Flexible estimation of parametric prospect models using hierarchical bayesian methods

Accommodating site variation in neuroimaging data using normative and hierarchical Bayesian models

Poverty is an important problem facing the world. Various ways are done to eradicate poverty. In planning poverty alleviation, policy makers need detailed information down to the smallest area level that can be produced. Currently, the demand for estimation at the small area level is increasing, while the success of estimation using the indirect method in reducing the Relative Standard Error (RSE) is very dependent on data conditions and the selection of the right method. This study aims to compare the results of estimating the percentage of poor people using direct estimates with indirect estimates using the Small Area Estimation (SAE) technique such as Empirical Best Linear Unbiased Predictor (EBLUP) and Hierarchical Bayesian (HB) method using a case study of poverty data at the sub-district level of Bengkulu Province. The data used are from the Social and Economic Survey (Susenas) in March 2022 and the 2021 Village Potential Data Collection (Podes). There is one sub-district that was not sampled in the March 2022 Susenas. The average RSE value of the direct estimator is 47.014 and the average RSE of the EBLUP estimator is 39.40 and the HB estimator is 15.318. In addition, the SAE EBLUP and HB methods can reduce the mean and median values of RSE estimation results when compared with direct estimates. The RSE of the direct estimator is greater than the RSE of the indirect estimator.

Delay discounting behavior has proven useful in assessing impulsivity across a wide range of populations. As such, accurate estimation of the shape of each individual's temporal discounting profile is paramount when drawing conclusions about how impulsivity relates to clinical and health outcomes such as gambling, addiction, and obesity. Here, we identify an estimation problem with current methods of assessing temporal discounting behavior, and propose a simple solution. First, through a simulation study we identify types of temporal discounting profiles that cannot reliably be estimated. Second, we show how imposing constraints through hierarchical modeling ameliorates these recovery problems. Finally, we apply our solution to a large data set from a temporal discounting task, and illustrate the importance of reliable estimation within patient populations. We conclude with a brief discussion on how hierarchical Bayesian methods can aid in model estimation, compensate for small samples, and improve predictions of externalizing psychopathology.

We propose the use of Bayesian estimation of risk preferences of individuals for applications of behavioral welfare economics to evaluate observed choices that involve risk. Bayesian estimation provides more systematic control of the use of informative priors over inferences about risk preferences for each individual in a sample. We demonstrate that these methods make a difference to the rigorous normative evaluation of decisions in a case study of insurance purchases. We also show that hierarchical Bayesian methods can be used to infer welfare reliably and efficiently even with significantly reduced demands on the number of choices that each subject has to make. Finally, we illustrate the natural use of Bayesian methods in the adaptive evaluation of welfare.

The Robustness of a Hierarchical Model for Multinomials and Contingency Tables

Abundance and catchability are crucial quantities in fisheries management, yet they are very difficult to estimate, particularly for short-lived invertebrates. Using two distinct approaches – a standard non-hierarchical model (NH) and a hierarchical Bayesian model (HB) – abundance and catchability coefficients from a fishery depletion process for banana prawns (Penaeus merguiensis) in northern Australia were estimated. Non-hierarchical models treated each stock and year separately and individually, whereas the hierarchical models assumed some form of common underlying population from which the parameters for the individual cases generated by the combination of stock and year were drawn. Two HBs were considered. In HB1 it was assumed that annual abundance and catchability parameters came from separate populations, or distributions, for each stock. In HB2 it was assumed that these stock region distributions were not separate, but had their parameters drawn from a common distribution. Thus in HB2 all stocks shared information at the regional level. The results for both NH and HB methods were similar in most cases, indicating a fair degree of stability irrespective of the particular form of model chosen. However, the NH method suffered because the data were analysed in generally small sections and in many cases these sections were too small to allow precise estimation of both parameters and confidence intervals. The deviations of point estimates between the HB1, HB2 and NH models were more marked in catchability coefficient estimates than in abundance estimates, and large relative deviations typically occurred in stock regions and years with low fishing efforts, low catch or poor depletion trends over time. We conclude that the combined analysis using HB was superior because it could handle limited data, yielded credible interval estimates for all parameters and was computationally more efficient.

Post-hurricane recovery and long-term viability of the Alabama beach mouse

Methylmercury data from walleye fillets collected by multiple agencies from northern Wisconsin lakes from 1982 to 2005 were examined for regional time trends. Hierarchical Bayesian methods were used to model dependencies and provide probability statements for parameters pertaining to individual lakes and the region as a whole. A missing data mechanism allowed the sex of the fish to be included as a predictor since the sexes grow at different rates. A slight regional decrease in methylmercury of 0.60% annually was found, consistent with declining atmospheric mercury deposition. Methylmercury was estimated to have decreased in 77% of the 420 lakes from which walleye were sampled, although uncertainty regarding time trends was greater for most individual lakes than for the region as a whole. Methylmercury in walleye varied widely from lake to lake, but generally accumulated in the fish at similar rates by length after accounting for differences in sex. Slower-growing male walleye had higher methylmercury concentrations than females for a given length, and skin-on fillets were 16% lower in methylmercury than skin-off fillets.

