{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting a model to data with both x and y errors with `Bilby`\n",
    "\n",
    "Usually when we fit a model to data with a Gaussian Likelihood we assume that we know x values exactly. This is almost never the case. Here we show how to fit a model with errors in both x and y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-05T04:49:50.806458Z",
     "iopub.status.busy": "2024-04-05T04:49:50.805874Z",
     "iopub.status.idle": "2024-04-05T04:49:52.171820Z",
     "shell.execute_reply": "2024-04-05T04:49:52.170990Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/envs/python310/lib/python3.10/site-packages/pandas/core/computation/expressions.py:21: UserWarning: Pandas requires version '2.8.4' or newer of 'numexpr' (version '2.7.3' currently installed).\n",
      "  from pandas.core.computation.check import NUMEXPR_INSTALLED\n"
     ]
    }
   ],
   "source": [
    "import bilby\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulate data\n",
    "\n",
    "First we create the data and plot it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-05T04:49:52.179173Z",
     "iopub.status.busy": "2024-04-05T04:49:52.178712Z",
     "iopub.status.idle": "2024-04-05T04:49:52.350571Z",
     "shell.execute_reply": "2024-04-05T04:49:52.349709Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define our model, a line\n",
    "def model(x, m, c, **kwargs):\n",
    "    y = m * x + c\n",
    "    return y\n",
    "\n",
    "\n",
    "# make a function to create and plot our data\n",
    "def make_data(points, m, c, xerr, yerr, seed):\n",
    "    np.random.seed(int(seed))\n",
    "    xtrue = np.linspace(0, 100, points)\n",
    "    ytrue = model(x=xtrue, m=m, c=c)\n",
    "\n",
    "    xerr_vals = xerr * np.random.randn(points)\n",
    "    yerr_vals = yerr * np.random.randn(points)\n",
    "    xobs = xtrue + xerr_vals\n",
    "    yobs = ytrue + yerr_vals\n",
    "\n",
    "    plt.errorbar(xobs, yobs, xerr=xerr, yerr=yerr, fmt=\"x\")\n",
    "    plt.errorbar(xtrue, ytrue, yerr=yerr, color=\"black\", alpha=0.5)\n",
    "    plt.xlim(0, 100)\n",
    "    plt.show()\n",
    "    plt.close()\n",
    "\n",
    "    data = {\n",
    "        \"xtrue\": xtrue,\n",
    "        \"ytrue\": ytrue,\n",
    "        \"xobs\": xobs,\n",
    "        \"yobs\": yobs,\n",
    "        \"xerr\": xerr,\n",
    "        \"yerr\": yerr,\n",
    "    }\n",
    "\n",
    "    return data\n",
    "\n",
    "\n",
    "data = make_data(points=30, m=5, c=10, xerr=5, yerr=5, seed=123)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define our prior and sampler settings\n",
    "\n",
    "Now lets set up the prior and bilby output directory/sampler settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-05T04:49:52.358888Z",
     "iopub.status.busy": "2024-04-05T04:49:52.358576Z",
     "iopub.status.idle": "2024-04-05T04:49:52.364837Z",
     "shell.execute_reply": "2024-04-05T04:49:52.363966Z"
    }
   },
   "outputs": [],
   "source": [
    "# setting up bilby priors\n",
    "priors = dict(\n",
    "    m=bilby.core.prior.Uniform(0, 30, \"m\"), c=bilby.core.prior.Uniform(0, 30, \"c\")\n",
    ")\n",
    "\n",
    "sampler_kwargs = dict(priors=priors, sampler=\"bilby_mcmc\", nsamples=1000, printdt=5, outdir=\"outdir\", verbose=False, clean=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit with exactly known x-values\n",
    "\n",
    "Our first step is to recover the straight line using a simple Gaussian Likelihood that only takes into account the y errors. Under the assumption we know x exactly. In this case, we pass in xtrue for x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-05T04:49:52.369028Z",
     "iopub.status.busy": "2024-04-05T04:49:52.368797Z",
     "iopub.status.idle": "2024-04-05T04:50:18.887972Z",
     "shell.execute_reply": "2024-04-05T04:50:18.887224Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:49 bilby INFO    : Running for label 'known_x', output will be saved to 'outdir'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Analysis priors:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : m=Uniform(minimum=0, maximum=30, name='m', latex_label='m', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : c=Uniform(minimum=0, maximum=30, name='c', latex_label='c', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Analysis likelihood class: <class 'bilby.core.likelihood.GaussianLikelihood'>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Analysis likelihood noise