Choice of Prior Distribution

2020 ◽  
pp. 33-40
Author(s):  
Edwin J. Green ◽  
Andrew O. Finley ◽  
William E. Strawderman
Keyword(s):  
Prior Distribution

Bayesian Applications in Auditory Research

2019 ◽  
Vol 62 (3) ◽  
pp. 577-586 ◽  
Author(s):  
Garnett P. McMillan ◽  
John B. Cannon
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Interim Analysis ◽  
Iterative Process ◽  
Bayes Theorem ◽  
Sound Therapy ◽  
The Many ◽  
Auditory Research

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592

scholarly journals Improved inference for areal unit count data using graph-based optimisation

2021 ◽  
Vol 31 (4) ◽  
Author(s):  
Duncan Lee ◽  
Kitty Meeks ◽  
William Pettersson
Keyword(s):  
Random Effects ◽  
Count Data ◽  
Prior Distribution ◽  
Disease Surveillance ◽  
Sharing Rule ◽  
Markov Random ◽  
Spatial Correlation Structure ◽  
Conditional Autoregressive ◽  
Spatio Temporal ◽  
Special Case

AbstractSpatio-temporal count data relating to a set of non-overlapping areal units are prevalent in many fields, including epidemiology and social science. The spatial autocorrelation inherent in these data is typically modelled by a set of random effects that are assigned a conditional autoregressive prior distribution, which is a special case of a Gaussian Markov random field. The autocorrelation structure implied by this model depends on a binary neighbourhood matrix, where two random effects are assumed to be partially autocorrelated if their areal units share a common border, and are conditionally independent otherwise. This paper proposes a novel graph-based optimisation algorithm for estimating either a static or a temporally varying neighbourhood matrix for the data that better represents its spatial correlation structure, by viewing the areal units as the vertices of a graph and the neighbour relations as the set of edges. The improved estimation performance of our methodology compared to the commonly used border sharing rule is evidenced by simulation, before the method is applied to a new respiratory disease surveillance study in Scotland between 2011 and 2017.

scholarly journals Toxic Elements in Traditional Kohl-Based Eye Cosmetics in Spanish and German Markets

2021 ◽  
Vol 18 (11) ◽  
pp. 6109
Author(s):  
Elisabet Navarro-Tapia ◽  
Mariona Serra-Delgado ◽  
Lucía Fernández-López ◽  
Montserrat Meseguer-Gilabert ◽  
María Falcón ◽  
...  
Keyword(s):  
Heavy Metals ◽  
Prior Distribution ◽  
Inductively Coupled Plasma ◽  
Toxic Elements ◽  
Optical Emission ◽  
The European Union ◽  
Inductively Coupled ◽  
Women And Children ◽  
Harmful Effects ◽  
The Eu

Kohl is a traditional cosmetic widely used in Asia and Africa. In recent years, demand for kohl-based eyelids and lipsticks has increased in Europe, linked to migratory phenomena of populations from these continents. Although the European legislation prohibits the use of heavy metals in cosmetics due to the harmful effects to human health, particularly to pregnant women and children, these elements are still present in certain products. The European Union recommended levels are Pb < 20 ppm, As < 5 ppm, Cd < 5 ppm, Sb < 100 ppm, and Ni < 200 ppm. In Germany, levels are more restrictive: Pb < 2 ppm, As < 0.5 ppm, Cd < 0.1 ppm, Sb < 0.5 ppm, and Ni < 10 ppm. Here, we analyzed 12 kohl-based cosmetics in different presentations (powder, paste, and pencil) that were purchased in Spanish and German local shops. An inductively coupled plasma optical emission spectrophotometer was used to identify toxic elements and heavy metals. Levels of Pb ranged between 1.7 and 410,000 ppm in six of the study samples, four of which had levels above the recommended limit of at least two heavy metals. Arsenic (a carcinogenic element) values were within the range allowed by the EU in only 58% of the studied samples. Moreover, two products doubled this limit, reaching levels of 9.2 and 12.6 ppm. In one of the products, cadmium, related to toxic keratitis, was four times higher (20.7 ppm) than that allowed, while in two other products, these limits were doubled (11.8 and 12.7 ppm). Our results indicate the need to supervise the manufacture of kohl-based traditional products and the analysis of their composition prior distribution in European countries.

scholarly journals Variance prior specification for a basket trial design using Bayesian hierarchical modeling

2018 ◽  
Vol 16 (2) ◽  
pp. 142-153 ◽  
Author(s):  
Kristen M Cunanan ◽  
Alexia Iasonos ◽  
Ronglai Shen ◽  
Mithat Gönen
Keyword(s):  
Standard Deviation ◽  
Prior Distribution ◽  
Hierarchical Modeling ◽  
Bayesian Hierarchical Modeling ◽  
Bayesian Hierarchical ◽  
Inverse Gamma ◽  
Wide Range ◽  
Basket Trial ◽  
Basket Trials ◽  
Variance Parameter

