Updating Knowledge in The Estimation of The Genetics Parameters Multi-trait and Multi-Environment Bayesian Analysis in Rice (Oryza Sativa L.)

Among the multi-trait models used to jointly study several traits and environments, the Bayesian framework has been a preferable tool for using a more complex and biologically realistic model. In most cases, the non-informative prior distributions are adopted in studies using the Bayesian approach. Still, the Bayesian approach tends to present more accurate estimates when it uses informative prior distributions. The present study was developed to evaluate the efficiency and applicability of multi-trait multi-environment (MTME) models under a Bayesian framework utilizing a strategy for eliciting informative prior distribution using previous data from rice. The study involved data pertained to rice genotypes in three environments and five agricultural years (2010/2011 until 2014/2015) for the following traits: grain yield (GY), flowering in days (FLOR) and plant height (PH). Variance components and genetic and non-genetic parameters were estimated by the Bayesian method. In general, the informative prior distribution in Bayesian MTME models provided higher estimates of heritability and variance components, as well as minor lengths for the highest probability density interval (HPD), compared to their respective non-informative prior distribution analyses. The use of more informative prior distributions makes it possible to detect genetic correlations between traits, which cannot be achieved with the use of non-informative prior distributions. Therefore, this mechanism presented for updating knowledge to the elicitation of an informative prior distribution can be efficiently applied in rice genetic selection.

Hierarchical Bayesian Small Area Estimation Using Weakly Informative Priors in Ecologically Homogeneous Areas of the Interior Western Forests

The U.S. Forest Inventory and Analysis Program (FIA) collects inventory data on and computes estimates for many forest attributes to monitor the status and trends of the nation's forests. Increasingly, FIA needs to produce estimates in small geographic and temporal regions. In this application, we implement area level hierarchical Bayesian (HB) small area estimators of several forest attributes for ecosubsections in the Interior West of the US. We use a remotely-sensed auxiliary variable, percent tree canopy cover, to predict response variables derived from ground-collected data such as basal area, biomass, tree count, and volume. We implement four area level HB estimators that borrow strength across ecological provinces and sections and consider prior information on the between-area variation of the response variables. We compare the performance of these HB estimators to the area level empirical best linear unbiased prediction (EBLUP) estimator and to the industry-standard post-stratified (PS) direct estimator. Results suggest that when borrowing strength to areas which are believed to be homogeneous (such as the ecosection level) and a weakly informative prior distribution is placed on the between-area variation parameter, we can reduce variance substantially compared the analogous EBLUP estimator and the PS estimator. Explorations of bias introduced with the HB estimators through comparison with the PS estimator indicates little to no addition of bias. These results illustrate the applicability and benefit of performing small area estimation of forest attributes in a HB framework, as they allow for more precise inference at the ecosubsection level.

Global Information for Multidimensional Tests

New measures of test information, termed global information, quantify test information relative to the entire range of the trait being assessed. Estimating global information relative to a non-informative prior distribution results in a measure of how much information could be gained by administering the test to an unspecified examinee. Currently, such measures have been developed only for unidimensional tests. This study introduces measures of multidimensional global test information and validates them in simulated data. Then, the utility of global test information is tested in neuropsychological data collected as part of Rush University’s Memory and Aging Project. These measures allow for direct comparison of complex tests calibrated in different samples, facilitating test development and selection.

Constrained Adjusted Maximum a Posteriori Estimation of Bayesian Network Parameters

Maximum a posteriori estimation (MAP) with Dirichlet prior has been shown to be effective in improving the parameter learning of Bayesian networks when the available data are insufficient. Given no extra domain knowledge, uniform prior is often considered for regularization. However, when the underlying parameter distribution is non-uniform or skewed, uniform prior does not work well, and a more informative prior is required. In reality, unless the domain experts are extremely unfamiliar with the network, they would be able to provide some reliable knowledge on the studied network. With that knowledge, we can automatically refine informative priors and select reasonable equivalent sample size (ESS). In this paper, considering the parameter constraints that are transformed from the domain knowledge, we propose a Constrained adjusted Maximum a Posteriori (CaMAP) estimation method, which is featured by two novel techniques. First, to draw an informative prior distribution (or prior shape), we present a novel sampling method that can construct the prior distribution from the constraints. Then, to find the optimal ESS (or prior strength), we derive constraints on the ESS from the parameter constraints and select the optimal ESS by cross-validation. Numerical experiments show that the proposed method is superior to other learning algorithms.