evidence: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Single likelihood evaluation took nan s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Using sampler Bilby_MCMC with kwargs {'nsamples': 1000, 'nensemble': 1, 'pt_ensemble': False, 'ntemps': 1, 'Tmax': None, 'Tmax_from_SNR': 20, 'initial_betas': None, 'adapt': True, 'adapt_t0': 100, 'adapt_nu': 10, 'pt_rejection_sample': False, 'burn_in_nact': 10, 'thin_by_nact': 1, 'fixed_discard': 0, 'autocorr_c': 5, 'L1steps': 100, 'L2steps': 3, 'printdt': 5, 'check_point_delta_t': 1800, 'min_tau': 1, 'proposal_cycle': 'default', 'stop_after_convergence': False, 'fixed_tau': None, 'tau_window': None, 'evidence_method': 'stepping_stone', 'initial_sample_method': 'prior', 'initial_sample_dict': None}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Initializing BilbyPTMCMCSampler with:\n",
      "  Convergence settings: ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n",
      "  Parallel-tempering settings: ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n",
      "  proposal_cycle: default\n",
      "  pt_rejection_sample: False\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Setting parallel tempering inputs=ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Initializing BilbyPTMCMCSampler with:ntemps=1, nensemble=1, pt_ensemble=False, initial_betas=[1], initial_sample_method=prior, initial_sample_dict=None\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Using initial sample {'m': 26.71740826551804, 'c': 1.6916325823002654}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Using ProposalCycle:\n",
      "  AdaptiveGaussianProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  DifferentialEvolutionProposal(acceptance_ratio:nan,n:0,)\n",
      "  UniformProposal(acceptance_ratio:nan,n:0,)\n",
      "  KDEProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "  FisherMatrixProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  GMMProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Setting convergence_inputs=ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Drawing 1000 samples\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Checkpoint every check_point_delta_t=1800s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Print update every printdt=5s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Reached convergence: exiting sampling\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Checkpoint start\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Written checkpoint file outdir/known_x_resume.pickle\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Zero-temperature proposals:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : AdaptiveGaussianProposal(acceptance_ratio:0.23,n:2.8e+04,scale:0.0049,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : DifferentialEvolutionProposal(acceptance_ratio:0.47,n:2.6e+04,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : UniformProposal(acceptance_ratio:1,n:1.7e+03,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : KDEProposal(acceptance_ratio:0.00014,n:2.9e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : FisherMatrixProposal(acceptance_ratio:0.56,n:2.6e+04,scale:1,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : GMMProposal(acceptance_ratio:0,n:3.1e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Current taus={'m': 1, 'c': 1}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Creating diagnostic plots\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Checkpoint finished\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Sampling time: 0:00:15.017339\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Summary of results:\n",
      "nsamples: 1306\n",
      "ln_noise_evidence:    nan\n",
      "ln_evidence:    nan +/-    nan\n",
      "ln_bayes_factor:    nan +/-    nan\n",
      "\n"
     ]
    }
   ],
   "source": [
    "known_x = bilby.core.likelihood.GaussianLikelihood(\n",
    "    x=data[\"xtrue\"], y=data[\"yobs\"], func=model, sigma=data[\"yerr\"]\n",
    ")\n",
    "result_known_x = bilby.run_sampler(\n",
    "    likelihood=known_x,\n",
    "    label=\"known_x\",\n",
    "    **sampler_kwargs,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-05T04:50:18.894904Z",
     "iopub.status.busy": "2024-04-05T04:50:18.894522Z",
     "iopub.status.idle": "2024-04-05T04:50:20.057062Z",
     "shell.execute_reply": "2024-04-05T04:50:20.056257Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 550x550 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = result_known_x.plot_corner(truth=dict(m=5, c=10), titles=True, save=False)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit with unmodeled uncertainty in the x-values\n",
