Merge pull request #84 from theislab/add/birth_death_desc

describe birth death parameters

.pre-commit-config.yaml

@@ -2,8 +2,8 @@ fail_fast: false
 default_language_version:
   python: python3
 default_stages:
-  - commit
-  - push
+  - pre-commit
+  - pre-push
 minimum_pre_commit_version: 3.0.0
 repos:
   - repo: https://github.com/pre-commit/pre-commit-hooks

examples/problems/800_score_genes_for_marginals.ipynb

@@ -207,7 +207,15 @@
    "source": [
     "Assuming a cell with value `4.0` corresponds to day `2`, this means that this cell is expected to proliferate such that at day `3` the cell gave rise to another 3 cells. This indeed might be realistic. \n",
     "\n",
-    "Nevertheless, if we would like to adapt our prior estimates, we can do this via the `marginal_kwargs` estimate in `~moscot.problems.time.TemporalProblem.prepare`. Either we can use the parameters corresponding to the birth process\n",
+    "Nevertheless, if we would like to adapt our prior estimates, we can do this via the `marginal_kwargs` estimate in `~moscot.problems.time.TemporalProblem.prepare`.\n",
+    "\n",
+    "We could use the parameters corresponding to the birth-death process on gene expression space with birth rate $\\beta$ and death rate $\\delta$: during a time interval $\\Delta t$, the probability of a birth is $\\beta \\Delta t$ and the probability of a death is $\\delta \\Delta t$.\n",
+    "\n",
+    "The $\\Delta t$ is inferred automatically from `~moscot.problems.time.TemporalProblem.temporal_key` in this case and works with any problem with `temporal_key` present - e.g. `~moscot.problems.time.LineageProblem.temporal_key` and `~moscot.problems.spatiotemporal.SpatioTemporalProblem.temporal_key`.\n",
+    "\n",
+    "Then the birth process is\n",
+    "\n",
+    "$\\beta_{max}$ - maximum birth rate in optimal conditions, $\\beta_{min}$ - minimum birth rate (e.g. in absence of proliferative signals), $\\beta_{center}$ - peak value of probabilistic birth rate distribution, $\\beta_{width}$ - variability of the birth rate.\n",
     "\n",
     "```python\n",
     "    beta_max: float = 1.7,\n",
@@ -218,6 +226,8 @@
     "\n",
     "and the death process\n",
     "\n",
+    "$\\delta_{max}$ - highest possible death rate, $\\delta_{min}$ - minimum death rate, $\\delta_{center}$ - peak value of the death rate distribution, $\\delta_{width}$ - variability of the death rate.\n",
+    "\n",
     "```python\n",
     "    delta_max: float = 1.7,\n",
     "    delta_min: float = 0.3,\n",
@@ -338,7 +348,7 @@
    "notebook_metadata_filter": "-all"
   },
   "kernelspec": {
-   "display_name": "Python 3.10.10 ('moscot_env7')",
+   "display_name": "moscot_dev",
    "language": "python",
    "name": "python3"
   },
@@ -352,12 +362,7 @@
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    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.10"
-  },
-  "vscode": {
-   "interpreter": {
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+   "version": "3.11.5"
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