{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ce71e8df",
   "metadata": {},
   "source": [
    "# Bayesian Methods for Credit Risk\n",
    "\n",
    "Companion notebook to [Data Science Module 7](https://rodoslay.com/data-science/07-bayesian-methods-for-risk) at **rodoslay.com**.\n",
    "\n",
    "The low-default toolkit with nothing beyond `numpy`/`scipy`: beta-binomial updating in the\n",
    "pseudo-loan parameterization, the **zero-default problem** with credible intervals (vs. the rule of\n",
    "three), prior-sensitivity analysis, and **empirical-Bayes shrinkage** across twenty segments — with\n",
    "the out-of-sample test that shows shrinkage winning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "843032dd",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-14T02:09:35.970524Z",
     "iopub.status.busy": "2026-07-14T02:09:35.970230Z",
     "iopub.status.idle": "2026-07-14T02:09:37.411541Z",
     "shell.execute_reply": "2026-07-14T02:09:37.410463Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "\n",
    "rng = np.random.default_rng(31)\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 4.5)\n",
    "plt.rcParams[\"axes.grid\"] = True\n",
    "plt.rcParams[\"grid.alpha\"] = 0.3\n",
    "\n",
    "def posterior(prior_mean, prior_strength, k, n):\n",
    "    \"\"\"Beta-binomial: prior as (mean, pseudo-loans); returns the posterior Beta distribution.\"\"\"\n",
    "    a0, b0 = prior_mean * prior_strength, (1 - prior_mean) * prior_strength\n",
    "    return stats.beta(a0 + k, b0 + n - k)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "625be979",
   "metadata": {},
   "source": [
    "## 1. The zero-default problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6cf5bd78",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-14T02:09:37.414655Z",
     "iopub.status.busy": "2026-07-14T02:09:37.414253Z",
     "iopub.status.idle": "2026-07-14T02:09:37.695868Z",
     "shell.execute_reply": "2026-07-14T02:09:37.694365Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MLE:                       0.000%   <- 'risk-free', on the evidence of not-yet\n",
      "posterior mean (informed): 0.375%\n",
      "90% credible interval:     0.044% – 0.975%\n",
      "flat-prior 95% upper:      0.990%\n",
      "rule of three (3/n):       1.000%   <- the classical emergency approximation\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n, k = 300, 0                                       # five years, three hundred loans, zero defaults\n",
    "prior_mean, prior_strength = 0.015, 100             # reference class: ~1.5% PD, worth 100 pseudo-loans\n",
    "\n",
    "post = posterior(prior_mean, prior_strength, k, n)\n",
    "flat = posterior(0.5, 2, k, n)                      # near-flat prior for comparison\n",
    "\n",
    "print(f\"MLE:                       {k/n:.3%}   <- 'risk-free', on the evidence of not-yet\")\n",
    "print(f\"posterior mean (informed): {post.mean():.3%}\")\n",
    "print(f\"90% credible interval:     {post.ppf(0.05):.3%} – {post.ppf(0.95):.3%}\")\n",
    "print(f\"flat-prior 95% upper:      {flat.ppf(0.95):.3%}\")\n",
    "print(f\"rule of three (3/n):       {3/n:.3%}   <- the classical emergency approximation\")\n",
    "\n",
    "x = np.linspace(0, 0.05, 500)\n",
    "plt.plot(x, posterior(prior_mean, prior_strength, 0, 0).pdf(x), \"--\", color=\"#5c5c5c\", label=\"prior\")\n",
    "plt.plot(x, post.pdf(x), color=\"#1f4d3a\", lw=2, label=\"posterior after 300 clean loans\")\n",
    "plt.axvline(0, color=\"#b3341e\", lw=1, label=\"MLE = 0\")\n",
    "plt.legend(); plt.xlabel(\"PD\"); plt.title(\"Zero defaults ≠ zero PD\"); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69ae6c63",
   "metadata": {},
   "source": [
    "## 2. How fast does evidence move belief?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fc17d19c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-14T02:09:37.698395Z",
     "iopub.status.busy": "2026-07-14T02:09:37.698154Z",
     "iopub.status.idle": "2026-07-14T02:09:37.717786Z",
     "shell.execute_reply": "2026-07-14T02:09:37.716526Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>clean loans observed</th>\n",
       "      <th>posterior mean</th>\n",
