{
 "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": "2024-12-07T00:37:01.894999Z",
     "iopub.status.busy": "2024-12-07T00:37:01.894213Z",
     "iopub.status.idle": "2024-12-07T00:37:03.174529Z",
     "shell.execute_reply": "2024-12-07T00:37:03.173284Z"
    }
   },
   "outputs": [],
   "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": "2024-12-07T00:37:03.179302Z",
     "iopub.status.busy": "2024-12-07T00:37:03.178996Z",
     "iopub.status.idle": "2024-12-07T00:37:03.280732Z",
     "shell.execute_reply": "2024-12-07T00:37:03.280112Z"
    }
   },
   "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": "2024-12-07T00:37:03.286446Z",
     "iopub.status.busy": "2024-12-07T00:37:03.286241Z",
     "iopub.status.idle": "2024-12-07T00:37:03.290539Z",
     "shell.execute_reply": "2024-12-07T00:37:03.289936Z"
    }
   },
   "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": "2024-12-07T00:37:03.293617Z",
     "iopub.status.busy": "2024-12-07T00:37:03.293415Z",
     "iopub.status.idle": "2024-12-07T00:37:27.374714Z",
     "shell.execute_reply": "2024-12-07T00:37:27.374021Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Running for label 'known_x', output will be saved to 'outdir'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Analysis priors:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : m=Uniform(minimum=0, maximum=30, name='m', latex_label='m', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : c=Uniform(minimum=0, maximum=30, name='c', latex_label='c', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Analysis likelihood class: <class 'bilby.core.likelihood.GaussianLikelihood'>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Analysis likelihood noise evidence: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Single likelihood evaluation took 6.259e-05 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 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": [
      "00:37 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": [
      "00:37 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": [
      "00:37 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": [
      "00:37 bilby INFO    : Using initial sample {'m': 7.676503755227243, 'c': 22.911250747927127}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 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": [
      "00:37 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": [
      "00:37 bilby INFO    : Drawing 1000 samples\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Checkpoint every check_point_delta_t=1800s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Print update every printdt=5s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Reached convergence: exiting sampling\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Checkpoint start\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Written checkpoint file outdir/known_x_resume.pickle\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Zero-temperature proposals:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : AdaptiveGaussianProposal(acceptance_ratio:0.23,n:3e+04,scale:0.0038,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : DifferentialEvolutionProposal(acceptance_ratio:0.47,n:2.4e+04,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : UniformProposal(acceptance_ratio:1,n:1.3e+03,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : KDEProposal(acceptance_ratio:0.00021,n:2.8e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : FisherMatrixProposal(acceptance_ratio:0.55,n:2.9e+04,scale:1,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : GMMProposal(acceptance_ratio:0.0001,n:3e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Current taus={'m': 1.2, 'c': 1.3}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Creating diagnostic plots\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Checkpoint finished\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Sampling time: 0:00:15.017687\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Summary of results:\n",
      "nsamples: 1326\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": "2024-12-07T00:37:27.379116Z",
     "iopub.status.busy": "2024-12-07T00:37:27.378758Z",
     "iopub.status.idle": "2024-12-07T00:37:28.436216Z",
     "shell.execute_reply": "2024-12-07T00:37:28.435526Z"
    }
   },
   "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": "2024-12-07T00:37:28.442741Z",
     "iopub.status.busy": "2024-12-07T00:37:28.442353Z",
     "iopub.status.idle": "2024-12-07T00:37:51.729582Z",
     "shell.execute_reply": "2024-12-07T00:37:51.728889Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Running for label 'incorrect_x', output will be saved to 'outdir'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Analysis priors:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : m=Uniform(minimum=0, maximum=30, name='m', latex_label='m', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : c=Uniform(minimum=0, maximum=30, name='c', latex_label='c', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Analysis likelihood class: <class 'bilby.core.likelihood.GaussianLikelihood'>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Analysis likelihood noise evidence: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Single likelihood evaluation took 8.029e-05 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 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": [
      "00:37 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": [
      "00:37 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": [
      "00:37 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": [
      "00:37 bilby INFO    : Using initial sample {'m': 4.357196094079371, 'c': 6.787234268232631}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 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": [
      "00:37 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": [
