explained by the others with more bogy gestures, voice intonation or even language. Then, we accept/understand that there is an external object that has some properties and that it can be discretized and counted. But even in the case of the simple one-to-one matching task, we need numbers in order to understand the notion of quantity and to perform correctly this action (Frank et al. ).

(b)

Base choice: At the same time, there is a semantic of numerals that must be learned by their users. For example, consider the use of base and the cultural divergences. A look at the history of mathematics shows us the differences, Babylonian used base 60 (sexagesimal), while Mayans base 20, Greeks base 10, Leibniz suggested base 2, a very simple base used later by computers (as well as hexadecimal and, sometimes, octal).

Even in our contemporary decimal system, the sexagesimal (60) base for geometric grades (360) survives like cultural fossils. For time measurements (seconds/minutes) and also the duodecimal (12) system is in use, for example when we buy eggs (e.g., one dozen, two dozens.). Even the decimal system is not so strict, when we count 12 months for a year, and the number of days change from month to month. Despite some attempts to change this, like the French Republican Calendar (1793) of 12 months for exactly 30 days with each month one divided into three decades, things remain the same. Concepts are culturally embedded and sometimes survive by tradition, laziness, and disgust toward change. There are more bases: 3-ternary, 4-quaternary, 5-quinary, 6-senary, 7-septenary, 8-octal, 9-nonary, 11-undecimal, 16-hexadecimal .

Consequently, there is no natural way to choose a mathematical base; this reflects a cultural process with some practical points that need our consideration. Perhaps we feel comfortable with base 10 just because most of us have learnt it from our parents, in school and from a variety of social environments that surround us, nothing else. The classic remark that we have 10 fingers and that this is the basis of the decimal system is not strong enough because we know that several cultures make use of hands to calculate relying on several subsections like phalanges or even combining methods to count differently. Counting with hands differs very strongly among European countries and more when compared with Japan, China, or some countries of Africa (Ifrah ).

(c)

Discrete semantics of arithmetic: They take into the consideration the basic operation As a result, there is an ontological stability that makes it possible to engage in any work with numbers, or at least our success defining some temporary states as stable make it possible.

(d)

Finally, there are also psychological constraints: following the study of the human (in) capacity to deal with long lists of numbers, we remember the classic study of Miller () which demonstrated that generally people have problems to remember greater numbers than those of nine units (that is, for example, 798428197). And our necessity to deal with greater numbers has a strong relationship with commerce, war, or even with the time calculation (calendars) and human body regularities.

The embodied cognitive inference could explain this, as Zaslavsky () suggests:

The cyclical Nature of menstruation has played a major role in the development of counting, mathematics, and the measuring of time Lunar markings found on prehistoric bone fragments show how early women marked their cycles and thus began to mark time. Women were possibly the first observers of the basic periodicity of Nature, the periodicity upon which all later scientific observations were made (quoted from Thomson , page 97).

In this later case, for an understanding of a 28 day cycle we need a notation system, something beyond intuition and that requires us to take a step forward. The fact is that the analysis of natural cycles, especially astronomical ones, has been the basis of mathematical advances throughout history. We will see in the following chapters that the technical analytic requirements of astronomy led to the birth of modern statistical analysis.

Well, we have been talking about numbers as external entities that must be captured by symbols that have a body correlation. However, another aspect must be considered: the numbers inside the body. Beyond any symbolic instantiation of numbers, human bodies perform several calculations through their nervous systems, generating internal probabilities distributions rather than deterministically selected information based on all the available information (Vul and Pashler : 6).

Light

Font size:

↓

↑

Reset

Interval:

↓

↑

Bookmark:

Make

Similar books «Bayesians Versus Frequentists: a Philosophical Debate on Statistical Reasoning»

Look at similar books to Bayesians Versus Frequentists: a Philosophical Debate on Statistical Reasoning. We have selected literature similar in name and meaning in the hope of providing readers with more options to find new, interesting, not yet read works.

Leda Berio

Talking About Thinking: Language, Thought, and Mentalizing

John Glenn

Neorealism Versus Strategic Culture

Ray Maghroori

Globalism Versus Realism: International Relations Third Debate

David S. Moore

Statistics: Concepts and Controversies

Parmenides

Plato versus Parmenides: the debate over coming-into-being in Greek philosophy

Bassham Gregory

The Ultimate Harry Potter and Philosophy: Hogwarts for Muggles

William Briggs

Uncertainty: The Soul of Modeling, Probability & Statistics

Drew M. Dalton

The Ethics of Resistance: Tyranny of the Absolute

Hacking

The Emergence of Probability: A Philosophical Study of Early Ideas about Probability, Induction and Statistical Inference Cambridge Series on Statistical & Probabilistic Mathematics

Tabery

Beyond versus : the struggle to understand the interaction of nature and nurture

Peter Sedlmeier

Improving statistical reasoning: theoretical models and practical implications

Rae R. Newton

Your Statistical Consultant: Answers to Your Data Analysis Questions

Reviews about «Bayesians Versus Frequentists: a Philosophical Debate on Statistical Reasoning»

Discussion, reviews of the book Bayesians Versus Frequentists: a Philosophical Debate on Statistical Reasoning and just readers' own opinions. Leave your comments, write what you think about the work, its meaning or the main characters. Specify what exactly you liked and what you didn't like, and why you think so.