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Author: Renna Jiang
Publisher:
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Languages : en
Pages : 0
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Book Description
We present a Bayesian approach for analyzing aggregate level sales data in a market with differentiated products. We consider the aggregate share model proposed by Berry, Levinsohn and Pakes (1995) which introduces a common demand shock into an aggregated random coefficient logit model. A full likelihood approach is possible with a specification of the distribution of the common demand shock. We introduce a re-parameterization of the covariance matrix to improve the performance of the random walk Metropolis for covariance parameters. We illustrate the usefulness of our approach with both actual and simulated data. Sampling experiments show that our approach performs well relative to the GMM estimator even in the presence of a mis-specified shock distribution. We view our approach as useful for those who willing to trade off one additional distributional assumption for increased efficiency in estimation.
Author: Renna Jiang
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We present a Bayesian approach for analyzing aggregate level sales data in a market with differentiated products. We consider the aggregate share model proposed by Berry, Levinsohn and Pakes (1995) which introduces a common demand shock into an aggregated random coefficient logit model. A full likelihood approach is possible with a specification of the distribution of the common demand shock. We introduce a re-parameterization of the covariance matrix to improve the performance of the random walk Metropolis for covariance parameters. We illustrate the usefulness of our approach with both actual and simulated data. Sampling experiments show that our approach performs well relative to the GMM estimator even in the presence of a mis-specified shock distribution. We view our approach as useful for those who willing to trade off one additional distributional assumption for increased efficiency in estimation.
Author: Andres Musalem
Publisher:
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Languages : en
Pages : 0
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This article discusses the use of Bayesian methods for estimating logit demand models using aggregate data, i.e. information solely on how many consumers chose each product. We analyze two different demand systems: independent samples and consumer panel. Under the first system, there is a different and independent random sample of N consumers in each period and each consumer makes only a single purchase decision. Under the second system, the same N consumers make a purchase decision in each of T periods. The proposed methods are illustrated using simulated and real data, and managerial insights available via data augmentation are discussed in detail.
Author: German Zenetti
Publisher:
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Languages : en
Pages : 0
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Book Description
The random coefficients logit model is a workhorse in marketing and empirical industrial organizations research. When only aggregate data are available, it is customary to calibrate the model based on market shares as data input, even if the data are available in the form of aggregate counts. However, market shares are functionally related to model primitives in the random coefficients model whereas finite aggregate counts are only probabilistic functions of these model primitives. A recent paper by Park & Gupta (2009) stresses this distinction but is hamstrung by numerical problems when demonstrating its potential practical importance. We develop Bayesian inference for the likelihood function proposed by Park & Gupta, sidestepping the numerical problem encountered by these authors. We show how taking account of the amount of information about shares by modeling counts directly results in improved inference.
Author: Hairong Song
Publisher:
ISBN:
Category :
Languages : en
Pages : 268
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Author: Brian J. Reich
Publisher: CRC Press
ISBN: 0429514344
Category : Mathematics
Languages : en
Pages : 259
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Book Description
Bayesian Statistical Methods provides data scientists with the foundational and computational tools needed to carry out a Bayesian analysis. This book focuses on Bayesian methods applied routinely in practice including multiple linear regression, mixed effects models and generalized linear models (GLM). The authors include many examples with complete R code and comparisons with analogous frequentist procedures. In addition to the basic concepts of Bayesian inferential methods, the book covers many general topics: Advice on selecting prior distributions Computational methods including Markov chain Monte Carlo (MCMC) Model-comparison and goodness-of-fit measures, including sensitivity to priors Frequentist properties of Bayesian methods Case studies covering advanced topics illustrate the flexibility of the Bayesian approach: Semiparametric regression Handling of missing data using predictive distributions Priors for high-dimensional regression models Computational techniques for large datasets Spatial data analysis The advanced topics are presented with sufficient conceptual depth that the reader will be able to carry out such analysis and argue the relative merits of Bayesian and classical methods. A repository of R code, motivating data sets, and complete data analyses are available on the book’s website. Brian J. Reich, Associate Professor of Statistics at North Carolina State University, is currently the editor-in-chief of the Journal of Agricultural, Biological, and Environmental Statistics and was awarded the LeRoy & Elva Martin Teaching Award. Sujit K. Ghosh, Professor of Statistics at North Carolina State University, has over 22 years of research and teaching experience in conducting Bayesian analyses, received the Cavell Brownie mentoring award, and served as the Deputy Director at the Statistical and Applied Mathematical Sciences Institute.
