A Comparison of Bayes Factor Approximation Methods Including Two New Methods
ثبت نشده
چکیده
Bayes Factors play an important role in comparing the fit of models ranging from multiple regression to mixture models. Full Bayesian analysis calculates a Bayes Factor from an explicit prior distribution. However, computational limitations or lack of an appropriate prior sometimes prevent researchers from using an exact Bayes Factor. Instead, it is approximated, often using Schwarz’s (1978) Bayesian Information Criterion (BIC), or a variant of the BIC. In this paper we provide a comparison of several Bayes Factor approximations, including two new approximations, the SPBIC and IBIC. The SPBIC is justified by using a scaled unit information prior distribution that is more general than the BIC’s unit information prior, and the IBIC approximation utilizes more terms of approximation than in the BIC. In a simulation study we show that several measures perform well in large samples, that performance declines in smaller samples, and that SPBIC and IBIC can provide improvement to existing measures under some conditions, including small sample sizes. We then illustrate the use of the fit measures in an empirical example from the crime data of Ehrlich (1973). We conclude with recommendations for researchers.
منابع مشابه
Modified Linear Approximation for Assessment of Rigid Block Dynamics
This study proposes a new linear approximation for solving the dynamic response equations of a rocking rigid block. Linearization assumptions which have already been used by Hounser and other researchers cannot be valid for all rocking blocks with various slenderness ratios and dimensions; hence, developing new methods which can result in better approximation of governing equations while keepin...
متن کاملImproving the Performance of Bayesian Estimation Methods in Estimations of Shift Point and Comparison with MLE Approach
A Bayesian analysis is used to detect a change-point in a sequence of independent random variables from exponential distributions. In This paper, we try to estimate change point which occurs in any sequence of independent exponential observations. The Bayes estimators are derived for change point, the rate of exponential distribution before shift and the rate of exponential distribution after s...
متن کاملApproximating Bayes Estimates by Means of the Tierney Kadane, Importance Sampling and Metropolis-Hastings within Gibbs Methods in the Poisson-Exponential Distribution: A Comparative Study
Here, we work on the problem of point estimation of the parameters of the Poisson-exponential distribution through the Bayesian and maximum likelihood methods based on complete samples. The point Bayes estimates under the symmetric squared error loss (SEL) function are approximated using three methods, namely the Tierney Kadane approximation method, the importance sampling method and the Metrop...
متن کاملارزیابی ژنومی صفات آستانه ای با معماری های ژنتیکی متفاوت با استفاده از روشهای بیزی
The current study was carried out to evaluate accuracy of some Bayesian methods for genomic breeding values prediction for threshold traits with different types of genetic architecture based on distribution of gene effect and QTL numbers. A genome consisted of 3 chromosomes of 100 CM with 2000 single nucleotide polymorphisms (SNP) was simulated. The QTL numbers were 0.01, 0.05 and 0.1 of total ...
متن کاملEMPIRICAL BAYES ANALYSIS OF TWO-FACTOR EXPERIMENTS UNDER INVERSE GAUSSIAN MODEL
A two-factor experiment with interaction between factors wherein observations follow an Inverse Gaussian model is considered. Analysis of the experiment is approached via an empirical Bayes procedure. The conjugate family of prior distributions is considered. Bayes and empirical Bayes estimators are derived. Application of the procedure is illustrated on a data set, which has previously been an...
متن کامل