Assessing convergence diagnostic tests for Bayesian Cox regression

The Markov chain Monte Carlo (MCMC) method generates samples from the posterior distribution and uses these samples to approximate expectations of quantities of interest. For the process, researchers have to decide whether the Markov chain has reached the desired posterior distribution. Using convergence diagnostic tests are very important to decide whether the Markov chain has reached the target distribution. Our interest in this study was to compare the performances of convergence diagnostic tests for all parameters of Bayesian Cox regression model with different number of iterations by using a simulation and a real lung cancer dataset.     

A comparison of different procedures for principal component analysis in the presence of outliers

Principal component analysis (PCA) is a popular technique that is useful for dimensionality reduction but it is affected by the presence of outliers. The outlier sensitivity of classical PCA (CPCA) has caused the development of new approaches. Effects of using estimates obtained by expectation–maximization – EM and multiple imputation – MI instead of outliers were examined on the artificial and a real data set. Furthermore, robust PCA based on minimum covariance determinant (MCD), PCA based on estimates obtained by EM instead of outliers and PCA based on estimates obtained by MI instead of outliers were compared with the results of CPCA. In this study, we tried to show the effects of using estimates obtained by MI and EM instead of outliers, depending on the ratio of outliers in data set. Finally, when the ratio of outliers exceeds 20%, we suggest the use of estimates obtained by MI and EM instead of outliers as an alternative approach.     

On the BLUEs in Two Linear Models via C. R. Rao's Pandora's Box

We consider the estimation of the parameters in two partitioned linear models, denoted by 𝒜 = {y, X ₁ β ₁ + X ₂ β ₂, V _𝒜} and ? = {y, X ₁ β ₁ + X ₂ β ₂, V _?}, which we call full models. Correspondingly, we define submodels 𝒜₁ = {y, X ₁ β ₁, V _𝒜} and ?₁ = {y, X ₁ β ₁, V _?}. Using the so-called Pandora's Box approach introduced by Rao (1971 Rao , C. R. ( 1971 ). Unified theory of linear estimation . Sankhy?, Ser. A 33 : 371 – 394 . [Corrigendum (1972), 34, p. 194, 477.]  [Google Scholar], we give new necessary and sufficient conditions for the equality between the best linear unbiased estimators (BLUEs) of X ₁ β ₁ under 𝒜₁ and ?₁ as well as under 𝒜 and ?. In our considerations we will utilise the Frisch–Waugh–Lovell theorem which provides a connection between the full model 𝒜 and the reduced model 𝒜 _r  = {M ₂ y, M ₂ X ₁ β ₁, M ₂ V _𝒜 M ₂} with M ₂ being an appropriate orthogonal projector. Moreover, we consider the equality of the BLUEs under the full models assuming that they are equal under the submodels.     

Using informative priors for handling missing data problem in Cox regression

The aim of this study is to determine the effect of informative priors for variables with missing value and to compare Bayesian Cox regression and Cox regression analysis. For this purpose, firstly simulated data sets with different sample size within different missing rate were generated and each of data sets were analysed by Cox regression and Bayesian Cox regression with informative prior. Secondly lung cancer data set as real data set was used for analysis. Consequently, using informative priors for variables with missing value solved the missing data problem.     

Flexibility Structure and Capacity Design with Human Resource Considerations

Most service systems consist of multidepartmental structures with multiskill agents that can deal with several types of service requests. The design of flexibility in terms of agents' skill sets and assignments of requests is a critical issue for such systems. The objective of this study was to identify preferred flexibility structures when demand is random and capacity is finite. We compare structures recommended by the flexibility literature to structures we observe in practice within call centers. To enable a comparison of flexibility structures under optimal capacity, the capacity optimization problem for this setting is formulated as a two‐stage stochastic optimization problem. A simulation‐based optimization procedure for this problem using sample‐path gradient estimation is proposed and tested, and used in the subsequent comparison of the flexibility structures being studied. The analysis illustrates under what conditions on demand, cost, and human resource considerations, the structures found in practice are preferred.