Documentation/tutorial #112
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kaiserls
commented
Dec 6, 2023
| "close the cycle between the data and parameters, we can again sample\n", | ||
| "from this distribution and use the forward model to get a discrete\n", | ||
| "distribution of the parameters.\n", | ||
| "That's enough maths for now - let's take a look at an example! We start with something simple: the average temperatures in different locations, i.e. a model for the dependence of the temperature $y$ on the latitude $q$. In the real world, problems with a known continous data distribution are rare. Instead, we often rely on discrete measurements. Hence, EPI starts with discrete data points as input and derives a continous distribution using Kernel Density Estimation (KDE) techniques. From this data distribution the EPI algorithm derives the parameter distribution. To close the cycle between the data and parameters, we can again sample from this distribution and use the forward model to get a finite sample of the parameters.\n", |
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to get a finite sample of the parameters
to get a finite sample of the data?
| @@ -119,12 +115,12 @@ | |||
| "\n", | |||
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"Additionally, the attributes \n",
"- `param_dim`\n",
"- `data_dim`\n",
"- `PARAM_LIMITS`\n",
"- `CENTRAL_PARAM`\n",
See a few lines above. Maybe say that you need to pass central_param and param_limits to the constructor? PARAM_LIMITS and CENTRAL_PARAM are just for convenience in our example models. But that's just a small detail, which I noticed while looking over the tutorial.
| "\n", | ||
| "Now we can now use EPI to infer the parameter distribution from the data.By default, the `inference` method uses Markov chain Monte Carlo sampling (this can be changed using the inference_type argument). `inference` returns a tuple containing samples from the parameter Markov chain $y_i$, the corresponding data points $q_i = s(y_i)$, the estimated densities $\\Phi_Q (q_i)$ scaled by a constant $c$, and a `ResultManager` object that can be used to load and manipulate the results of EPI." | ||
| "Now we can now use `eulerpi` to infer the parameter distribution from the data. By default, the `inference` method uses Markov chain Monte Carlo (MCMC) sampling (this can be changed using the inference_type argument). `inference` returns a tuple containing three dicts with the samples from the parameter Markov chain $q_i$, the corresponding data points $y_i = s(q_i)$, the estimated densities $\\Phi_Q (q_i)$ scaled by a constant $c$, as well as a `ResultManager` object that can be used to load and manipulate the results of EPI." |
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is
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "The two plots correspond to the inferred parameter distribution $\\hat{\\Phi}_{\\mathcal{Q}}$ and a KDE of the pushforward of the inferred sample, i.e. $s(\\hat{q_i})$. We will come back to the plotting function when we defined a more interesting model:\n", |
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Maybe already give a hint/reminder, what the plot of the KDE of
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Description
Fixes #107
Fixes #101
Type of change
How Has This Been Tested?
Please note/describe at least one tests that you ran to verify your changes.
Checklist For Contributor
[unreleased]sectionChecklist For Maintainers