       "      <th>95% upper bound</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1.500%</td>\n",
       "      <td>3.880%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>100</td>\n",
       "      <td>0.750%</td>\n",
       "      <td>1.947%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>300</td>\n",
       "      <td>0.375%</td>\n",
       "      <td>0.975%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1000</td>\n",
       "      <td>0.136%</td>\n",
       "      <td>0.355%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3000</td>\n",
       "      <td>0.048%</td>\n",
       "      <td>0.126%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>10000</td>\n",
       "      <td>0.015%</td>\n",
       "      <td>0.039%</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   clean loans observed posterior mean 95% upper bound\n",
       "0                     0         1.500%          3.880%\n",
       "1                   100         0.750%          1.947%\n",
       "2                   300         0.375%          0.975%\n",
       "3                  1000         0.136%          0.355%\n",
       "4                  3000         0.048%          0.126%\n",
       "5                 10000         0.015%          0.039%"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ns = [0, 100, 300, 1000, 3000, 10000]\n",
    "rows = []\n",
    "for n_ in ns:\n",
    "    p_ = posterior(prior_mean, prior_strength, 0, n_)\n",
    "    rows.append([n_, f\"{p_.mean():.3%}\", f\"{p_.ppf(0.95):.3%}\"])\n",
    "pd.DataFrame(rows, columns=[\"clean loans observed\", \"posterior mean\", \"95% upper bound\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22b841bc",
   "metadata": {},
   "source": [
    "The upper bound decays roughly like 1/n — evidence buys certainty at a knowable rate, and the\n",
    "table is a defensible answer to \"how long until we can call this book low-risk?\"\n",
    "\n",
    "## 3. Prior sensitivity — the analysis a validator will demand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c312b3b2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-14T02:09:37.719961Z",
     "iopub.status.busy": "2026-07-14T02:09:37.719719Z",
     "iopub.status.idle": "2026-07-14T02:09:37.741849Z",
     "shell.execute_reply": "2026-07-14T02:09:37.740418Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data: 2 defaults in 400 loans (MLE 0.500%)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>prior</th>\n",
       "      <th>mean/strength</th>\n",
       "      <th>posterior mean</th>\n",
       "      <th>90% CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>flat (Jeffreys-ish)</td>\n",
       "      <td>50.00%/2</td>\n",
       "      <td>0.746%</td>\n",
       "      <td>0.204%–1.562%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>agency IG reference</td>\n",
       "      <td>0.50%/100</td>\n",
       "      <td>0.500%</td>\n",
       "      <td>0.115%–1.105%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>chosen prior</td>\n",
       "      <td>1.50%/100</td>\n",
       "      <td>0.700%</td>\n",
       "      <td>0.217%–1.403%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>chosen, 3x stronger</td>\n",
       "      <td>1.50%/300</td>\n",
       "      <td>0.929%</td>\n",
       "      <td>0.422%–1.593%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>pessimistic</td>\n",
       "      <td>4.00%/100</td>\n",
       "      <td>1.200%</td>\n",
       "      <td>0.525%–2.095%</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 prior mean/strength posterior mean         90% CI\n",
       "0  flat (Jeffreys-ish)      50.00%/2         0.746%  0.204%–1.562%\n",
       "1  agency IG reference     0.50%/100         0.500%  0.115%–1.105%\n",
       "2         chosen prior     1.50%/100         0.700%  0.217%–1.403%\n",
       "3  chosen, 3x stronger     1.50%/300         0.929%  0.422%–1.593%\n",
       "4          pessimistic     4.00%/100         1.200%  0.525%–2.095%"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k_obs, n_obs = 2, 400\n",
    "scenarios = [(\"flat (Jeffreys-ish)\", 0.5, 2), (\"agency IG reference\", 0.005, 100),\n",
    "             (\"chosen prior\", 0.015, 100), (\"chosen, 3x stronger\", 0.015, 300),\n",
    "             (\"pessimistic\", 0.04, 100)]\n",
