What do you mean by fit_t_, fit_tau_, fit_tau, and fit_t_ in the parameters of the inference ?

[yujinmath]

Hi,everyone!
There is a problem that bothers me recently. What do you mean by fit_t_, fit_tau_, fit_tau, and fit_t_ in the parameters of the inference output of the dynamics model?
Thanks in advance for your help!

[VolkerBergen]

That's bit cryptic indeed - will update the docs. It's only being used internally, thus a full description if yet missing. Hope this helps for now:

• fit_t corresponds to the gene-wise latent times.
• fit_t_ are the swicthing timepoints.
• fit_tau_ are the timepoints of assigning observatins to the off-state (necessary to generate likelihoods after the fitting)
• fit_tau same as above, but for the on-state.

[yujinmath]

Thanks for your reply. by the way, based on the above fitting timepoints, can we infer the time of the gene from on-state to off-state and then infer the transcriptional burst frequency of genes?

[VolkerBergen]

Timepoints are inferred and can be further leveraged. Transcription rate is being modeled as constant within the window from on- to off-state, so that needs to be extended when modeling transcriptional bursting kinetics.

[anorak94]

Hey i was going through the results of the recover dynamics and in the adata object. fit_tau_ and fit_tau and fit_t have the shape n_cells x n_genes while fit_t_ has shape n_genes. Since fit_t_ are the switching time points it makes sense that we have one switching time point per gene and similarly fit_t corresponds to the latent time for each cell. But what do fit_tau_ and fit_tau mean. For a cell if its current latent time is greater than fit_tau_ it is assigned to the off state and this lets us write the log-likelihood to be minimized and the same for fit_tau but then how do we estimate these two quantities on a per gene per cell basis. Is it by using the analytical equations. For instance we know alpha_induction_ss and alpha_repression_ss = 0. So we just compute $\tau$ from the analytical equation assuming $t_0 = 0$