scholarly journals Modelling monotonic effects of ordinal predictors in Bayesian regression models

2020 ◽  
Vol 73 (3) ◽  
pp. 420-451 ◽  
Author(s):  
Paul‐Christian Bürkner ◽  
Emmanuel Charpentier
Keyword(s):  
Regression Models ◽  
Bayesian Regression ◽  
Ordinal Predictors

scholarly journals Modeling Monotonic Effects of Ordinal Predictors in Bayesian Regression Models

2018 ◽  
Author(s):  
Paul - Christian Bürkner ◽  
Emmanuel Charpentier
Keyword(s):  
Regression Models ◽  
Prior Information ◽  
Estimation Method ◽  
Predictive Performance ◽  
R Package ◽  
Bayesian Regression ◽  
Simulation Studies ◽  
Interaction Terms ◽  
Fully Bayesian ◽  
Ordinal Predictors

Ordinal predictors are commonly used in regression models. They are often incorrectly treated as either nominal or metric, thus under- or overestimating the contained information. Such practices may lead to worse inference and predictions compared to methods which are specifically designed for this purpose. We propose a new method for modeling ordinal predictors that applies in situations in which it is reasonable to assume their effects to be monotonic. The parameterization of such monotonic effects is realized in terms of a scale parameter $b$ representing the direction and size of the effect and a simplex parameter $\zeta$ modeling the normalized differences between categories. This ensures that predictions increase or decrease monotonically, while changes between adjacent categories may vary across categories. This formulation generalizes to interaction terms as well as multilevel structures. Monotonic effects may not only be applied to ordinal predictors, but also to other discrete variables for which a monotonic relationship is plausible. In simulation studies, we show that the model is well calibrated and, in case of monotonicity, has similar or even better predictive performance than other approaches designed to handle ordinal predictors. Using Stan, we developed a Bayesian estimation method for monotonic effects, which allows to incorporate prior information and to check the assumption of monotonicity. We have implemented this method in the R package brms, so that fitting monotonic effects in a fully Bayesian framework is now straightforward.

scholarly journals Smartphone GPS Locations of Students’ Movements to and from Campus

2021 ◽  
Vol 10 (8) ◽  
pp. 517
Author(s):  
Patricia K. Doyle-Baker ◽  
Andrew Ladle ◽  
Angela Rout ◽  
Paul Galpern
Keyword(s):  
Student Engagement ◽  
Environmental Factors ◽  
University Students ◽  
Regression Models ◽  
Bayesian Regression ◽  
Daily Movement ◽  
Campus Visit ◽  
Canadian City ◽  
Campus Activities ◽  
Ability And Willingness

For many university students, commuting to and from campus constitutes a large proportion of their daily movement, and therefore it may influence their ability and willingness to spend time on campus or to participate in campus activities. To assess student engagement on campus, we collected smartphone GPS location histories from volunteers (n = 280) attending university in a major Canadian city. We investigated how campus visit length and frequency were related to characteristics of the commute using Bayesian regression models. Slower commutes and commutes over longer distances were associated with more time spent but less frequent visits to campus. Our results demonstrate that exposure to campus life, and therefore the potential for student engagement, may relate not just to whether a student lives on or near campus, but also to urban environmental factors that interact to influence the commuting experience.

scholarly journals Robust Bayesian Regression with Synthetic Posterior Distributions

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 661 ◽  
Author(s):  
Shintaro Hashimoto ◽  
Shonosuke Sugasawa
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Bayesian Variable Selection ◽  
Bayesian Regression ◽  
Simulation Studies ◽  
Posterior Distributions ◽  
Linear Regression Models ◽  
Computation Algorithm ◽  
Shrinkage Priors ◽  
Variable Selection And Estimation

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on γ-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets.

scholarly journals Bitcoin Network Mechanics: Forecasting the BTC Closing Price Using Vector Auto-Regression Models Based on Endogenous and Exogenous Feature Variables

2020 ◽  
Vol 13 (9) ◽  
pp. 189 ◽  
Author(s):  
Ahmed Ibrahim ◽  
Rasha Kashef ◽  
Menglu Li ◽  
Esteban Valencia ◽  
Eric Huang
Keyword(s):  
Regression Models ◽  
Prediction Models ◽  
Vector Autoregression ◽  
State Of The Art ◽  
Bayesian Regression ◽  
Major Question ◽  
Factors Of Influence ◽  
Vector Auto Regression ◽  
Auto Regression ◽  
Price Discovery Process

