{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
\n", "\n", "**This is a fixed-text formatted version of a Jupyter notebook**\n", "\n", "- Try online [![Binder](https://static.mybinder.org/badge.svg)](https://mybinder.org/v2/gh/gammapy/gammapy-webpage/v0.16?urlpath=lab/tree/mcmc_sampling.ipynb)\n", "- You can contribute with your own notebooks in this\n", "[GitHub repository](https://github.com/gammapy/gammapy/tree/master/tutorials).\n", "- **Source files:**\n", "[mcmc_sampling.ipynb](../_static/notebooks/mcmc_sampling.ipynb) |\n", "[mcmc_sampling.py](../_static/notebooks/mcmc_sampling.py)\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Fitting and error estimation with MCMC\n", "\n", "## Introduction\n", "\n", "The goal of Markov Chain Monte Carlo (MCMC) algorithms is to approximate the posterior distribution of your model parameters by random sampling in a probabilistic space. For most readers this sentence was probably not very helpful so here we'll start straight with and example but you should read the more detailed mathematical approaches of the method [here](https://www.pas.rochester.edu/~sybenzvi/courses/phy403/2015s/p403_17_mcmc.pdf) and [here](https://github.com/jakevdp/BayesianAstronomy/blob/master/03-Bayesian-Modeling-With-MCMC.ipynb).\n", "\n", "### How does it work ?\n", "\n", "The idea is that we use a number of walkers that will sample the posterior distribution (i.e. sample the Likelihood profile).\n", "\n", "The goal is to produce a \"chain\", i.e. a list of $\\theta$ values, where each $\\theta$ is a vector of parameters for your model.
\n", "If you start far away from the truth value, the chain will take some time to converge until it reaches a stationary state. Once it has reached this stage, each successive elements of the chain are samples of the target posterior distribution.
\n", "This means that, once we have obtained the chain of samples, we have everything we need. We can compute the distribution of each parameter by simply approximating it with the histogram of the samples projected into the parameter space. This will provide the errors and correlations between parameters.\n", "\n", "\n", "Now let's try to put a picture on the ideas described above. With this notebook, we have simulated and carried out a MCMC analysis for a source with the following parameters:
\n", "$Index=2.0$, $Norm=5\\times10^{-12}$ cm$^{-2}$ s$^{-1}$ TeV$^{-1}$, $Lambda =(1/Ecut) = 0.02$ TeV$^{-1}$ (50 TeV) for 20 hours.\n", "\n", "The results that you can get from a MCMC analysis will look like this :\n", "\n", "\n", "\n", "On the first two top panels, we show the pseudo-random walk of one walker from an offset starting value to see it evolve to a better solution.\n", "In the bottom right panel, we show the trace of each 16 walkers for 500 runs (the chain described previsouly). For the first 100 runs, the parameter evolve towards a solution (can be viewed as a fitting step). Then they explore the local minimum for 400 runs which will be used to estimate the parameters correlations and errors.\n", "The choice of the Nburn value (when walkers have reached a stationary stage) can be done by eye but you can also look at the autocorrelation time.\n", "\n", "### Why should I use it ?\n", "\n", "When it comes to evaluate errors and investigate parameter correlation, one typically estimate the Likelihood in a gridded search (2D Likelihood profiles). Each point of the grid implies a new model fitting. If we use 10 steps for each parameters, we will need to carry out 100 fitting procedures. \n", "\n", "Now let's say that I have a model with $N$ parameters, we need to carry out that gridded analysis $N*(N-1)$ times. \n", "So for 5 free parameters you need 20 gridded search, resulting in 2000 individual fit. \n", "Clearly this strategy doesn't scale well to high-dimensional models.