Estimation of Parameters of PTRC SRGM using Non-informative Priors

Reliability is an essentially important characteristic of software. The reliability of software has been assessed by considering Poisson Type occurrence of software failures and the failure intensity of one parameter say (η_1 ) Rayleigh class. Here, it is assumed that the software contains fixed number of inherent faults say (η_0 ). The scale parameter of Rayleigh density (η_1 ) and fixed number of inherent faults contained in software are the parameters of interest. The failure intensity and mean failure function of this Poisson Type Rayleigh Class (PTRC) Software Reliability Growth Model (SRGM) have been studied. The estimates of above parameters can be obtained by using maximum likelihood method. Bayesian technique has been used to about estimates of η_0 and η_1 if prior knowledge about these parameters is available. The prior knowledge about these parameters is considered in the form of non- informative priors for both the parameters. The proposed Bayes estimators are compared with their corresponding maximum likelihood estimators on the basis of risk efficiencies under squared error loss. The Monte Carlo simulation technique is used for calculating risk efficiencies. It is seen that both the proposed Bayes estimators can be preferred over corresponding MLEs for the proper choice of the values of execution time.

Comparing probabilistic accounts of probability judgments

Bayesian theories of cognitive science hold that cognition is fundamentally probabilistic, but people’s explicit probability judgments often violate the laws of probability. Two recent proposals, the “Probability Theory plus Noise” (Costello & Watts, 2014) and “Bayesian Sampler” (Zhu et al., 2020) theories of probability judgments, both seek to account for these biases while maintaining that mental credences are fundamentally probabilistic. These theories fit quite differently into the larger project of Bayesian cognitive science, but their many similarities complicate comparisons of their predictive accuracy. In particular, comparing the models demands a careful accounting of model complexity. Here, I cast these theories into a Bayesian data analysis framework that supports principled model comparison using information criteria. Comparing the fits of both models on data collected by Zhu and colleagues (2020) I find the data are best explained by a modified version of the Bayesian Sampler model under which people may hold informative priors about probabilities.

Genotype-Guided P2Y 12 Inhibitor Therapy After Percutaneous Coronary Intervention: A Bayesian Analysi

Background: Among patients receiving percutaneous coronary intervention (PCI), the role of a genotype-guided approach for antiplatelet therapy compared with usual care is unclear. We conducted a Bayesian analysis of the entire TAILOR-PCI (Tailored Antiplatelet Initiation to Lessen Outcomes Due to Decreased Clopidogrel Response After Percutaneous Coronary Intervention) randomized clinical trial population to evaluate the effect of the genotype-guided antiplatelet therapy post-PCI compared with the usual care on the risk of major adverse cardiovascular events (MACE). Methods: The primary outcome for our study was the composite of MACE (myocardial infarction, stroke, and cardiovascular death). Secondary outcomes included cardiovascular death, stroke, myocardial infarction, stent thrombosis, and major/minor bleeding. Bayesian modeling was used to estimate the probability of clinical benefit of genotype-guided therapy using (1) noninformative priors (ie, analyzing the TAILOR-PCI trial) and (2) informative priors derived from the ADAPT, POPular Genetics, IAC-PCI, and PHARMCLO trials (ie, analyzing TAILOR-PCI trial in the context of prior evidence). Risk ratio (RR: ratio of cumulative outcome incidence between genotype-guided and conventional therapy group) and 95% credible interval (CrI) were estimated for the study outcomes, and probability estimates for RR <1 were computed. Results: Using noninformative priors, in TAILOR-PCI the RR for MACE was 0.78 (95% CrI, 0.55–1.07) in genotype-guided therapy after PCI, and the probability of RR <1 was 94%. Using noninformative priors, the probability of RR <1 for cardiovascular death (RR, 0.95 [95% CrI, 0.52–1.74]), stroke (RR, 0.68 [95% CrI, 0.44–1.06]), myocardial infarction (RR, 0.84 [95% CrI, 0.37–1.89]), stent thrombosis (RR, 0.75 [95% CrI, 0.37–1.45]), and major or minor bleeding (RR, 1.22 [95% CrI, 0.84–1.77]) were 57%, 96%, 67%, 94%, and 15%, respectively. Using informative priors, the posterior probability of RR <1 for MACE, from genotype-guided therapy, was 99% (RR, 0.69 [95% CrI, 0.57–0.84]). Using informative priors, the posterior probability of RR <1 for cardiovascular death (RR, 0.86 [95% CrI, 0.61–1.19]), stroke (RR, 0.69 [95% CrI, 0.48–0.99]), myocardial infarction (RR:0.56 [95% CrI, 0.40–0.78]), stent thrombosis (RR, 0.59 [95% CrI, 0.38–0.94]), and major or minor bleeding (RR, 0.84 [95% CrI, 0.70–0.99]) were 81%, 99%, 99%, 99%, and 99%, respectively. Conclusions: Bayesian analysis of the TAILOR-PCI trial provides clinically meaningful data on the posterior probability of reducing MACE using genotype-guided P2Y 12 inhibitor therapy after PCI.

MCMC Method for Exponentiated Lomax Distribution based on Accelerated Life Testing with Type I Censoring

Accelerated Life Testing (ALT) is an effective technique which has been used in different fields to obtain more failures in a shorter period of time. It is more economical than traditional reliability testing. In this article, we propose Bayesian inference approach for planning optimal constant stress ALT with Type I censoring. The lifetime of a test unit follows an exponentiated Lomax distribution. Bayes point estimates of the model parameters and credible intervals under uniform and log-normal priors are obtained. Besides, optimum test plan based on constant stress ALT under Type I censoring is developed by minimizing the pre-posterior variance of a specified low percentile of the lifetime distribution at use condition. Gibbs sampling method is used to find the optimal stress with changing time. The performance of the estimation methods is demonstrated for both simulated and real data sets. Results indicate that both the priors and the sample size affect the optimal Bayesian plans. Further, informative priors provide better results than non-informative priors.