A Similarity-Weighted Informative Prior Distribution for Bayesian Multiple Regression Models

Specifying accurate informative prior distributions is a question of carefully selecting studies that comprise the body of comparable background knowledge. Psychological research, however, consists of studies that are being conducted under different circumstances, with different samples and varying instruments. Thus, results of previous studies are heterogeneous, and not all available results can and should contribute equally to an informative prior distribution. This implies a necessary weighting of background information based on the similarity of the previous studies to the focal study at hand. Current approaches to account for heterogeneity by weighting informative prior distributions, such as the power prior and the meta-analytic predictive prior are either not easily accessible or incomplete. To complicate matters further, in the context of Bayesian multiple regression models there are no methods available for quantifying the similarity of a given body of background knowledge to the focal study at hand. Consequently, the purpose of this study is threefold. We first present a novel method to combine the aforementioned sources of heterogeneity in the similarity measure ω. This method is based on a combination of a propensity-score approach to assess the similarity of samples with random- and mixed-effects meta-analytic models to quantify the heterogeneity in outcomes and study characteristics. Second, we show how to use the similarity measure ωas a weight for informative prior distributions for the substantial parameters (regression coefficients) in Bayesian multiple regression models. Third, we investigate the performance and the behavior of the similarity-weighted informative prior distribution in a comprehensive simulation study, where it is compared to the normalized power prior and the meta-analytic predictive prior. The similarity measure ω and the similarity-weighted informative prior distribution as the primary results of this study provide applied researchers with means to specify accurate informative prior distributions.

999. Using the F/TDF Adherence-Efficacy Relationship to Calculate Background HIV incidence: Results from the DISCOVER trial

Background RRandomized trials of new PrEP agents compare to oral emtricitabine+tenofovir disoproxil fumarate (F/TDF) and do not have a placebo arm. We used the well-characterized adherence-efficacy relationship for F/TDF from iPrEX OLE, to back-calculate the (non-PrEP) background HIV incidence (bHIV) in the F/TDF arm of DISCOVER and estimate comparative efficacy (to bHIV). Methods TDISCOVER is an ongoing randomized active-controlled trial in 5,387 men who have sex with men and transgender women that demonstrated non-inferiority of F+tenofovir alafenamide (F/TAF) to F/TDF (IRR 0.47 (95% CI 0.19, 1.15). TFV-DP levels in DBS were assessed for all diagnosed with HIV and in a randomized subset of 10%. We used a Bayesian model with a prior distribution, derived from iPrEx OLE, relating TFV-DP levels to HIV prevention efficacy: eg TFV-DP levels of < 350 (low), 350 to < 700 (medium) and ≥700 (high) fmol/punch were assumed to provide 0%, 86% and 98% HIV protection, respectively. This prior, combined with F/TDF seroconversion rate and TFV-DP levels, yields Bayesian inferences on the bHIV. In R, STAN was used to sample 10,000 realizations from the posterior distribution. Results There were 6 vs. 11 post-baseline HIV infections (0.14 v. 0.25 per 100 person-years [PY]) on F/TAF and F/TDF. Of the 11 on F/TDF, 10 had low, 0 had medium, and 1 had high TFV-DP levels; among HIV-negative controls, 5% of the person-time had low, 9% had medium, and 86% had high TFV-DP levels. A non-informative prior distribution for bHIV, combined with the prior for TFV-DP level-efficacy relationship, yielded a posterior bHIV incidence [0.80 Bayesian credible interval (CrI)] of 3.4/100 [1.9, 6.0/100] PY; which suggests a median F/TAF efficacy [0.95 CrI] of 96% [88%,99%] and 93% [87%,96%] for F/TDF compared to bHIV. If we chose a conservative prior distribution for bHIV of 1.0/100 PY, the model yields a median posterior bHIV [0.80 CrI] of 2.8/100 [1.7, 4.7/100] PY; which suggests a median efficacy [0.95 Cr] of 95% [86%, 99%] for F/TAF and 92% [86%, 67%] for F/TDF compared to bHIV with corresponding number of HIV infections averted of 117 and 114, respectively (Figure). Figure. Conclusion The F/TDF adherence-efficacy relationship can be used to back-calculate bHIV incidence in MSM/TW PrEP trials and assess the efficacy of new PrEP agents compared to bHIV. Disclosures David V. Glidden, MD, Gilead Sciences Inc. (Other Financial or Material Support, Personal fees) David T. Dunn, MD, Gilead Sciences Inc. (Other Financial or Material Support, Personal fees)Viiv Healthcare (Other Financial or Material Support, Personal fees) Moupali Das, MD, Gilead Sciences Inc. (Employee, Shareholder) Ramin Ebrahimi, MSc, Gilead Sciences Inc. (Employee, Shareholder) Lijie Zhong, PhD, Gilead Sciences Inc. (Employee, Shareholder) Oliver T. Stirrup, MD, Gilead Sciences Inc. (Other Financial or Material Support, Personal fees) Peter L. Anderson, PharmD, Gilead Sciences Inc. (Other Financial or Material Support, Personal fees)