In the last years, subspace‐based multi‐view face recognition has attracted increasing attention and many related methods have been proposed. However, the most existing methods ignore the specific local structure of different views. This drawback can cause these methods' discriminating ability to degrade when many noisy samples exist in data. To tackle this problem, a multi‐view low‐rank representation method is proposed, which exploits both intrinsic relationships and specific local structures of different views simultaneously. It is achieved by hierarchical Bayesian methods that constrain the low‐rank representation of each view so that it matches a linear combination of an intrinsic representation matrix and a specific representation matrix to obtain common and specific characteristics of different views. The intrinsic representation matrix holds the consensus information between views, and the specific representation matrices indicate the diversity among views. Furthermore, the model injects a clustering structure into the low‐rank representation. This approach allows for adaptive adjustment of the clustering structure while pursuing the optimization of the low‐rank representation. Hence, the model can well capture both the relationship between data and the clustering structure explicitly. Extensive experiments on several datasets demonstrated the effectiveness of the proposed method compared to similar state‐of‐the‐art methods in classification and clustering.

Bayesian hierarchical surplus production model of the common whelk Buccinum undatum in Icelandic waters

Appropriate inference for stocks or species with low-quality data (poor data) or limited data (data poor) is extremely important. Hierarchical Bayesian methods are especially applicable to small-area, small-sample-size estimation problems because they allow poor-data species to borrow strength from species with good-quality data. We used a hammerhead shark complex as an example to investigate the advantages of using hierarchical Bayesian models in assessing the status of poor-data and data-poor exploited species. The hammerhead shark complex (Sphyrna spp.) along the Atlantic and Gulf of Mexico coasts of the United States is composed of three species: the scalloped hammerhead (S. lewini), the great hammerhead (S. mokarran), and the smooth hammerhead (S. zygaena) sharks. The scalloped hammerhead comprises 70-80% of the catch and has catch and relative abundance data of good quality, whereas great and smooth hammerheads have relative abundance indices that are both limited and of low quality presumably because of low stock density and limited sampling. Four hierarchical Bayesian state-space surplus production models were developed to simulate variability in population growth rates, carrying capacity, and catchability of the species. The results from the hierarchical Bayesian models were considerably more robust than those of the nonhierarchical models. The hierarchical Bayesian approach represents an intermediate strategy between traditional models that assume different population parameters for each species and those that assume all species share identical parameters. Use of the hierarchical Bayesian approach is suggested for future hammerhead shark stock assessments and for modeling fish complexes with species-specific data, because the poor-data species can borrow strength from the species with good data, making the estimation more stable and robust.

The effects of area-level deprivation on colorectal cancer incidence at the small area-level in Pennsylvania from 2008 to 2017.

Severe health, safety and environmental hazards are being created by the growing population of urban poor in low-income countries due to lack of access to sanitation and to inadequate existing sanitation systems. We developed a multi-faceted motivational framework to examine the constituents that explain user motivation regarding a personalised sanitation system. In 2012 we interviewed slum dwellers in Nairobi, Kenya, to estimate individual motivational factor importance rankings from anchored best–worst scaling (ABWS) using hierarchical Bayesian methods. We found that personal safety, avoidance of discomfort with shared toilets, cleanliness and convenience for children were ranked of highest importance. Motivational factors related to health were only relatively highly ranked. Thus factors contributing to overall individual wellbeing, beyond health benefits, drive adoption and use of the low-cost personal sanitation solution studied. This suggests that non-health benefits of low-cost sanitation solutions should be better acknowledged and communicated to raise awareness and encourage adoption of improved sanitation in urban slums. These findings may help develop policies to promote personal sanitation, improve public health and safety and reduce environmental risks.

A Bayesian analysis of mouse infectivity data to evaluate the effectiveness of using ultraviolet light as a drinking water disinfectant

To describe the spatial distribution of diseases, a number of methods have been proposed to model relative risks within areas. Most models use Bayesian hierarchical methods, in which one models both spatially structured and unstructured extra-Poisson variance present in the data. For modelling a single disease, the conditional autoregressive (CAR) convolution model has been very popular. More recently, a combined model was proposed that 'combines' ideas from the CAR convolution model and the well-known Poisson-gamma model. The combined model was shown to be a good alternative to the CAR convolution model when there was a large amount of uncorrelated extra-variance in the data. Less solutions exist for modelling two diseases simultaneously or modelling a disease in two sub-populations simultaneously. Furthermore, existing models are typically based on the CAR convolution model. In this paper, a bivariate version of the combined model is proposed in which the unstructured heterogeneity term is split up into terms that are shared and terms that are specific to the disease or subpopulation, while spatial dependency is introduced via a univariate or multivariate Markov random field. The proposed method is illustrated by analysis of disease data in Georgia (USA) and Limburg (Belgium) and in a simulation study. We conclude that the bivariate combined model constitutes an interesting model when two diseases are possibly correlated. As the choice of the preferred model differs between data sets, we suggest to use the new and existing modelling approaches together and to choose the best model via goodness-of-fit statistics. Copyright © 2016 John Wiley & Sons, Ltd.