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Author: Tilmann Gneiting Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Model diagnostics and forecast evaluation are closely related tasks, with the former concerning in-sample goodness (or lack) of fit and the latter addressing predictive performance out-of-sample. We review the ubiquitous setting in which forecasts are cast in the form of quantiles or quantile-bounded prediction intervals. We distinguish unconditional calibration, which corresponds to classical coverage criteria, from the stronger notion of conditional calibration, as can be visualized in quantile reliability diagrams. Consistent scoring functions--including, but not limited to, the widely used asymmetricpiecewise linear score or pinball loss--provide for comparative assessment and ranking, and link to the coefficient of determination and skill scores. We illustrate the use of these tools on Engel's food expenditure data, the Global Energy Forecasting Competition 2014, and the US COVID-19 Forecast Hub.
Author: Tilmann Gneiting Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Model diagnostics and forecast evaluation are closely related tasks, with the former concerning in-sample goodness (or lack) of fit and the latter addressing predictive performance out-of-sample. We review the ubiquitous setting in which forecasts are cast in the form of quantiles or quantile-bounded prediction intervals. We distinguish unconditional calibration, which corresponds to classical coverage criteria, from the stronger notion of conditional calibration, as can be visualized in quantile reliability diagrams. Consistent scoring functions--including, but not limited to, the widely used asymmetricpiecewise linear score or pinball loss--provide for comparative assessment and ranking, and link to the coefficient of determination and skill scores. We illustrate the use of these tools on Engel's food expenditure data, the Global Energy Forecasting Competition 2014, and the US COVID-19 Forecast Hub.
Author: Joan Aguilar Fargas Publisher: ISBN: Category : Languages : en Pages : 65
Book Description
In this thesis a methodology to construct prediction intervals for a generic black-box point forecast model is presented. The prediction intervals are learned from the forecasts of the black-box model and the actual realizations of the forecasted variable by using quantile regression on the observed prediction error distribution, the distribution of which is not assumed. An independent meta-model that runs in parallel to the original point forecast model is responsible for learning and generating the prediction intervals, thus requiring no modification to the original setup. This meta-model uses both the inputs and output of the black-box model and calculates a lower and an upper bound for each of its forecasts with the goal that a predefined percentage of future realizations are included in the interval formed by both bounds. Metrics for the performance of the meta-model are established, paying special attention to the conditional interval coverage with respect to both time and the inputs. A series of cases studies are performed to determine the capabilities of this approach and to compare it to standard practices.
Author: Alicia A. Johnson Publisher: CRC Press ISBN: 1000529568 Category : Mathematics Languages : en Pages : 606
Book Description
Praise for Bayes Rules!: An Introduction to Applied Bayesian Modeling “A thoughtful and entertaining book, and a great way to get started with Bayesian analysis.” Andrew Gelman, Columbia University “The examples are modern, and even many frequentist intro books ignore important topics (like the great p-value debate) that the authors address. The focus on simulation for understanding is excellent.” Amy Herring, Duke University “I sincerely believe that a generation of students will cite this book as inspiration for their use of – and love for – Bayesian statistics. The narrative holds the reader’s attention and flows naturally – almost conversationally. Put simply, this is perhaps the most engaging introductory statistics textbook I have ever read. [It] is a natural choice for an introductory undergraduate course in applied Bayesian statistics." Yue Jiang, Duke University “This is by far the best book I’ve seen on how to (and how to teach students to) do Bayesian modeling and understand the underlying mathematics and computation. The authors build intuition and scaffold ideas expertly, using interesting real case studies, insightful graphics, and clear explanations. The scope of this book is vast – from basic building blocks to hierarchical modeling, but the authors’ thoughtful organization allows the reader to navigate this journey smoothly. And impressively, by the end of the book, one can run sophisticated Bayesian models and actually understand the whys, whats, and hows.” Paul Roback, St. Olaf College “The authors provide a compelling, integrated, accessible, and non-religious introduction to statistical modeling using a Bayesian approach. They outline a principled approach that features computational implementations and model assessment with ethical implications interwoven throughout. Students and instructors will find the conceptual and computational exercises to be fresh and engaging.” Nicholas Horton, Amherst College An engaging, sophisticated, and fun introduction to the field of Bayesian statistics, Bayes Rules!: An Introduction to Applied Bayesian Modeling brings the power of modern Bayesian thinking, modeling, and computing to a broad audience. In particular, the book is an ideal resource for advanced undergraduate statistics students and practitioners with comparable experience. Bayes Rules! empowers readers to weave Bayesian approaches into their everyday practice. Discussions and applications are data driven. A natural progression from fundamental to multivariable, hierarchical models emphasizes a practical and generalizable model building process. The evaluation of these Bayesian models reflects the fact that a data analysis does not exist in a vacuum. Features • Utilizes data-driven examples and exercises. • Emphasizes the iterative model building and evaluation process. • Surveys an interconnected range of multivariable regression and classification models. • Presents fundamental Markov chain Monte Carlo simulation. • Integrates R code, including RStan modeling tools and the bayesrules package. • Encourages readers to tap into their intuition and learn by doing. • Provides a friendly and inclusive introduction to technical Bayesian concepts. • Supports Bayesian applications with foundational Bayesian theory.
