Details on the model specifications are provided in Additional file 1. Bayesian models' inference was made by using Markov Chain Monte Carlo (MCMC) simulations on the software R, version 2.9.2 via the library R2WinBUGS [ 30], which connects with the software WinBUGS [ 31].
Non-parametric GP regression is used to model gene expression over time and the model inference is carried using the Bayesian reasoning.
In contrast, Cases 2 and 3 have latent variables and model inference is only feasible with informative prior knowledge of some parameters.
As topic model inference is an area of active research, we expect improvements in inference (e.g. of relevant phrases instead of words) to directly improve the usability of our method.
For the HLR model, inference is straightforward since the number of terms in the partition function is only T× K. We can easily enumerate all of them to get the exact values of those marginal probabilities.
Depending on the gene set size, the average size of vocabularies is around 15K. Topic model inference is a commonly used approach for uncovering the main themes from large yet unstructured collection of documents.
In turn, accurate model inference is central to revealing the core patterns and processes of viral evolution, and to accurately estimating the time-scale of their emergence and spread through populations [ 12, 13].
We have expanded the explanation of this method and its advantages in the corresponding part of the Materials and methods section, multi-model selection and inference: "Multi-model inference is increasingly recognised as an alternative approach the interest is in finding strong and consistent predictors of a particular outcome".
In this model, we studied the effect of seasonality, physico-chemical characteristics of the water, and community composition (Table 4), all of which were introduced as fixed effects without interactions.> Multi-model inference is increasingly recognised as an alternative approach to the use of null hypothesis testing (Burnham and Anderson, 2002; Grueber et al., 2011).
By exploring uncertainties inherent in multiple working hypotheses, we have shown that multi-model inference is a fruitful and efficient approach to recover the nature, timing and geographical context of the Tabebuia aurea population dynamic in response to the Quaternary climate changes.
