Proper Prior Information Research Articles

Bayesian empirical likelihood inference for the mean absolute deviation

The mean absolute deviation (MAD) is a direct measure of the dispersion of a random variable about its mean. In this paper, the empirical likelihood (EL) and the adjusted EL methods for the MAD are proposed. The Bayesian empirical likelihood, the Bayesian adjusted empirical likelihood, the Bayesian jackknife empirical likelihood and the Bayesian adjusted jackknife empirical likelihood methods are used to construct credible intervals for the MAD. Simulation results show that the proposed EL method performs better than the JEL in Zhao et al. [Jackknife empirical likelihood inference for the mean absolute deviation. Comput Stat Data Anal. 2015;91:92–101], and the proper prior information improves coverage rates of confidence/credible intervals. Two real datasets are used to illustrate the new procedures.

Combining a Pharmacological Network Model with a Bayesian Signal Detection Algorithm to Improve the Detection of Adverse Drug Events.

Introduction: Improving adverse drug event (ADE) detection is important for post-marketing drug safety surveillance. Existing statistical approaches can be further optimized owing to their high efficiency and low cost. Objective: The objective of this study was to evaluate the proposed approach for use in pharmacovigilance, the early detection of potential ADEs, and the improvement of drug safety. Methods: We developed a novel integrated approach, the Bayesian signal detection algorithm, based on the pharmacological network model (ICPNM) using the FDA Adverse Event Reporting System (FAERS) data published from 2004 to 2009 and from 2014 to 2019Q2, PubChem, and DrugBank database. First, we used a pharmacological network model to generate the probabilities for drug-ADE associations, which comprised the proper prior information component (IC). We then defined the probability of the propensity score adjustment based on a logistic regression model to control for the confounding bias. Finally, we chose the Side Effect Resource (SIDER) and the Observational Medical Outcomes Partnership (OMOP) data to evaluate the detection performance and robustness of the ICPNM compared with the statistical approaches [disproportionality analysis (DPA)] by using the area under the receiver operator characteristics curve (AUC) and Youden’s index. Results: Of the statistical approaches implemented, the ICPNM showed the best performance (AUC, 0.8291; Youden’s index, 0.5836). Meanwhile, the AUCs of the IC, EBGM, ROR, and PRR were 0.7343, 0.7231, 0.6828, and 0.6721, respectively. Conclusion: The proposed ICPNM combined the strengths of the pharmacological network model and the Bayesian signal detection algorithm and performed better in detecting true drug-ADE associations. It also detected newer ADE signals than a DPA and may be complementary to the existing statistical approaches.

3-D Model-Based Inversion Using Supervised Descent Method for Aspect-Limited Microwave Data of Metallic Targets

In this work, we apply the supervised descent method (SDM) to 3-D limited data inversion. In the measurement of the far field, the scattered field in 3-D measurement is small in magnitude and easily polluted by noise. Combining with limited observed data, the inversion problem is highly nonunique and ill-posed. To mitigate the ill-posedness, the model-based inversion is adopted by describing metallic targets based on prior information. Then, a series of generic descent directions is learned in the training stage iteratively using SDM. During inversion, the values of these model-based parameters are reconstructed directly using the learned directions. This approach is validated using both synthetic and experimental data. All simulations and experiments are conducted in a monostatic measurement setup to match real measurement conditions. The results show that by choosing proper prior information, the model-based SDM inversion can effectively compensate for the lack of data and achieve decent accuracy.

Prior-image-based Reconstruction for On-board CBCT Imaging: Application in Image-guided Radiotherapy for Head and Neck Cancer