Background: In the era of targeted therapies, clinical trials in oncology are rapidly evolving, wherein patients from multiple diseases are now enrolled and treated according to their genomic mutation(s). In such trials, known as basket trials, the different disease cohorts form the different baskets for inference. Several approaches have been proposed in the literature to efficiently use information from all baskets while simultaneously screening to find individual baskets where the drug works. Most proposed methods are developed in a Bayesian paradigm that requires specifying a prior distribution for a variance parameter, which controls the degree to which information is shared across baskets. Methods: A common approach used to capture the correlated binary endpoints across baskets is Bayesian hierarchical modeling. We evaluate a Bayesian adaptive design in the context of a non-randomized basket trial and investigate three popular prior specifications: an inverse-gamma prior on the basket-level variance, a uniform prior and half-t prior on the basket-level standard deviation. Results: From our simulation study, we can see that the inverse-gamma prior is highly sensitive to the input hyperparameters. When the prior mean value of the variance parameter is set to be near zero [Formula: see text], this can lead to unacceptably high false-positive rates [Formula: see text] in some scenarios. Thus, use of this prior requires a fully comprehensive sensitivity analysis before implementation. Alternatively, we see that a prior that places sufficient mass in the tail, such as the uniform or half-t prior, displays desirable and robust operating characteristics over a wide range of prior specifications, with the caveat that the upper bound of the uniform prior and the scale parameter of the half-t prior must be larger than 1. Conclusion: Based on the simulation results, we recommend that those involved in designing basket trials that implement hierarchical modeling avoid using a prior distribution that places a majority of the density mass near zero for the variance parameter. Priors with this property force the model to share information regardless of the true efficacy configuration of the baskets. Many commonly used inverse-gamma prior specifications have this undesirable property. We recommend to instead consider the more robust uniform prior or half-t prior on the standard deviation.

scholarly journals Simulation Studies as a Tool to Understand Bayes Factors

2021 ◽  
Vol 4 (1) ◽  
pp. 251524592097262
Author(s):  
Don van Ravenzwaaij ◽  
Alexander Etz
Keyword(s):  
Simulation Study ◽  
Prior Distribution ◽  
Bayes Factor ◽  
R Package ◽  
Bayes Factors ◽  
Simulation Studies ◽  
Social Scientists ◽  
Simple Simulation ◽  
Set Up

When social scientists wish to learn about an empirical phenomenon, they perform an experiment. When they wish to learn about a complex numerical phenomenon, they can perform a simulation study. The goal of this Tutorial is twofold. First, it introduces how to set up a simulation study using the relatively simple example of simulating from the prior. Second, it demonstrates how simulation can be used to learn about the Jeffreys-Zellner-Siow (JZS) Bayes factor, a currently popular implementation of the Bayes factor employed in the BayesFactor R package and freeware program JASP. Many technical expositions on Bayes factors exist, but these may be somewhat inaccessible to researchers who are not specialized in statistics. In a step-by-step approach, this Tutorial shows how a simple simulation script can be used to approximate the calculation of the Bayes factor. We explain how a researcher can write such a sampler to approximate Bayes factors in a few lines of code, what the logic is behind the Savage-Dickey method used to visualize Bayes factors, and what the practical differences are for different choices of the prior distribution used to calculate Bayes factors.

scholarly journals Priors for Macroeconomic Time Series and Their Application

1994 ◽  
Vol 10 (3-4) ◽  
pp. 609-632 ◽  
Author(s):  
John Geweke
Keyword(s):  
Time Series ◽  
Prior Distribution ◽  
Odds Ratio ◽  
General Trend ◽  
Stationary Model ◽  
Posterior Odds ◽  
Posterior Odds Ratio ◽  
The Family ◽  
Macroeconomic Time Series ◽  
Posterior Moments

This paper takes up Bayesian inference in a general trend stationary model for macroeconomic time series with independent Student-t disturbances. The model is linear in the data, but nonlinear in parameters. An informative but nonconjugate family of prior distributions for the parameters is introduced, indexed by a single parameter that can be readily elicited. The main technical contribution is the construction of posterior moments, densities, and odd ratios by using a six-step Gibbs sampler. Mappings from the index parameter of the family of prior distribution to posterior moments, densities, and odds ratios are developed for several of the Nelson–Plosser time series. These mappings show that the posterior distribution is not even approximately Gaussian, and they indicate the sensitivity of the posterior odds ratio in favor of difference stationarity to the choice of the prior distribution.

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