Author: Rob J Hyndman Publisher: OTexts ISBN: 0987507117 Category : Business & Economics Languages : en Pages : 380
Book Description
Forecasting is required in many situations. Stocking an inventory may require forecasts of demand months in advance. Telecommunication routing requires traffic forecasts a few minutes ahead. Whatever the circumstances or time horizons involved, forecasting is an important aid in effective and efficient planning. This textbook provides a comprehensive introduction to forecasting methods and presents enough information about each method for readers to use them sensibly.
Author: Beate Weidenhammer Publisher: ISBN: Category : Languages : en Pages :
Book Description
In this paper we will present recent work on a new unit-level small area methodology that can be used with continuous and discrete outcomes. The proposed method is based on constructing a model-based estimator of the distribution function by using a nested-error regression model for the quantiles of the target outcome. A general set of domain-specific parameters that extends beyond averages is then estimated by sampling from the estimated distribution function. For fitting the model we exploit the link between the Asymmetric Laplace Distribution and maximum likelihood estimation for quantile regression. The specification of the distribution of the random effects is considered in some detail by exploring the use of parametric and non-parametric alternatives. The use of the proposed methodology with discrete (count) outcomes requires appropriate transformations, in particular jittering. For the case of discrete outcomes the methodology relaxes the restrictive assumptions of the Poisson generalised linear mixed model and allows for what is potentially a more flexible mean-variance relationship. Mean Squared Error estimation is discussed. Extensive model-based simulations are used for comparing the proposed methodology to alternative unit-level methodologies for estimating a broad range of complex parameters.
Author: Cristina Davino Publisher: John Wiley & Sons ISBN: 111997528X Category : Mathematics Languages : en Pages : 288
Book Description
A guide to the implementation and interpretation of Quantile Regression models This book explores the theory and numerous applications of quantile regression, offering empirical data analysis as well as the software tools to implement the methods. The main focus of this book is to provide the reader with a comprehensive description of the main issues concerning quantile regression; these include basic modeling, geometrical interpretation, estimation and inference for quantile regression, as well as issues on validity of the model, diagnostic tools. Each methodological aspect is explored and followed by applications using real data. Quantile Regression: Presents a complete treatment of quantile regression methods, including, estimation, inference issues and application of methods. Delivers a balance between methodolgy and application Offers an overview of the recent developments in the quantile regression framework and why to use quantile regression in a variety of areas such as economics, finance and computing. Features a supporting website (www.wiley.com/go/quantile_regression) hosting datasets along with R, Stata and SAS software code. Researchers and PhD students in the field of statistics, economics, econometrics, social and environmental science and chemistry will benefit from this book.
Author: Filippo Maria Bianchi Publisher: Springer ISBN: 3319703382 Category : Computers Languages : en Pages : 74
Book Description
The key component in forecasting demand and consumption of resources in a supply network is an accurate prediction of real-valued time series. Indeed, both service interruptions and resource waste can be reduced with the implementation of an effective forecasting system. Significant research has thus been devoted to the design and development of methodologies for short term load forecasting over the past decades. A class of mathematical models, called Recurrent Neural Networks, are nowadays gaining renewed interest among researchers and they are replacing many practical implementations of the forecasting systems, previously based on static methods. Despite the undeniable expressive power of these architectures, their recurrent nature complicates their understanding and poses challenges in the training procedures. Recently, new important families of recurrent architectures have emerged and their applicability in the context of load forecasting has not been investigated completely yet. This work performs a comparative study on the problem of Short-Term Load Forecast, by using different classes of state-of-the-art Recurrent Neural Networks. The authors test the reviewed models first on controlled synthetic tasks and then on different real datasets, covering important practical cases of study. The text also provides a general overview of the most important architectures and defines guidelines for configuring the recurrent networks to predict real-valued time series.
Author: Tilmann Gneiting
Author: Tilmann Gneiting
Author: Johannes Resin
Author: Joan Aguilar Fargas
Author: Alicia A. Johnson
Author: Raffaella Giacomini
Author: Rob J Hyndman
Author: Beate Weidenhammer
Author: Cristina Davino
Author: Filippo Maria Bianchi
Author: Leena Kalliovirta