2 edition of **Some applications of belief functions to statistical inference.** found in the catalog.

Some applications of belief functions to statistical inference.

Larry Alan Wasserman

- 254 Want to read
- 11 Currently reading

Published
**1988**
.

Written in English

The Physical Object | |
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Pagination | 116 leaves |

Number of Pages | 116 |

ID Numbers | |

Open Library | OL20697349M |

Computational statistics and statistical computing are two areas that employ computational, graphical, and numerical approaches to solve statistical problems, making the versatile R language an ideal computing environment for these fields. One of the first books on these topics to feature R, Statistical Computing with R covers the traditional core material of computational statistics, with an 5/5(1). Statistical Evidence and Belief Functions Teddy Seidenfeld University of Pittsburgh In his recent monograph [71, Professor Shafer has offered us an alternative to Bayesian inference with his novel theory of belief functions and, in his current paper [8l, has characterized his position by pointing to two.

In particular, statistical properties and ergodic theorems for relative entropy densities of HMPs were developed. Consistency and asymptotic normality of the maximum-likelihood (ML) parameter estimator were proved under some mild conditions. Similar results were established for switching autoregressive processes. These processes generalize HMPs. Then we deﬁne some notation and review some basic concepts from probability theory and statistical inference. What Is Nonparametric Inference? The basic idea of nonparametric inference is to use data to infer an unknown quantity while making as few assumptions as possible. Usually, this means using statistical models that are inﬁnite.

Motivation: Examples and Applications The Classical Scientific Method and Statistical Inference Definitions and Examples. Some Important Study Designs in Medical Research. Problems. 2. Exploratory Data Analysis and Descriptive Statistics Examples of Random Variables and Associated Data Types. In May of we organized an international research colloquium on foundations of probability, statistics, and statistical theories of science at the University of Western Ontario. During the past four decades there have been striking formal advances in our understanding of logic, semantics.

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The Dempster Shafer theory of belief functions is a method of quantifying uncertainty that generalizes probability theory. We review the theory of belief functions in the context of statistical inference.

We mainly focus on a particular belief function based on the likelihood function and its application to problems with partial prior by: First, we express statistical inference as a process of converting observations into degrees of belief, and we give a clear mathematical definition of what it means for statistical inference to be.

Belief functions and statistical inference. Applications Statistical inference Foreword The theory of belief functions (BF) is not a theory of Imprecise Probability (IP). In particular, it does not represent uncertainty using sets of probability measures.

However, as IP theory, BF theory doesextend Probability theory by allowing some imprecision (using a multi-valued mapping in. The monograph examines some of the consequences of extending standard concepts of ancillarity, sufficiency and complete ness into this setting.

The reader should note that the development is mathematically "mature" in its use of Hilbert space methods but not, we believe, mathematically difficult. After a reminder of general concepts of the theory, we show how this approach can be applied to statistical inference by viewing the normalized likelihood function as defining a consonant belief.

Statistics is a subject with a vast field of application, involving problems which vary widely in their character and r, in tackling these, we use a relatively small core of central ideas and methods.

This book attempts to concentrateattention on these ideas: they are placed in a general settingand illustrated by relatively simple examples, avoidingwherever possible the. The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory (DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability introduced by Arthur P.

Dempster in the context of statistical inference, the theory was later developed by Glenn. Statistical inference techniques, if not applied to the real world, will lose their import and appear to be deductive exercises. Furthermore, it is my belief that in a statistical course emphasis should be given to both mathematical theory of statistics and to the application of the theory to practical problems.

This book constitutes the thoroughly refereed proceedings of the Third International Conference on Belief Functions, BELIEFheld in Oxford, UK, in September The 47 revised full papers presented in this book were carefully selected and reviewed from 56 submissions.

This book discusses stochastic models that are increasingly used in scientific research and describes some of their applications. Organized into three parts encompassing 12 chapters, this book begins with an overview of the basic concepts and procedures of statistical inference.

Concept. A linear belief function intends to represent our belief regarding the location of the true value as follows: We are certain that the truth is on a so-called certainty hyperplane but we do not know its exact location; along some dimensions of the certainty hyperplane, we believe the true value could be anywhere from –∞ to +∞ and the probability of being at a particular location.

Statistical inference is the process of analysing the result and making conclusions from data subject to random variation. It is also called inferential statistics. Hypothesis testing and confidence intervals are the applications of the statistical inference.

Statistical inference is a method of making decisions about the parameters of a. Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available.

Bayesian inference is an important technique in statistics, and especially in mathematical an updating is particularly important in the dynamic analysis of a sequence of data. The new organization presents information in a logical, easy-to-grasp sequence, incorporating the latest trends and scholarship in the field of probability and statistical inference.

Balanced coverage of probability and statistics includes: Five chapters that focus on probability and probability distributions, including discrete data, order statistics, multivariate distributions, and normal. On -characteristic functions and applications to asymptotic statistical inference.

Communications in Statistics - Theory and Methods: Vol. 46, No. 4, pp. ation of DS inference that does have some of the de-sired frequency properties. The goal of the present paper is to review and extend the work of Zhang and Liu [25] on the theory of statistical inference with weak beliefs (WBs).

The WB method starts with a belief function on X× T, but before condi-tioning on the observed data X, a weakening. emission that it follows Poisson model with some unknown >0 and the value x= 5 has been once observed. Our goal is somehow to utilized this knowledge.

First, we note that the Poisson model is in fact not only a function of xbut also of p(xj) = xe x!: Let us plug in the observed x = 5, so that we get a function of that is called likelihood function.

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Toward the end of the vide. This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts.

Abstract. This chapter collects some known statistical inference methods for analyzing univariate independent data with a common distribution function in the domain of attraction of an extreme value distribution with a positive extreme value index, i.e., () and () hold with some γ > 0.Statistical inference is the process of using data analysis to deduce properties of an underlying distribution of probability.

Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving is assumed that the observed data set is sampled from a larger population.

Inferential statistics can be contrasted with descriptive statistics.Role of formal theory of inference 3 Some simple models 3 Formulation of objectives 7 Two broad approaches to statistical inference 7 Some further discussion 10 Parameters 13 Notes 1 14 2 Some concepts and simple applications 17 Summary 17 Likelihood 17 Sufﬁciency 18 Exponential family