    "\n",
    "As expected this is easy to recover and the sampler does a good job. However this was made too easy - by passing in the 'true' values of x. Lets see what happens when we pass in the observed values of x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-05T04:50:20.067688Z",
     "iopub.status.busy": "2024-04-05T04:50:20.066363Z",
     "iopub.status.idle": "2024-04-05T04:50:45.505661Z",
     "shell.execute_reply": "2024-04-05T04:50:45.504885Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Running for label 'incorrect_x', output will be saved to 'outdir'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Analysis priors:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : m=Uniform(minimum=0, maximum=30, name='m', latex_label='m', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : c=Uniform(minimum=0, maximum=30, name='c', latex_label='c', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Analysis likelihood class: <class 'bilby.core.likelihood.GaussianLikelihood'>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Analysis likelihood noise evidence: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Single likelihood evaluation took nan s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Using sampler Bilby_MCMC with kwargs {'nsamples': 1000, 'nensemble': 1, 'pt_ensemble': False, 'ntemps': 1, 'Tmax': None, 'Tmax_from_SNR': 20, 'initial_betas': None, 'adapt': True, 'adapt_t0': 100, 'adapt_nu': 10, 'pt_rejection_sample': False, 'burn_in_nact': 10, 'thin_by_nact': 1, 'fixed_discard': 0, 'autocorr_c': 5, 'L1steps': 100, 'L2steps': 3, 'printdt': 5, 'check_point_delta_t': 1800, 'min_tau': 1, 'proposal_cycle': 'default', 'stop_after_convergence': False, 'fixed_tau': None, 'tau_window': None, 'evidence_method': 'stepping_stone', 'initial_sample_method': 'prior', 'initial_sample_dict': None}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Initializing BilbyPTMCMCSampler with:\n",
      "  Convergence settings: ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n",
      "  Parallel-tempering settings: ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n",
      "  proposal_cycle: default\n",
      "  pt_rejection_sample: False\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Setting parallel tempering inputs=ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Initializing BilbyPTMCMCSampler with:ntemps=1, nensemble=1, pt_ensemble=False, initial_betas=[1], initial_sample_method=prior, initial_sample_dict=None\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Using initial sample {'m': 3.8321032421915167, 'c': 26.15152772540474}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Using ProposalCycle:\n",
      "  AdaptiveGaussianProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  DifferentialEvolutionProposal(acceptance_ratio:nan,n:0,)\n",
      "  UniformProposal(acceptance_ratio:nan,n:0,)\n",
      "  KDEProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "  FisherMatrixProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  GMMProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Setting convergence_inputs=ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Drawing 1000 samples\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Checkpoint every check_point_delta_t=1800s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Print update every printdt=5s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Reached convergence: exiting sampling\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Checkpoint start\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Written checkpoint file outdir/incorrect_x_resume.pickle\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Zero-temperature proposals:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : AdaptiveGaussianProposal(acceptance_ratio:0.23,n:2.8e+04,scale:0.0035,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : DifferentialEvolutionProposal(acceptance_ratio:0.46,n:2.7e+04,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : UniformProposal(acceptance_ratio:1,n:1.4e+03,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : KDEProposal(acceptance_ratio:3.2e-05,n:3.1e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : FisherMatrixProposal(acceptance_ratio:0.55,n:2.6e+04,scale:1,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : GMMProposal(acceptance_ratio:7.6e-05,n:2.6e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Current taus={'m': 1.0, 'c': 1}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Creating diagnostic plots\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Checkpoint finished\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Sampling time: 0:00:15.014865\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Summary of results:\n",
