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This is problematic for a probabilistic HMM approach that models these distributions using Gaussian Mixture Models (GMMs) and has an underlying assumption that they are relatively well clustered.
iASeq models these distributions hierarchically in two steps.
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An N-state HSMM λ is specified by a set of state output probability distributions b i ∙ i = 1 N and a complementary set of state duration probability distributions p i ∙ i = 1 N. To model these distributions, a number of distinct decision trees are used for output and duration probability distributions.
This section describes how to model these distributions with an infinite Markov model.
Therefore, we employ a heteroscedastic model called two-dimensional generalized autoregressive conditional heteroscedastic (2-D garch) for statistical modeling of these distributions.
We use thus a non-parametric estimate of these PDFs: this is a reasonable approach since our a priori knowledge of the problem hardly suggests a mathematical model for these distributions.
Epidemic scenarios were randomly chosen from predefined distributions for each of the model parameters; these distributions are presented in Supplementary Material S1, S2.2.
In the LEV model, these normal distributions were replaced by equal-variance Laplace distributions.
Nevertheless, planners should consider adding upslope buffers to conservation areas designated using current distributions of endemic species, and future research could model these species distributions under future climate scenarios.
For example, in dental caries research and many other areas, proportions of observations with zero counts are often higher than expected under the Poisson or negative binomial distributions, and regression models based on these distributions may result in biased estimates and poor predictions.
A Gaussian mixture model was applied to model these two distributions.
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