On-board cone-beam CT (CBCT) imaging has been widely used to reduce set-up errors in head and neck cancer treated with IMRT/VMAT. However, its frequent use has raised concerns for excessive imaging dose and increased risk of developing secondary malignancies. This work investigates the feasibility of significantly reducing CBCT radiation dose by taking advantage of high-quality planning CT and a prior-image-based reconstruction approach. In image-guided radiotherapy for head and neck cancer, one standard protocol (Full-fan, 200 deg rotation, 100 kVp, 0.3 mAs/projection, 500 projections, 150 mAs in total) is employed for kV-CBCT scans. Since the high-quality planning CT scan is a rich source of patient-specific anatomical knowledge, it offers an opportunity to integrate the planning CT into on-board CBCT reconstruction for radiation dose reduction. Therefore, we studied a prior-image-based reconstruction approach for on-board CBCT imaging, which only requires partial projections and thus substantially reduces radiation dose. The prior-image-based reconstruction takes into consideration differences in attenuation coefficients (via histogram matching) and patient positioning (via affine registration) between the planning CT and on-board CBCT scans. Additionally, proper prior information control is applied to ensure the prior-image-based reconstruction does not introduce false features when there are anatomical changes between scans. An anthropomorphic head phantom and two head and neck patient datasets were used to validate the efficacy of the proposed approach. We extracted certain number of projections from the 500 projections to emulate different radiation dose levels. As we decrease the number of projections to as low as 100 (30 mAs equivalent, CTDIvol = 0.63 mGy), the standard FDK reconstructed images are degraded with severe noise and streak artifacts, and the conventional model-based iterative reconstruction generates images with inferior image quality, which could jeopardize the accuracy of patient set-up. In contrast, our proposed prior-image-based reconstruction can yield comparable image quality as the ground truth images reconstructed with the full projections, in terms of noise, resolution, and contrast-to-noise ratio. This indicates an 80% radiation dose reduction for on-board CBCT imaging by the proposed reconstruction scheme. The proposed prior-image-based reconstruction framework provides an opportunity to substantially reduce the radiation dose for on-board CBCT, without compromising image quality. This work offers a solution to reduce cumulative imaging dose as the use of CBCT for image-guided radiotherapy increases.

Bayesian methods for analysis of biosimilar phase III trials.

A biologic is a product made from living organisms. A biosimilar is a new version of an already approved branded biologic. Regulatory guidelines recommend a totality-of-the-evidence approach with stepwise development for a new biosimilar. Initial steps for biosimilar development are (a) analytical comparisons to establish similarity in structure and function followed by (b) potential animal studies and a human pharmacokinetics/pharmacodynamics equivalence study. The last step is a phase III clinical trial to confirm similar efficacy, safety, and immunogenicity between the biosimilar and the biologic. A high degree of analytical and pharmacokinetics/pharmacodynamics similarity could provide justification for an eased statistical threshold in the phase III trial, which could then further facilitate an overall abbreviated approval process for biosimilars. Bayesian methods can help in the analysis of clinical trials, by adding proper prior information into the analysis, thereby potentially decreasing required sample size. We develop proper prior information for the analysis of a phase III trial for showing that a proposed biosimilar is similar to a reference biologic. For the reference product, we use a meta-analysis of published results to set a prior for the probability of efficacy, and we propose priors for the proposed biosimilar informed by the strength of the evidence generated in the earlier steps of the approval process. A simulation study shows that with few exceptions, the Bayesian relative risk analysis provides greater power, shorter 90% credible intervals with more than 90% frequentist coverage, and better root mean squared error.

Diversified Hidden Markov Models for Sequential Labeling

Labeling of sequential data is a prevalent meta-problem for a wide range of real world applications. While the first-order Hidden Markov Models (HMM) provides a fundamental approach for unsupervised sequential labeling, the basic model does not show satisfying performance when it is directly applied to real world problems, such as part-of-speech tagging (PoS tagging) and optical character recognition (OCR). Aiming at improving performance, important extensions of HMM have been proposed in the literatures. One of the common key features in these extensions is the incorporation of proper prior information. In this paper, we propose a new extension of HMM, termed diversified Hidden Markov Models (dHMM), which utilizes a diversity-encouraging prior over the state-transition probabilities and thus facilitates more dynamic sequential labellings. Specifically, the diversity is modeled by a continuous determinantal point process prior, which we apply to both unsupervised and supervised scenarios. Learning and inference algorithms for dHMM are derived. Empirical evaluations on benchmark datasets for unsupervised PoS tagging and supervised OCR confirmed the effectiveness of dHMM, with competitive performance to the state-of-the-art.

Contrast of Bayesian and Classical Sample Size Determination

Sample size determination is a prerequisite for statistical surveys. A comprehensive overview of the Bayesian approach for computation of the sample size, and a comparison with classical approaches, is presented. Two surveys are taken as example to illustrate the accuracy and efficiency of each approach, and to make recommendations about which method is preferred. The Bayesian approach of sample size determination may require fewer subjects if proper prior information is available.