      "nsamples: 1288\n",
      "ln_noise_evidence:    nan\n",
      "ln_evidence:    nan +/-    nan\n",
      "ln_bayes_factor:    nan +/-    nan\n",
      "\n"
     ]
    }
   ],
   "source": [
    "incorrect_x = bilby.core.likelihood.GaussianLikelihood(\n",
    "    x=data[\"xobs\"], y=data[\"yobs\"], func=model, sigma=data[\"yerr\"]\n",
    ")\n",
    "result_incorrect_x = bilby.run_sampler(\n",
    "    likelihood=incorrect_x,\n",
    "    label=\"incorrect_x\",\n",
    "    **sampler_kwargs,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-05T04:50:45.513941Z",
     "iopub.status.busy": "2024-04-05T04:50:45.513376Z",
     "iopub.status.idle": "2024-04-05T04:50:45.754757Z",
     "shell.execute_reply": "2024-04-05T04:50:45.753975Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 550x550 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = result_incorrect_x.plot_corner(truth=dict(m=5, c=10), titles=True, save=False)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit with modeled uncertainty in x-values\n",
    "\n",
    "This is not good as there is unmodelled uncertainty in our `x` values.\n",
    "Getting around this requires marginalisation of the true x values or sampling over them. \n",
    "See discussion in section 7 of https://arxiv.org/pdf/1008.4686.pdf.\n",
    "\n",
    "For this, we will have to define a new likelihood class.\n",
    "By subclassing the base `bilby.core.likelihood.Likelihood` class we can do this fairly simply."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-05T04:50:45.765648Z",
     "iopub.status.busy": "2024-04-05T04:50:45.764759Z",
     "iopub.status.idle": "2024-04-05T04:50:45.778958Z",
     "shell.execute_reply": "2024-04-05T04:50:45.777988Z"
    }
   },
   "outputs": [],
   "source": [
    "class GaussianLikelihoodUncertainX(bilby.core.likelihood.Likelihood):\n",
    "    def __init__(self, xobs, yobs, xerr, yerr, function):\n",
    "        \"\"\"\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        xobs, yobs: array_like\n",
    "            The data to analyse\n",
    "        xerr, yerr: array_like\n",
    "            The standard deviation of the noise\n",
    "        function:\n",
    "            The python function to fit to the data\n",
    "        \"\"\"\n",
    "        super(GaussianLikelihoodUncertainX, self).__init__(dict())\n",
    "        self.xobs = xobs\n",
    "        self.yobs = yobs\n",
    "        self.yerr = yerr\n",
    "        self.xerr = xerr\n",
    "        self.function = function\n",
    "\n",
    "    def log_likelihood(self):\n",
    "        variance = (self.xerr * self.parameters[\"m\"]) ** 2 + self.yerr**2\n",
    "        model_y = self.function(self.xobs, **self.parameters)\n",
    "        residual = self.yobs - model_y\n",
    "\n",
    "        ll = -0.5 * np.sum(residual**2 / variance + np.log(variance))\n",
    "\n",
    "        return -0.5 * np.sum(residual**2 / variance + np.log(variance))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-05T04:50:45.785780Z",
     "iopub.status.busy": "2024-04-05T04:50:45.785514Z",
     "iopub.status.idle": "2024-04-05T04:51:11.372872Z",
     "shell.execute_reply": "2024-04-05T04:51:11.372122Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Running for label 'unknown_x', output will be saved to 'outdir'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Analysis priors:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : m=Uniform(minimum=0, maximum=30, name='m', latex_label='m', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : c=Uniform(minimum=0, maximum=30, name='c', latex_label='c', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Analysis likelihood class: <class '__main__.GaussianLikelihoodUncertainX'>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Analysis likelihood noise evidence: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Single likelihood evaluation took nan s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Using sampler Bilby_MCMC with kwargs {'nsamples': 1000, 'nensemble': 1, 'pt_ensemble': False, 'ntemps': 1, 'Tmax': None, 'Tmax_from_SNR': 20, 'initial_betas': None, 'adapt': True, 'adapt_t0': 100, 'adapt_nu': 10, 'pt_rejection_sample': False, 'burn_in_nact': 10, 'thin_by_nact': 1, 'fixed_discard': 0, 'autocorr_c': 5, 'L1steps': 100, 'L2steps': 3, 'printdt': 5, 'check_point_delta_t': 1800, 'min_tau': 1, 'proposal_cycle': 'default', 'stop_after_convergence': False, 'fixed_tau': None, 'tau_window': None, 'evidence_method': 'stepping_stone', 'initial_sample_method': 'prior', 'initial_sample_dict': None}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Initializing BilbyPTMCMCSampler with:\n",
