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Network Meta-Analysis
Published in Ding-Geng (Din) Chen, Karl E. Peace, Applied Meta-Analysis with R and Stata, 2021
Bayesian inference can also be used in terms of unobserved data , known as predictive inferences. The distribution of is called the posterior predictive distribution since it is also conditional on the observed data y. And it is expressed as an average of conditional predictions over the posterior distribution of θ:
Bayesian Methods for Meta-Analysis
Published in Christopher H. Schmid, Theo Stijnen, Ian R. White, Handbook of Meta-Analysis, 2020
Christopher H. Schmid, Bradley P. Carlin, Nicky J. Welton
Prediction is central to problems requiring decisions. Many regulatory agencies now require a systematic review of the evidence from companies seeking to market a new drug or device. Businesses also use meta-analysis for the planning of new product lines. Such users see meta-analysis as helping them to predict the results of a future study. The Bayesian approach is well suited to problems of prediction through the use of the predictive distribution. For example, when monitoring a single trial, one can use the posterior predictive distribution to determine the probability of reaching a successful result. It is also useful in decision modeling when one needs to predict the results of a new study population that is similar to those in the studies in a meta-analysis (Ades, Lu and Higgins, 2005).
Bayesian Tail Probabilities for Decision Making
Published in Emmanuel Lesaffre, Gianluca Baio, Bruno Boulanger, Bayesian Methods in Pharmaceutical Research, 2020
The predictive distribution (3.10) is sometimes called posterior predictive distribution, since it is conditional on the observed data x. In contrast, the prior predictive distribution is derived from the sampling and the prior distribution alone. The prior predictive distribution plays a key role in Bayesian model selection, since the Bayes factor (3.5) compares (3.12) under the two hypotheses. Note that (3.12) is well defined only for proper priors .
The relationship between moderate to vigorous physical activity and metabolic syndrome: a Bayesian measurement error approach
Published in Journal of Applied Statistics, 2023
Daniel Ries, Alicia Carriquiry
We can still explore population level relationships between MetS risk factors and MVPA by calculating the proportion of the population with high levels of MetS risk factors as a function of minutes in MVPA. This can be computed directly from the posterior predictive distribution of the MetS risk factors conditioned on minutes in MVPA. The posterior predictive distribution is: 5 shows the probability of an individual having a high level of each risk factor as a function of minutes in MVPA (rf explained in Section 1). There is a fast drop in probability for both systolic blood pressure and glucose, as suggested by the values of parameter estimates. Notice that even with 60 min of MVPA a day on average, 46% of the represented population is still expected to have a large waistline. This suggests that factors other than exercise could have a major impact on one's weight and waistline.
Bayesian regression model for recurrent event data with event-varying covariate effects and event effect
Published in Journal of Applied Statistics, 2018
Li-An Lin, Sheng Luo, Barry R. Davis
We use the conditional predictive ordinate (CPO) [15] statistic for our model selection, derived from the posterior predictive distribution (PPD). Let the parameter vector i, the CPO statistic is defined as 5), i deleted. There is no analytic solution for the above integration. In the absence of a closed form, a Monte Carlo approximation of 10] as mth iteration of a total of M posterior samples after burn-in. A large CPO value indicates a better fit. The summary statistic of the CPO is the log pseudo-marginal likelihood (LPML), defined as
Bayesian integrative analysis for multi-fidelity computer experiments
Published in Journal of Applied Statistics, 2019
In addition, the density of the posterior predictive distribution Generate the parameters Approximate the density