Bayesian estimation of truncated data with applications to operational risk measurement

Data insufficiency and reporting threshold are two main issues in operational risk modelling. When these conditions are present, maximum likelihood estimation (MLE) may produce very poor parameter estimates. In this study, we first investigate four methods to estimate the parameters of truncated distributions for small samples—MLE, expectation-maximization algorithm, penalized likelihood estimators, and Bayesian methods. Without any proper prior information, Jeffreys’ prior for truncated distributions is used. Based on a simulation study for the log-normal distribution, we find that the Bayesian method gives much more credible and reliable estimates than the MLE method. Finally, an application to the operational loss severity estimation using real data is conducted using the truncated log-normal and log-gamma distributions. With the Bayesian method, the loss distribution parameters and value-at-risk measure for every cell with loss data can be estimated separately for internal and external data. Moreover, confidence intervals for the Bayesian estimates are obtained via a bootstrap method.

Multitemporal-patch ensemble inversion of coupled surface–atmosphere radiative transfer models for land surface characterization

In the last few years, encouraging results using radiative transfer model inversion techniques were obtained for land biophysical variables retrieval. However, the inversion of radiative transfer models is a severely ill-posed problem that may lead to significant uncertainties in the biophysical variables estimates. Improvement of performances of the inversion process requires more information to be exploited including better radiative transfer models, exploitation of proper prior information on the distribution of canopy and atmosphere variables, knowledge of uncertainties in satellite measurements, as well as possible spatial and temporal constraints. In this study we focus on the use of coupled atmosphere–surface radiative transfer models (SMAC + SAIL + PROSPECT) to estimate some key biophysical variables from top of atmosphere canopy reflectance data. The inversion is achieved over an ensemble of pixels belonging to a spatial window where aerosol properties are supposed to be constant, and over a temporal window of few days where vegetation state is assumed not to vary. The ensemble inversion scheme accounting for the spatial and temporal constraints is described. Top of atmosphere reflectance observations are simulated for 13 bands within the visible and near infrared domains. The coupled model is inverted with a variational method implementation dedicated to solve very large inverse problems. It is based on the use of the adjoint model and a Quasi-Newton optimisation technique with BFGS update. The multitemporal-patch inversion approach exploiting the spatial and temporal constraints is compared to the classical instantaneous-local inversion applied on single pixel and date. The ‘ensemble’ approach shows significant performance improvements when retrieving aerosol optical thickness τ 550 and some canopy characteristics (LAI, LAI × C ab and ALA). Conclusions are drawn on the interest of such approaches, and perspectives are given, with due attention to their applicability within operational algorithms.

The Uncertainty in the True End Point of a Fossil's Stratigraphic Range When Stratigraphic Sections Are Sampled Discretely

Stratigraphic sections are often sampled at well-defined discrete points. Because of the incompleteness of the fossil record, a particular species may not be observed even when it is extant at a sampling point. We introduce a model and Bayesian analysis for estimating the true time of disappearance of a lineage from a section in the face of the possibility that failure to find the species beyond its observed stratigraphic range may represent false negatives. We incorporate proper prior information, including an estimated longevity of the species and the probability that it will be observed if extant. Our analysis produces a posterior density for the true extinction time of the species. Summaries of this probability distribution provide a point estimate of the extinction time, a standard deviation for the uncertainty in the estimate, and confidence intervals for the time of extinction. We apply our model to stratigraphic ranges of benthic foraminifera collected from the early Late Cretaceous (Cenomanian and Turonian) from Eastbourne, England.

Experience with a bayesian bootstrap method incorporating proper prior information

Although bootstrapping has become widely used in statistical analysis, there has been little reported concerning bootstrapped Bayesian analyses, especially when there is proper prior informa-tion concerning the parameter of interest. In this paper, we first propose an operationally implementable definition of a Bayesian bootstrap. Thereafter, in simulated studies of the estimation of means and variances, this Bayesian bootstrap is compared to various parametric procedures. It turns out that little information is lost in using the Bayesian bootstrap even when the sampling distribution is known. On the other hand, the parametric procedures are at times very sensitive to incorrectly specified sampling distributions, implying that the Bayesian bootstrap is a very robust procedure for determining the posterior distribution of the parameter.