Common Bayesian Models Research Articles

A hierarchical Bayesian entry time realignment method to study the long-term natural history of diseases

A major question in clinical science is how to study the natural course of a chronic disease from inception to end, which is challenging because it is impractical to follow patients over decades. Here, we developed BETR (Bayesian entry time realignment), a hierarchical Bayesian method for investigating the long-term natural history of diseases using data from patients followed over short durations. A simulation study shows that BETR outperforms an existing method that ignores patient-level variation in progression rates. BETR, when combined with a common Bayesian model comparison tool, can identify the correct disease progression function nearly 100% of the time, with high accuracy in estimating the individual disease durations and progression rates. Application of BETR in patients with geographic atrophy, a disease with a known natural history model, shows that it can identify the correct disease progression model. Applying BETR in patients with Huntington’s disease demonstrates that the progression of motor symptoms follows a second order function over approximately 20 years.

Reconstruction, analysis and interpretation of posterior probability distributions of PET images, using the posterior bootstrap

The uncertainty of reconstructed PET images remains difficult to assess and to interpret for the use in diagnostic and quantification tasks. Here we provide (1) an easy-to-use methodology for uncertainty assessment for almost any Bayesian model in PET reconstruction from single datasets and (2) a detailed analysis and interpretation of produced posterior image distributions. We apply a recent posterior bootstrap framework to the PET image reconstruction inverse problem and obtain simple parallelizable algorithms based on random weights and on existing maximum a posteriori (MAP) (posterior maximum) optimization-based algorithms. Posterior distributions are produced, analyzed and interpreted for several common Bayesian models. Their relationship with the distribution of the MAP image estimate over multiple dataset realizations is exposed. The coverage properties of posterior distributions are validated. More insight is obtained for the interpretation of posterior distributions in order to open the way for including uncertainty information into diagnostic and quantification tasks.

An Application of the Bayesian Hierarchical Approach to Refining the Information on Main Life History Parameters for Small Yellow Croaker, Larimichthys polyactis, off the Coast of China

Small yellow croaker, Larimichthys polyactis, is a commercially important species in China. The uncertainty in its main life history parameters has not been addressed. Evaluation of the uncertainty in these parameters is urgently needed for quant if ic a t i on of the uncertainty level in stock assessment. Small yellow croaker off the coast of China was divided into five groups according to the intensive survey regions. The posterior probability distributions of the parameters on the growth, length-weight relationship, length-fecundity relationship (LFR) and the natural mortality rate were estimated for each group using the Bayesian hierarchical model (BHM). The posteriors of these parameters were also calculated just at species level using the common Bayesian model (CBM). The estimate of a particular life history parameter and its possible range were obtained for each group of small yellow croaker, which can be used to quantify the uncertainty level in stock assessment. But The LFR parameter, especially af, is still uncertain for all groups. More studies are also needed to reduce the uncertainty in natural mortality rate for small yellow croaker in Bohai Sea and North Yellow Sea. BHM can improve the estimate of the parameter. But the precision of the estimate is influenced by both the dataset size and the dataset dispersion of a group. At species level the parameter was estimated more precisely by CBM than by BHM due to the simple model structure and the large dataset size.

Bayesian Estimation of Above-Average Performance in Tertiary Institutions: A Case Study of University of Lagos, Akoka, Nigeria.

Bayesian approach for parameter estimation has the capacity to yield more precise estimates than methods based on sampling theory. There are several common Bayesian models; in this study we applied Empirical Bayes (EB) model called Beta-binomial model. The study is motivated by the need to beam searchlight on universities, faculties or fields of study with graduates who may not be eligible for further educational pursuits. This study provides means of assessment or a basis of evaluation of students' performances among faculties or fields of study and overall performance of a university. This study uses Bayesian methods of inference to estimate the proportion of above-average performance of graduates from the various faculties in University of Lagos. The model adopted generated results which are of smaller variances compared with variances of sample Proportions, showing that the posterior proportions generated are more efficient estimators. This is further evidenced in narrow widths of the computed confidence intervals. The overall result shows that the proportion of above-average performance of graduates of University of Lagos, who are eligible for further educational pursuits (i.e. higher degrees), is approximately 72% of the university graduates.