Author: Ruth King
Publisher: CRC Press
ISBN: 1439811881
Category : Mathematics
Languages : en
Pages : 457
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Book Description
Emphasizing model choice and model averaging, this book presents up-to-date Bayesian methods for analyzing complex ecological data. It provides a basic introduction to Bayesian methods that assumes no prior knowledge. The book includes detailed descriptions of methods that deal with covariate data and covers techniques at the forefront of research, such as model discrimination and model averaging. Leaders in the statistical ecology field, the authors apply the theory to a wide range of actual case studies and illustrate the methods using WinBUGS and R. The computer programs and full details of the data sets are available on the book's website.
Author: William G. FORTNEY
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Languages : en
Pages :
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Author:
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Languages : en
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Random Coefficient Autoregressive (RCA) models are obtained by introducing random coefficients to an AR or more generally ARMA model. These models have second order properties similar to that of ARCH and GARCH models. Historically an RCA model has been used to model the conditional mean of a time series, but it can also be viewed as a volatility model. In this thesis, we consider both Frequentist and Bayesian approaches to analyze the first order RCA models. For a weakly stationary RCA(1), it has been shown that the Maximum Likelihood Estimates (MLEs) are strongly consistent and satisfy a classical Central Limit Theorem. We consider a broader class of RCA(1) models whose parameters lie in the region of strict stationarity and ergodicity. We show that similar asymptotic properties can be extended to this class of models which includes the unit-root RCA(1) as a special case. The existence of a unit root in an RCA(1) has significant impact on the inference of data especially in the aspect of model forecasting. We develop the Wald criterion based on MLEs for testing unit root and evaluate its power via simulation studies. In addition to the Frequentist approach to RCA(1) models, Bayesian methods can also be used. We propose non-informative priors for the model parameters and apply them in Bayesian estimation procedure. Two model selection criteria are investigated to see their performance in choosing between RCA(1) and AR(1) models. We use two Bayesian methods to test for the unit-root hypothesis: one is based on the Posterior Interval (PI), and the other one is by means of Bayes Factor (BF). We apply both flat and mixed priors for the stationarity parameter in RCA(1) and compare the performance of different Bayesian unit-root testing criteria using these two types of prior densities through simulation. At the end of the thesis, two real life examples involving the daily stock volume transaction data are presented to show the applicability of the proposed methods.
Author: Santiago Barreda
Publisher: Taylor & Francis
ISBN: 1000869784
Category : Psychology
Languages : en
Pages : 485
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Book Description
This comprehensive book is an introduction to multilevel Bayesian models in R using brms and the Stan programming language. Featuring a series of fully worked analyses of repeated measures data, the focus is placed on active learning through the analyses of the progressively more complicated models presented throughout the book. In this book, the authors offer an introduction to statistics entirely focused on repeated measures data beginning with very simple two-group comparisons and ending with multinomial regression models with many ‘random effects’. Across 13 well-structured chapters, readers are provided with all the code necessary to run all the analyses and make all the plots in the book, as well as useful examples of how to interpret and write up their own analyses. This book provides an accessible introduction for readers in any field, with any level of statistical background. Senior undergraduate students, graduate students, and experienced researchers looking to ‘translate’ their skills with more traditional models to a Bayesian framework will benefit greatly from the lessons in this text.
Author: John Geweke
Publisher: Oxford University Press
ISBN: 0191618268
Category : Business & Economics
Languages : en
Pages : 576
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Book Description
Bayesian econometric methods have enjoyed an increase in popularity in recent years. Econometricians, empirical economists, and policymakers are increasingly making use of Bayesian methods. This handbook is a single source for researchers and policymakers wanting to learn about Bayesian methods in specialized fields, and for graduate students seeking to make the final step from textbook learning to the research frontier. It contains contributions by leading Bayesians on the latest developments in their specific fields of expertise. The volume provides broad coverage of the application of Bayesian econometrics in the major fields of economics and related disciplines, including macroeconomics, microeconomics, finance, and marketing. It reviews the state of the art in Bayesian econometric methodology, with chapters on posterior simulation and Markov chain Monte Carlo methods, Bayesian nonparametric techniques, and the specialized tools used by Bayesian time series econometricians such as state space models and particle filtering. It also includes chapters on Bayesian principles and methodology.