An Improved Parameter-Estimating Method in Bayesian Networks Applied for Cognitive Diagnosis Assessment

Bayesian networks (BNs) can be employed to cognitive diagnostic assessment (CDA). Most of the existing researches on the BNs for CDA utilized the MCMC algorithm to estimate parameters of BNs. When EM algorithm and gradient descending (GD) learning method are adopted to estimate the parameters of BNs, some challenges may emerge in educational assessment due to the monotonic constraints (greater skill should lead to better item performance) cannot be satisfied in the above two methods. This paper proposed to train the BN first based on the ideal response pattern data contained in every CDA and continue to estimate the parameters of BN based on the EM or the GD algorithm regarding the parameters based on the IRP training method as informative priors. Both the simulation study and realistic data analysis demonstrated the validity and feasibility of the new method. The BN based on the new parameter estimating method exhibits promising statistical classification performance and even outperforms the G-DINA model in some conditions.

Comparison between Maximum Likelihood and Bayesian Estimation in Structural Equation Modelling and Effects of Informative Priors

The aims of this study are to compare the maximum likelihood and Bayesian methods for estimation in structural equation modelling in real large data sets with different degrees of multivariate non-normality and to investigate the effects of non-informative and informative priors on parameter estimates in Bayesian structural equation modelling. Two data sets from the British Household Panel Survey are taken for the analyses, with total respondents of 6,522 and 7,150. In each of them, eighteen questions are drawn to be indicators for seven latent variables. In this dissertation, three separate hypothesised models are constructed in order to increase a variety of multivariate non-normality degrees; these are Models A, B and C. The research findings provided from classical structural equation modelling show that Model A and Model B are well fitted with a non-significant chi-square statistic at a bootstrap probability of more than 0.05, while Model C is also reasonably fitted with a significant chi-square statistic at a bootstrap probability of just below 0.05. The comparative fit indices in all models illustrate very high values; additionally, the root mean square error of approximation values are rather low. Furthermore, all estimated parameters are significant at a p-value of 0.001 and there are no zero values lying between their bootstrap confidence intervals. Under the multivariate non-normal condition, maximum likelihood estimators seem to lose their efficiency property, but not by much, and are robust to violation due to the large sample size. As for the findings from Bayesian structural equation modelling, all the estimated parameters of the three models are also significant. When incorporated with non-informative priors, the estimates and their standard errors are equivalent to the ones yielded by classical structural equation modelling. On the other hand, the parameters generated with informative priors vary according to the prior means but the standard errors are diminished consistently for all estimates, in comparison with the ones provided from classical structural equation modelling and Bayesian structural equation modelling with non-informative priors. The posterior distributions after being updated by the informative priors appear to be more normal owing to a decrease in skewness and kurtosis; moreover, the ones produced from Model B, which has the highest non-normality, are most affected by the informative priors according to the change in skewness and kurtosis.

Weight effects on stress: lexicon and grammar

This thesis examines weight effects on stress and proposes a probabilistic approach based on the notion that weight is gradient, not categorical. Arguments for this proposal are divided into three main chapters, which examine and statistically model weight in the lexicon (Chapter 1), weight in the grammar (Chapter 2), and the interaction of weight and footing (Chapter 3). The statistical analyses in Chapters 2 and 3 also discuss how our linguistic expectations regarding weight effects can be incorporated in statistical models through the use of mildly informative priors, and to what extent the fit of such models compare with that of models based on non-informative priors.

Systematically Defined Informative Priors in Bayesian Estimation: An Empirical Application on the Transmission of Internalizing Symptoms Through Mother-Adolescent Interaction Behavior

BackgroundBayesian estimation with informative priors permits updating previous findings with new data, thus generating cumulative knowledge. To reduce subjectivity in the process, the present study emphasizes how to systematically weigh and specify informative priors and highlights the use of different aggregation methods using an empirical example that examined whether observed mother-adolescent positive and negative interaction behavior mediate the associations between maternal and adolescent internalizing symptoms across early to mid-adolescence in a 3-year longitudinal multi-method design.MethodsThe sample consisted of 102 mother-adolescent dyads (39.2% girls, Mage T1 = 13.0). Mothers and adolescents reported on their internalizing symptoms and their interaction behaviors were observed during a conflict task. We systematically searched for previous studies and used an expert-informed weighting system to account for their relevance. Subsequently, we aggregated the (power) priors using three methods: linear pooling, logarithmic pooling, and fitting a normal distribution to the linear pool by means of maximum likelihood estimation. We compared the impact of the three differently specified informative priors and default priors on the prior predictive distribution, shrinkage, and the posterior estimates.ResultsThe prior predictive distributions for the three informative priors were quite similar and centered around the observed data mean. The shrinkage results showed that the logarithmic pooled priors were least affected by the data. Most posterior estimates were similar across the different priors. Some previous studies contained extremely specific information, resulting in bimodal posterior distributions for the analyses with linear pooled prior distributions. The posteriors following the fitted normal priors and default priors were very similar. Overall, we found that maternal, but not adolescent, internalizing symptoms predicted subsequent mother-adolescent interaction behavior, whereas negative interaction behavior seemed to predict subsequent internalizing symptoms. Evidence regarding mediation effects remained limited.ConclusionA systematic search for previous information and an expert-built weighting system contribute to a clear specification of power priors. How information from multiple previous studies should be included in the prior depends on theoretical considerations (e.g., the prior is an updated Bayesian distribution), and may also be affected by pragmatic considerations regarding the impact of the previous results at hand (e.g., extremely specific previous results).