\n", "\n", "Just for fun: if each fit procedure takes 10s, we're talking about 5h of computing time to estimate the correlation plots. \n", "\n", "There are many MCMC packages in the python ecosystem but here we will focus on [emcee](https://emcee.readthedocs.io), a lightweight Python package. A description is provided here : [Foreman-Mackey, Hogg, Lang & Goodman (2012)](https://arxiv.org/abs/1202.3665)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import astropy.units as u\n", "from astropy.coordinates import SkyCoord\n", "from gammapy.irf import load_cta_irfs\n", "from gammapy.maps import WcsGeom, MapAxis\n", "from gammapy.modeling.models import (\n", " ExpCutoffPowerLawSpectralModel,\n", " GaussianSpatialModel,\n", " SkyModel,\n", ")\n", "from gammapy.cube import MapDataset, MapDatasetMaker\n", "from gammapy.data import Observation\n", "from gammapy.modeling.sampling import (\n", " run_mcmc,\n", " par_to_model,\n", " plot_corner,\n", " plot_trace,\n", ")" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import logging\n", "\n", "logging.basicConfig(level=logging.INFO)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulate an observation\n", "\n", "Here we will start by simulating an observation using the `simulate_dataset` method." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING: AstropyDeprecationWarning: The truth value of a Quantity is ambiguous. In the future this will raise a ValueError. [astropy.units.quantity]\n", "WARNING:astropy:AstropyDeprecationWarning: The truth value of a Quantity is ambiguous. In the future this will raise a ValueError.\n" ] } ], "source": [ "irfs = load_cta_irfs(\n", " \"$GAMMAPY_DATA/cta-1dc/caldb/data/cta/1dc/bcf/South_z20_50h/irf_file.fits\"\n", ")\n", "\n", "observation = Observation.create(\n", " pointing=SkyCoord(0 * u.deg, 0 * u.deg, frame=\"galactic\"),\n", " livetime=20 * u.h,\n", " irfs=irfs,\n", ")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SkyModel\n", "\n", " Name : nK97eTZ3\n", " Spectral model type : ExpCutoffPowerLawSpectralModel\n", " Spatial model type : GaussianSpatialModel\n", " Temporal model type : \n", " Parameters:\n", " lon_0 : 0.000 deg \n", " lat_0 : 0.000 deg \n", " sigma : 0.200 deg \n", " e (frozen) : 0.000 \n", " phi (frozen) : 0.000 deg \n", " index : 2.000 \n", " amplitude : 3.00e-12 1 / (cm2 s TeV)\n", " reference (frozen) : 1.000 TeV \n", " lambda_ : 0.050 1 / TeV \n", " alpha (frozen) : 1.000 \n", "\n", "\n" ] } ], "source": [ "# Define sky model to simulate the data\n", "spatial_model = GaussianSpatialModel(\n", " lon_0=\"0 deg\", lat_0=\"0 deg\", sigma=\"0.2 deg\", frame=\"galactic\"\n", ")\n", "\n", "spectral_model = ExpCutoffPowerLawSpectralModel(\n", " index=2,\n", " amplitude=\"3e-12 cm-2 s-1 TeV-1\",\n", " reference=\"1 TeV\",\n", " lambda_=\"0.05 TeV-1\",\n", ")\n", "\n", "sky_model_simu = SkyModel(\n", " spatial_model=spatial_model, spectral_model=spectral_model\n", ")\n", "print(sky_model_simu)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Define map geometry\n", "axis = MapAxis.from_edges(\n", " np.logspace(-1, 2, 30), unit=\"TeV\", name=\"energy\", interp=\"log\"\n", ")\n", "geom = WcsGeom.create(\n", " skydir=(0, 0), binsz=0.05, width=(2, 2), frame=\"galactic\", axes=[axis]\n", ")\n", "\n", "empty_dataset = MapDataset.create(geom=geom)\n", "maker = MapDatasetMaker(selection=[\"background\", \"edisp\", \"psf\", \"exposure\"])\n", "dataset = maker.run(empty_dataset, observation)\n", "dataset.models = sky_model_simu\n", "dataset.fake()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dataset.counts.sum_over_axes().plot(add_cbar=True);" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# If you want to fit the data for comparison with MCMC later\n", "\n", "# fit = Fit(dataset)\n", "# result = fit.run(optimize_opts={\"print_level\": 1})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate parameter correlations with MCMC\n", "\n", "Now let's analyse the simulated data.\n", "Here we just fit it again with the same model we had before as a starting point.\n", "The data that would be needed are the following: \n", "- counts cube, psf cube, exposure cube and background model\n", "\n", "Luckily all those maps are already in the Dataset object.\n", "\n", "We will need to define a Likelihood function and define priors on parameters.
\n", "Here we will assume a uniform prior reading the min, max parameters from the sky model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define priors\n", "\n", "This steps is a bit manual for the moment until we find a better API to define priors.
