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The simulation of this population average was then repeated for each of the 1000 different parameter configurations represented in the posterior sample (the entire posterior simulation therefore involved a total of 10 simulated patients), resulting in inferences that reflect posterior parameter uncertainty as well as intertrial and interpatient variation.
It develops a Markov chain Monte Carlo algorithm for posterior simulation that is reliable and practical given the number of attributes, choices and sample sizes characteristic of discrete choice experiments.
As in Nieto-Barajas et al. (2004), posterior simulation for our model is aided by the strategic introduction of an additional latent variable (Supplementary Material for details).
All treatment effects were based on posterior simulation (n = 2,500) with 95% credible intervals that were interpreted as statistical significant (p = 0.05%) when the interval did not overlap the reference value in question.
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Using posterior simulations, we obtained TP loading estimates from ungauged subwatersheds in the area that were twice as high relative to values historically used.
A posterior simulation-based analogue of Akaike's information reiteration through MCMC (AICM) test was used to compare demographic models for all four species.
> A posterior simulation-based analogue of Akaike's information reiteration through MCMC (AICM) test for northern group revealed that the expansion model favored over the other two models (Additional file 6: Table S4), and the BSP showed a demographic expansion.
After verifying that appropriate effective sample sizes were achieved, three model selection methods were applied: a posterior simulation-based analogue of the Akaike Information Criterion (AICM) [ 89, 90], and Bayes Factors (BF) between marginal likelihoods estimated through Path Sampling (PS) [ 91] and Stepping Stone Sampling (SS) [ 92].
A posterior simulation-based analogue of Akaike's information criterion through MCMC (AICM) [ 84] was used to compare all three models, which measured AIC from the posterior of each model, with score > 10 as strong evidence in favor of one model over the others [ 85].
Posterior predictive simulation was used for model checking as described by Gilks et al. [ 28].
Passing this prior parameter uncertainty through geostatistical simulation provides a realistic posterior model of uncertainty that accounts for the data configuration, conditioning, spatial correlation, and the domain limits.
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