On A Shape Parameter of Gompertz Inverse Exponential Distribution Using Classical and Non Classical Methods of Estimation

The Gompertz inverse exponential distribution is a three-parameter lifetime model with greater flexibility and performance for analyzing real life data. It has one scale parameter and two shape parameters responsible for the flexibility of the distribution. Despite the importance and necessity of parameter estimation in model fitting and application, it has not been established that a particular estimation method is better for any of these three parameters of the Gompertz inverse exponential distribution. This article focuses on the development of Bayesian estimators for a shape of the Gompertz inverse exponential distribution using two non-informative prior distributions (Jeffery and Uniform) and one informative prior distribution (Gamma prior) under Square error loss function (SELF), Quadratic loss function (QLF) and Precautionary loss function (PLF). These results are compared with the maximum likelihood counterpart using Monte Carlo simulations. Our results indicate that Bayesian estimators under Quadratic loss function (QLF) with any of the three prior distributions provide the smallest mean square error for all sample sizes and different values of parameters.

The Birthday Problem: Bayesian Inference with Multiple Discrete Hypotheses

The “Birthday Problem” expands consideration from two hypotheses to multiple, discrete hypotheses. In this chapter, interest is in determining the posterior probability that a woman named Mary was born in a given month; there are twelve alternative hypotheses. Furthermore, consideration is given to assigning prior probabilities. The priors represent a priori probabilities that each alternative hypothesis is correct, where a priori means “prior to data collection,” and can be “informative” or “non-informative.” A Bayesian analysis cannot be conducted without using a prior distribution, whether that is an informative prior distribution or a non-informative prior distribution. The chapter discusses objective priors, subjective priors, and prior sensitivity analysis. In addition, the concept of likelihood is explored more deeply.

Bayesian Methods of Representative Values of Variable Actions

In engineering practice, it is sometimes necessary to infer the representative value of variable action under the condition that the test data is insufficient, but the classical statistics methods adopted now do not take into account the influences of statistical uncertainty, and the inferring results are always small, especially when characteristic and frequent values are inferred. Variable actions usually obey a type I maximum distribution, so the linear regression estimation of the tantile of type I minimum distribution can be employed to infer their characteristic and frequent values. However, it is inconvenient to apply and cannot totally meet the demands of characteristic and frequent values inference. Applying Jeffreys non-informative prior distribution, Bayesian methods for inferring characteristic and frequent values of variable actions are put forward, including that with known standard deviation, which could yield more advantageous results. The methods proposed are convenient and flexible, possessing good precision.