\n", "Note the you **need** to define priors for each parameter otherwise your walkers can explore uncharted territories (e.g. negative norms)." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Models\n", "\n", "Component 0: SkyModel\n", "\n", " Name : nK97eTZ3\n", " Spectral model type : ExpCutoffPowerLawSpectralModel\n", " Spatial model type : GaussianSpatialModel\n", " Temporal model type : \n", " Parameters:\n", " lon_0 (frozen) : 0.000 deg \n", " lat_0 (frozen) : 0.000 deg \n", " sigma (frozen) : 0.200 deg \n", " e (frozen) : 0.000 \n", " phi (frozen) : 0.000 deg \n", " index : 2.000 \n", " amplitude : 3.20e-12 1 / (cm2 s TeV)\n", " reference (frozen) : 1.000 TeV \n", " lambda_ : 0.050 1 / TeV \n", " alpha (frozen) : 1.000 \n", "\n", "\n", "stat = -936335.9246409138\n" ] } ], "source": [ "# Define the free parameters and min, max values\n", "\n", "dataset.parameters[\"sigma\"].frozen = True\n", "dataset.parameters[\"lon_0\"].frozen = True\n", "dataset.parameters[\"lat_0\"].frozen = True\n", "dataset.parameters[\"amplitude\"].frozen = False\n", "dataset.parameters[\"index\"].frozen = False\n", "dataset.parameters[\"lambda_\"].frozen = False\n", "\n", "\n", "dataset.background_model.parameters[\"norm\"].frozen = True\n", "dataset.background_model.parameters[\"tilt\"].frozen = True\n", "\n", "dataset.background_model.parameters[\"norm\"].min = 0.5\n", "dataset.background_model.parameters[\"norm\"].max = 2\n", "\n", "dataset.parameters[\"index\"].min = 1\n", "dataset.parameters[\"index\"].max = 5\n", "dataset.parameters[\"lambda_\"].min = 1e-3\n", "dataset.parameters[\"lambda_\"].max = 1\n", "\n", "dataset.parameters[\"amplitude\"].min = (\n", " 0.01 * dataset.parameters[\"amplitude\"].value\n", ")\n", "dataset.parameters[\"amplitude\"].max = (\n", " 100 * dataset.parameters[\"amplitude\"].value\n", ")\n", "\n", "dataset.parameters[\"sigma\"].min = 0.05\n", "dataset.parameters[\"sigma\"].max = 1\n", "\n", "# Setting amplitude init values a bit offset to see evolution\n", "# Here starting close to the real value\n", "dataset.parameters[\"index\"].value = 2.0\n", "dataset.parameters[\"amplitude\"].value = 3.2e-12\n", "dataset.parameters[\"lambda_\"].value = 0.05\n", "\n", "print(dataset.models)\n", "print(\"stat =\", dataset.stat_sum())" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO:gammapy.modeling.sampling:Free parameters: ['index', 'amplitude', 'lambda_']\n", "INFO:gammapy.modeling.sampling:Starting MCMC sampling: nwalkers=6, nrun=150\n", "INFO:gammapy.modeling.sampling: 0%\n", "INFO:gammapy.modeling.sampling: 50%\n", "INFO:gammapy.modeling.sampling:100% => sampling completed\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 17 s, sys: 420 ms, total: 17.4 s\n", "Wall time: 17.8 s\n" ] } ], "source": [ "%%time\n", "# Now let's define a function to init parameters and run the MCMC with emcee\n", "# Depending on your number of walkers, Nrun and dimensionality, this can take a while (> minutes)\n", "sampler = run_mcmc(dataset, nwalkers=6, nrun=150) # to speedup the notebook\n", "# sampler=run_mcmc(dataset,nwalkers=12,nrun=1000) # more accurate contours" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot the results\n", "\n", "The MCMC will return a sampler object containing the trace of all walkers.
\n", "The most important part is the chain attribute which is an array of shape:
\n", "_(nwalkers, nrun, nfreeparam)_\n", "\n", "The chain is then used to plot the trace of the walkers and estimate the burnin period (the time for the walkers to reach a stationary stage)." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_corner(sampler, dataset, nburn=50)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot the model dispersion\n", "\n", "Using the samples from the chain after the burn period, we can plot the different models compared to the truth model. To do this we need to the spectral models for each parameter state in the sample." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "emin, emax = [0.1, 100] * u.TeV\n", "nburn = 50\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=(12, 6))\n", "\n", "for nwalk in range(0, 6):\n", " for n in range(nburn, nburn + 100):\n", " pars = sampler.chain[nwalk, n, :]\n", "\n", " # set model parameters\n", " par_to_model(dataset, pars)\n", " spectral_model = dataset.models[0].spectral_model\n", "\n", " spectral_model.plot(\n", " energy_range=(emin, emax),\n", " ax=ax,\n", " energy_power=2,\n", " alpha=0.02,\n", " color=\"grey\",\n", " )\n", "\n", "\n", "sky_model_simu.spectral_model.plot(\n", " energy_range=(emin, emax), energy_power=2, ax=ax, color=\"red\"\n", ");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fun Zone\n", "\n", "Now that you have the sampler chain, you have in your hands the entire history of each walkers in the N-Dimensional parameter space.
\n", "You can for example trace the steps of each walker in any parameter space." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Here we plot the trace of one walker in a given parameter space\n", "parx, pary = 0, 1\n", "\n", "plt.plot(sampler.chain[0, :, parx], sampler.chain[0, :, pary], \"ko\", ms=1)\n", "plt.plot(\n", " sampler.chain[0, :, parx],\n", " sampler.chain[0, :, pary],\n", " ls=\":\",\n", " color=\"grey\",\n", " alpha=0.5,\n", ")\n", "\n", "plt.xlabel(\"Index\")\n", "plt.ylabel(\"Amplitude\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PeVatrons in CTA ?\n", "\n", "Now it's your turn to play with this MCMC notebook. For example to test the CTA performance to measure a cutoff at very high energies (100 TeV ?).\n", "\n", "After defining your Skymodel it can be as simple as this :" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# dataset = simulate_dataset(model, geom, pointing, irfs)\n", "# sampler = run_mcmc(dataset)\n", "# plot_trace(sampler, dataset)\n", "# plot_corner(sampler, dataset, nburn=200)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.0" }, "nbsphinx": { "orphan": true } }, "nbformat": 4, "nbformat_minor": 4 }