      "00:37 bilby INFO    : Drawing 1000 samples\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Checkpoint every check_point_delta_t=1800s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Print update every printdt=5s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Reached convergence: exiting sampling\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Checkpoint start\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Written checkpoint file outdir/incorrect_x_resume.pickle\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Zero-temperature proposals:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : AdaptiveGaussianProposal(acceptance_ratio:0.23,n:3e+04,scale:0.0023,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : DifferentialEvolutionProposal(acceptance_ratio:0.47,n:2.8e+04,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : UniformProposal(acceptance_ratio:1,n:2e+03,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : KDEProposal(acceptance_ratio:7.3e-05,n:2.8e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : FisherMatrixProposal(acceptance_ratio:0.56,n:2.6e+04,scale:1,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : GMMProposal(acceptance_ratio:0.0001,n:2.9e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Current taus={'m': 1, 'c': 1}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Creating diagnostic plots\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Checkpoint finished\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Sampling time: 0:00:15.019086\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Summary of results:\n",
      "nsamples: 1222\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": "2024-12-07T00:37:51.733870Z",
     "iopub.status.busy": "2024-12-07T00:37:51.733649Z",
     "iopub.status.idle": "2024-12-07T00:37:51.929213Z",
     "shell.execute_reply": "2024-12-07T00:37:51.928568Z"
    }
   },
   "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": "2024-12-07T00:37:51.935574Z",
     "iopub.status.busy": "2024-12-07T00:37:51.935366Z",
     "iopub.status.idle": "2024-12-07T00:37:51.941412Z",
     "shell.execute_reply": "2024-12-07T00:37:51.940771Z"
    }
   },
   "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": "2024-12-07T00:37:51.944439Z",
     "iopub.status.busy": "2024-12-07T00:37:51.944252Z",
     "iopub.status.idle": "2024-12-07T00:38:14.921320Z",
     "shell.execute_reply": "2024-12-07T00:38:14.920586Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Running for label 'unknown_x', output will be saved to 'outdir'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Analysis priors:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : m=Uniform(minimum=0, maximum=30, name='m', latex_label='m', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : c=Uniform(minimum=0, maximum=30, name='c', latex_label='c', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Analysis likelihood class: <class '__main__.GaussianLikelihoodUncertainX'>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Analysis likelihood noise evidence: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Single likelihood evaluation took 9.341e-05 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 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": [
      "00:37 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": [
      "00:37 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": [
      "00:37 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": [
      "00:37 bilby INFO    : Using initial sample {'m': 22.70643226103247, 'c': 24.940223186232846}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 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": [
      "00:37 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": [
      "00:37 bilby INFO    : Drawing 1000 samples\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Checkpoint every check_point_delta_t=1800s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:37 bilby INFO    : Print update every printdt=5s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : Reached convergence: exiting sampling\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : Checkpoint start\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : Written checkpoint file outdir/unknown_x_resume.pickle\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : Zero-temperature proposals:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : AdaptiveGaussianProposal(acceptance_ratio:0.23,n:2.6e+04,scale:0.015,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : DifferentialEvolutionProposal(acceptance_ratio:0.46,n:2.9e+04,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : UniformProposal(acceptance_ratio:1,n:1.1e+03,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : KDEProposal(acceptance_ratio:0.00078,n:2.7e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : FisherMatrixProposal(acceptance_ratio:0.52,n:3.2e+04,scale:1,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : GMMProposal(acceptance_ratio:0.00084,n:2.7e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : Current taus={'m': 1.0, 'c': 1.2}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : Creating diagnostic plots\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : Checkpoint finished\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : Sampling time: 0:00:15.015231\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "00:38 bilby INFO    : Summary of results:\n",
      "nsamples: 1322\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": "2024-12-07T00:38:14.925647Z",
     "iopub.status.busy": "2024-12-07T00:38:14.925416Z",
     "iopub.status.idle": "2024-12-07T00:38:15.129605Z",
     "shell.execute_reply": "2024-12-07T00:38:15.128864Z"
    }
   },
   "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": "3.11.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}