The Bitcoin (BTC) market presents itself as a new unique medium currency, and it is often hailed as the “currency of the future”. Simulating the BTC market in the price discovery process presents a unique set of market mechanics. The supply of BTC is determined by the number of miners and available BTC and by scripting algorithms for blockchain hashing, while both speculators and investors determine demand. One major question then is to understand how BTC is valued and how different factors influence it. In this paper, the BTC market mechanics are broken down using vector autoregression (VAR) and Bayesian vector autoregression (BVAR) prediction models. The models proved to be very useful in simulating past BTC prices using a feature set of exogenous variables. The VAR model allows the analysis of individual factors of influence. This analysis contributes to an in-depth understanding of what drives BTC, and it can be useful to numerous stakeholders. This paper’s primary motivation is to capitalize on market movement and identify the significant price drivers, including stakeholders impacted, effects of time, as well as supply, demand, and other characteristics. The two VAR and BVAR models are compared with some state-of-the-art forecasting models over two time periods. Experimental results show that the vector-autoregression-based models achieved better performance compared to the traditional autoregression models and the Bayesian regression models.

Bayesian survival analysis in clinical trials: What methods are used in practice?

2016 ◽  
Vol 14 (1) ◽  
pp. 78-87 ◽  
Author(s):  
Caroline Brard ◽  
Gwénaël Le Teuff ◽  
Marie-Cécile Le Deley ◽  
Lisa V Hampson
Keyword(s):  
Clinical Trials ◽  
Survival Analysis ◽  
Bayesian Methods ◽  
Regression Models ◽  
Final Analysis ◽  
Bayesian Regression ◽  
Phase Iii ◽  
Informative Priors ◽  
Primary Analysis ◽  
Survival Analyses

Background Bayesian statistics are an appealing alternative to the traditional frequentist approach to designing, analysing, and reporting of clinical trials, especially in rare diseases. Time-to-event endpoints are widely used in many medical fields. There are additional complexities to designing Bayesian survival trials which arise from the need to specify a model for the survival distribution. The objective of this article was to critically review the use and reporting of Bayesian methods in survival trials. Methods A systematic review of clinical trials using Bayesian survival analyses was performed through PubMed and Web of Science databases. This was complemented by a full text search of the online repositories of pre-selected journals. Cost-effectiveness, dose-finding studies, meta-analyses, and methodological papers using clinical trials were excluded. Results In total, 28 articles met the inclusion criteria, 25 were original reports of clinical trials and 3 were re-analyses of a clinical trial. Most trials were in oncology (n = 25), were randomised controlled (n = 21) phase III trials (n = 13), and half considered a rare disease (n = 13). Bayesian approaches were used for monitoring in 14 trials and for the final analysis only in 14 trials. In the latter case, Bayesian survival analyses were used for the primary analysis in four cases, for the secondary analysis in seven cases, and for the trial re-analysis in three cases. Overall, 12 articles reported fitting Bayesian regression models (semi-parametric, n = 3; parametric, n = 9). Prior distributions were often incompletely reported: 20 articles did not define the prior distribution used for the parameter of interest. Over half of the trials used only non-informative priors for monitoring and the final analysis (n = 12) when it was specified. Indeed, no articles fitting Bayesian regression models placed informative priors on the parameter of interest. The prior for the treatment effect was based on historical data in only four trials. Decision rules were pre-defined in eight cases when trials used Bayesian monitoring, and in only one case when trials adopted a Bayesian approach to the final analysis. Conclusion Few trials implemented a Bayesian survival analysis and few incorporated external data into priors. There is scope to improve the quality of reporting of Bayesian methods in survival trials. Extension of the Consolidated Standards of Reporting Trials statement for reporting Bayesian clinical trials is recommended.

Tropical deforestation in Madagascar: analysis using hierarchical, spatially explicit, Bayesian regression models

2005 ◽  
Vol 185 (1) ◽  
pp. 105-131 ◽  
Author(s):  
Deepak K. Agarwal ◽  
John A. Silander ◽  
Alan E. Gelfand ◽  
Robert E. Dewar ◽  
John G. Mickelson
Keyword(s):  
Regression Models ◽  
Tropical Deforestation ◽  
Bayesian Regression ◽  
Spatially Explicit

scholarly journals R-squared for Bayesian Regression Models

2019 ◽  
Vol 73 (3) ◽  
pp. 307-309 ◽  
Author(s):  
Andrew Gelman ◽  
Ben Goodrich ◽  
Jonah Gabry ◽  
Aki Vehtari
Keyword(s):  
Regression Models ◽  
Bayesian Regression
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