Skip to main content Accessibility help
×
  1. Home
  2. Browse subjects
  3. Statistics and Probability
  4. General statistics and probability
  5. Content listing

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2703 results in General statistics and probability

Page 2 of 136

  • 4 - Markov Sequences

  • Luis E. Nieto-Barajas, Instituto Tecnológico Autónomo de México (ITAM)
  • Book:
    Dependence Models via Hierarchical Structures
    Published online:
    20 March 2025
    Print publication:
    27 March 2025, pp 51-69

  • Summary

    In this chapter we describe a general procedure to construct Markov sequences with invariant distributions. The procedure can be used with conjugate and non-conjugate models and with parametric and nonparametric distributions. We derive several examples in detail and finish with some applications in survival analysis.

  • 3 - Exchangeable Sequences

  • Luis E. Nieto-Barajas, Instituto Tecnológico Autónomo de México (ITAM)
  • Book:
    Dependence Models via Hierarchical Structures
    Published online:
    20 March 2025
    Print publication:
    27 March 2025, pp 33-50

  • Summary

    In this chapter we introduce the concept of exchangeability and show how to construct exchangeable sequences; we present our first result of how to construct exchangeable sequences and maintain a desirable marginal distribution and provide detailed examples. We finish with an application of exchangeable constructions in a meta analysis. Bugs and R code are provided.

  • 1 - Introduction

  • Luis E. Nieto-Barajas, Instituto Tecnológico Autónomo de México (ITAM)
  • Book:
    Dependence Models via Hierarchical Structures
    Published online:
    20 March 2025
    Print publication:
    27 March 2025, pp 1-22

  • Summary

    In this chapter we start by reviewing the different types of inference procedures: frequentist, Bayesian, parametric and non-parametric. We introduce notation by providing a list of the probability distributions that will be used later on, together with their first two moments. We review some results on conditional moments and carry out several examples. We review definitions of stochastic processes, stationary processes and Markov processes, and finish by introducing the most common discrete-time stochastic processes that show dependence in time and space.

Dependence Models via Hierarchical Structures
  • Luis E. Nieto-Barajas
  • Published online:
    20 March 2025
    Print publication:
    27 March 2025
  • Bringing together years of research into one useful resource, this text empowers the reader to creatively construct their own dependence models. Intended for senior undergraduate and postgraduate students, it takes a step-by-step look at the construction of specific dependence models, including exchangeable, Markov, moving average and, in general, spatio-temporal models. All constructions maintain a desired property of pre-specifying the marginal distribution and keeping it invariant. They do not separate the dependence from the marginals and the mechanisms followed to induce dependence are so general that they can be applied to a very large class of parametric distributions. All the constructions are based on appropriate definitions of three building blocks: prior distribution, likelihood function and posterior distribution, in a Bayesian analysis context. All results are illustrated with examples and graphical representations. Applications with data and code are interspersed throughout the book, covering fields including insurance and epidemiology.

Page 2 of 136