      "  Convergence settings: ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n",
      "  Parallel-tempering settings: ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n",
      "  proposal_cycle: default\n",
      "  pt_rejection_sample: False\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Setting parallel tempering inputs=ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Initializing BilbyPTMCMCSampler with:ntemps=1, nensemble=1, pt_ensemble=False, initial_betas=[1], initial_sample_method=prior, initial_sample_dict=None\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Using initial sample {'m': 8.938728536283739, 'c': 24.292869621251317}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Using ProposalCycle:\n",
      "  AdaptiveGaussianProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  DifferentialEvolutionProposal(acceptance_ratio:nan,n:0,)\n",
      "  UniformProposal(acceptance_ratio:nan,n:0,)\n",
      "  KDEProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "  FisherMatrixProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  GMMProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Setting convergence_inputs=ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Drawing 1000 samples\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Checkpoint every check_point_delta_t=1800s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:50 bilby INFO    : Print update every printdt=5s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : Reached convergence: exiting sampling\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : Checkpoint start\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : Written checkpoint file outdir/unknown_x_resume.pickle\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : Zero-temperature proposals:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : AdaptiveGaussianProposal(acceptance_ratio:0.23,n:2.8e+04,scale:0.013,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : DifferentialEvolutionProposal(acceptance_ratio:0.47,n:2.9e+04,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : UniformProposal(acceptance_ratio:1,n:1.5e+03,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : KDEProposal(acceptance_ratio:0.0012,n:2.7e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : FisherMatrixProposal(acceptance_ratio:0.52,n:2.7e+04,scale:1,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : GMMProposal(acceptance_ratio:0.00093,n:2.9e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : Current taus={'m': 1.0, 'c': 1}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : Creating diagnostic plots\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : Checkpoint finished\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : Sampling time: 0:00:15.016020\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "04:51 bilby INFO    : Summary of results:\n",
      "nsamples: 1315\n",
      "ln_noise_evidence:    nan\n",
      "ln_evidence:    nan +/-    nan\n",
      "ln_bayes_factor:    nan +/-    nan\n",
      "\n"
     ]
    }
   ],
   "source": [
    "gaussian_unknown_x = GaussianLikelihoodUncertainX(\n",
    "    xobs=data[\"xobs\"],\n",
    "    yobs=data[\"yobs\"],\n",
    "    xerr=data[\"xerr\"],\n",
    "    yerr=data[\"yerr\"],\n",
    "    function=model,\n",
    ")\n",
    "result_unknown_x = bilby.run_sampler(\n",
    "    likelihood=gaussian_unknown_x,\n",
    "    label=\"unknown_x\",\n",
    "    **sampler_kwargs,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-05T04:51:11.380169Z",
     "iopub.status.busy": "2024-04-05T04:51:11.379932Z",
     "iopub.status.idle": "2024-04-05T04:51:11.607240Z",
     "shell.execute_reply": "2024-04-05T04:51:11.606484Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 550x550 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = result_unknown_x.plot_corner(truth=dict(m=5, c=10), titles=True, save=False)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Success! The inferred posterior is consistent with the true values."
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}