Table 1 Subject-dependent parameters and population hyper-priors used in the best model
Model parameters | Priors | Hyper-priors |
|---|---|---|
Retention rate | \({\alpha }_{i} \sim 1/\left(1+{e}^{-\mathcal{N}\left({\theta }_{\alpha }, { \sigma }_{\alpha } \right)}\right)\) | \({\theta }_{\alpha } \sim \mathcal{N}\left(\text{2,1}\right)\) \({\sigma }_{\alpha } \sim \text{I}\text{n}\text{v}\text{G}\text{a}\text{m}\text{m}\text{a}\left(3, 2\right)\) |
Learning rate | \({\beta }_{i } \sim {\mathcal{N}}_{\left[0,{\infty }\right)}\left({\theta }_{\beta }, {\sigma }_{\beta }\right)\) | \({\theta }_{\beta } \sim \mathcal{N}\left(0, 1\right)\) \({\sigma }_{\beta } \sim \text{I}\text{n}\text{v}\text{G}\text{a}\text{m}\text{m}\text{a}\left(4, 2\right)\) |
Self-training rate | \({\gamma }_{i} \sim {\mathcal{N}}_{\left[0,{\infty }\right)}\left({\theta }_{\gamma },{\sigma }_{\gamma }\right)\) | \({\theta }_{{\upgamma }} \sim \mathcal{N}\left(0, 1\right)\) \({{\sigma }}_{{\gamma }} \sim \text{I}\text{n}\text{v}\text{G}\text{a}\text{m}\text{m}\text{a}\left(4, 2\right)\) |
Initial state of memory | \({x}_{i}^{0} \sim{ \mathcal{N}}_{\left[0,{\infty }\right)}\left(k \text{M}\text{A}{\text{L}}_{\text{i}\text{n}\text{i}}, {\sigma }_{\text{i}\text{n}\text{i}}\right)\) | \(k \sim {\mathcal{N}}_{\left[0,{\infty }\right)}\left(0, 2\right)\) \({\sigma }_{\text{i}\text{n}\text{i}} \sim \text{I}\text{n}\text{v}\text{G}\text{a}\text{m}\text{m}\text{a}\left(3, 2\right)\) |
Data | Likelihood | Hyper-priors |
|---|---|---|
MAL (measured) | \(\text{S}\text{t}\text{u}\text{d}\text{e}\text{n}\text{t}\text{T}\left({\text{M}\text{A}\text{L}}_{i}^{t} | {m}_{i}^{t}, { \sigma }_{\text{M}\text{A}\text{L}}, \nu \right)\) | \(\nu \sim \text{G}\text{a}\text{m}\text{m}\text{a}\left(2, 0.1\right)\) \({\sigma }_{\text{M}\text{A}\text{L}} \sim {\mathcal{N}}_{\left[0,{\infty }\right)}\left(0.25, 0.1\right)\) |