A Bayesian Subset Analysis Of Sensory Evaluation Data

In social sciences it is easy to carry out sensory experiments using say a J-point hedonic scale. One major problem with the J-point hedonic scale is that a conversion from the category scales to numeric scores might not be sensible because the panelists generally view increments on the hedonic scale as psychologically unequal. In the current problem several products are rated by a set of panelists on the J-point hedonic scale. One objective is to select the best subset of products and to assess the quality of the products by estimating the mean and standard deviation response for the selected products. A priori information about which subset is the best is incorporated, and a stochastic ordering is modified to select the best subset of the products. The method introduced in this article is sampling based, and it uses Monte Carlo integration with rejection sampling. The methodology is applied to select the best set of entrees in a military ration, and then to estimate the probability of at least a neutral response for the judged best entrees. A comparison is made with the method, which converts the category scales to numeric scores

Discussion of five papers at JSM2023 in an invited session in honor of Joe Sedransk

At JSM2023, I organized an invited session of five speakers on {\bf Contributions to Inference from Survey Samples: In Honor of Joe Sedransk}. I also served as the discussant of these five papers, which were presented by Qixuan Chen, Lu Chen, Glen Meeden, Mary Meyer and Mary Thompson in this order. This paper is a summary of my discussions at the meeting. The first 2.5 minutes was used to say congratulation to Professor Joe Sedransk, and because my time was limited to 15 minutes, I spoke about $2.5$ minutes on each paper, and I made a small point about each paper. I highlighted some of Joe's contributions and my collaborations with him

Bayesian Predictive Inference with Survey Weights for Binary Response: A Simulation Study and a Numerical Example

We consider the problem of Bayesian predictive inference for binary response with covariates and survey weights. Our method makes use of the combination of probability survey samples that have been enhanced by auxiliary data. The incorporation of survey weights into a logistic regression model, which creates a thorough and logical analytical paradigm, is at the core of our methodology. Our investigation covers six different models that were carefully created to include both normalized and unnormalized weighted likelihoods. Three iterations of adjusted survey weights—original, trimmed, and calibrated—are taken into account within this spectrum. The Metropolis-Hastings sampler is the implementation algorithm for our analysis. Building on this foundation, we use the stratification and surrogate sampling technique to expand our inferences to finite population parameters. We conduct a thorough evaluation that includes a simulation study and a real-world dataset focused on body mass index (BMI) in order to assess the performance and efficacy of our models. Our findings show how powerful models with normalized density functions and adjusted trimmed weights are. These models exhibit a unique capability for higher estimation accuracy while maintaining fidelity to the fundamental principles of Bayesian inference. The results of our study have broad implications for the field of research as a whole, highlighting the significance of the framework we proposed and the exceptional value of trimmed weights that have been adjusted for the purpose of driving effective predictive inference in survey-oriented research studies

Small area estimation of general parameters with application to poverty indicators: A hierarchical Bayes approach

Poverty maps are used to aid important political decisions such as allocation of development funds by governments and international organizations. Those decisions should be based on the most accurate poverty figures. However, often reliable poverty figures are not available at fine geographical levels or for particular risk population subgroups due to the sample size limitation of current national surveys. These surveys cannot cover adequately all the desired areas or population subgroups and, therefore, models relating the different areas are needed to 'borrow strength" from area to area. In particular, the Spanish Survey on Income and Living Conditions (SILC) produces national poverty estimates but cannot provide poverty estimates by Spanish provinces due to the poor precision of direct estimates, which use only the province specific data. It also raises the ethical question of whether poverty is more severe for women than for men in a given province. We develop a hierarchical Bayes (HB) approach for poverty mapping in Spanish provinces by gender that overcomes the small province sample size problem of the SILC. The proposed approach has a wide scope of application because it can be used to estimate general nonlinear parameters. We use a Bayesian version of the nested error regression model in which Markov chain Monte Carlo procedures and the convergence monitoring therein are avoided. A simulation study reveals good frequentist properties of the HB approach. The resulting poverty maps indicate that poverty, both in frequency and intensity, is localized mostly in the southern and western provinces and it is more acute for women than for men in most of the provinces.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS702 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bayesian Logistic Regression Model for Sub-Areas

Many population-based surveys have binary responses from a large number of individuals in each household within small areas. One example is the Nepal Living Standards Survey (NLSS II), in which health status binary data (good versus poor) for each individual from sampled households (sub-areas) are available in the sampled wards (small areas). To make an inference for the finite population proportion of individuals in each household, we use the sub-area logistic regression model with reliable auxiliary information. The contribution of this model is twofold. First, we extend an area-level model to a sub-area level model. Second, because there are numerous sub-areas, standard Markov chain Monte Carlo (MCMC) methods to find the joint posterior density are very time-consuming. Therefore, we provide a sampling-based method, the integrated nested normal approximation (INNA), which permits fast computation. Our main goal is to describe this hierarchical Bayesian logistic regression model and to show that the computation is much faster than the exact MCMC method and also reasonably accurate. The performance of our method is studied by using NLSS II data. Our model can borrow strength from both areas and sub-areas to obtain more efficient and precise estimates. The hierarchical structure of our model captures the variation in the binary data reasonably well

Sampling methods for the concentration parameter and discrete baseline of the Dirichlet Process

There are many models in the current statistical literature for making inferences based on samples selected from a finite population. Parametric models may be problematic because statistical inference is sensitive to parametric assumptions. The Dirichlet process (DP) prior is very flexible and determines the complexity of the model. It is indexed by two hyperparameters: the baseline distribution and concentration parameter. We address two distinct problems in the article. Firstly, we review the current sampling methods for the concentration parameter, which use the continuous baseline distribution. We compare three different methods: the adaptive rejection method, the mixture of Gammas method and the grid method. We also propose a new method based on the ratio of uniforms. Secondly, in practice, some survey responses are known to be discrete. If a continuous distribution is adopted as the baseline distribution, the model is misspecified and standard inference may be invalid. We propose a discrete baseline approach to the DP prior and sample the unobserved responses from the finite population both using a Polya urn scheme and a Multinomial distribution. We applied our discrete baseline approach to a Phytophthora data set