    "rows = []\n",
    "for name, m, s in scenarios:\n",
    "    p_ = posterior(m, s, k_obs, n_obs)\n",
    "    rows.append([name, f\"{m:.2%}/{s}\", f\"{p_.mean():.3%}\", f\"{p_.ppf(0.05):.3%}–{p_.ppf(0.95):.3%}\"])\n",
    "print(f\"data: {k_obs} defaults in {n_obs} loans (MLE {k_obs/n_obs:.3%})\")\n",
    "pd.DataFrame(rows, columns=[\"prior\", \"mean/strength\", \"posterior mean\", \"90% CI\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a6730f6",
   "metadata": {},
   "source": [
    "If the decision downstream (a PD floor, a price) flips between these rows, the prior is making\n",
    "the decision — say so out loud. Here the posterior means cluster: the data is already doing most of\n",
    "the talking at n = 400 with 2 events.\n",
    "\n",
    "## 4. Empirical-Bayes shrinkage across twenty segments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a88e65bc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-14T02:09:37.744135Z",
     "iopub.status.busy": "2026-07-14T02:09:37.743887Z",
     "iopub.status.idle": "2026-07-14T02:09:37.953760Z",
     "shell.execute_reply": "2026-07-14T02:09:37.952438Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fitted portfolio prior: mean 1.49%, strength ~361 pseudo-loans (truth: 1.96%, 153)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# truth: segment PDs drawn from a Beta hierarchy; small books observe noisy default counts\n",
    "TRUE_A, TRUE_B = 3, 150                              # true portfolio-level distribution (mean 2%)\n",
    "n_seg = 20\n",
    "true_pd = rng.beta(TRUE_A, TRUE_B, n_seg)\n",
    "n_loans = rng.integers(30, 800, n_seg)\n",
    "k_year1 = rng.binomial(n_loans, true_pd)\n",
    "\n",
    "# fit the prior FROM the cross-section (method of moments on observed rates)\n",
    "rates = k_year1 / n_loans\n",
    "m_hat = rates.mean()\n",
    "v_hat = rates.var(ddof=1) - m_hat * (1 - m_hat) * np.mean(1 / n_loans)   # subtract binomial noise\n",
    "v_hat = max(v_hat, 1e-7)\n",
    "s_hat = np.clip(m_hat * (1 - m_hat) / v_hat - 1, 20, 2000)   # implied prior strength\n",
    "print(f\"fitted portfolio prior: mean {m_hat:.2%}, strength ~{s_hat:.0f} pseudo-loans \"\n",
    "      f\"(truth: {TRUE_A/(TRUE_A+TRUE_B):.2%}, {TRUE_A+TRUE_B})\")\n",
    "\n",
    "shrunk = (s_hat * m_hat + k_year1) / (s_hat + n_loans)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9, 5))\n",
    "for i in range(n_seg):\n",
    "    ax.plot([0, 1], [rates[i], shrunk[i]], color=\"#5c5c5c\", lw=0.7)\n",
    "ax.scatter(np.zeros(n_seg), rates, s=n_loans / 8, color=\"#b3541e\", label=\"raw MLE (size = book)\")\n",
    "ax.scatter(np.ones(n_seg), shrunk, s=n_loans / 8, color=\"#1f4d3a\", label=\"shrunk\")\n",
    "ax.scatter(np.full(n_seg, 1.03), true_pd, marker=\"x\", color=\"k\", label=\"truth\")\n",
    "ax.set_xticks([0, 1]); ax.set_xticklabels([\"MLE\", \"shrunk\"]); ax.legend()\n",
    "ax.set_title(\"Small segments travel far; big ones barely move\"); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6d9254ef",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-14T02:09:37.956677Z",
     "iopub.status.busy": "2026-07-14T02:09:37.956369Z",
     "iopub.status.idle": "2026-07-14T02:09:37.973777Z",
     "shell.execute_reply": "2026-07-14T02:09:37.972932Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE vs (unobservable) truth — MLE: 7.81e-05   shrunk: 4.61e-05   (1.7x better)\n",
      "MSE vs future years (avg of 200) — MLE: 1.41e-04   shrunk: 1.09e-04\n",
      "shrinkage beats MLE in 86% of simulated future years\n"
     ]
    }
   ],
   "source": [
    "# the out-of-sample test: which estimate predicts FUTURE years better?\n",
    "# one future year is a coin flip's worth of evidence for 20 segments — so simulate 200 of them.\n",
    "mse_mle = np.mean((rates - true_pd) ** 2)\n",
    "mse_shrunk = np.mean((shrunk - true_pd) ** 2)\n",
    "print(f\"MSE vs (unobservable) truth — MLE: {mse_mle:.2e}   shrunk: {mse_shrunk:.2e}   \"\n",
    "      f\"({mse_mle/mse_shrunk:.1f}x better)\")\n",
    "\n",
    "wins, pred_mle_all, pred_shrunk_all = 0, [], []\n",
    "for _ in range(200):\n",
    "    rate_future = rng.binomial(n_loans, true_pd) / n_loans\n",
    "    pm = np.mean((rates - rate_future) ** 2)\n",
    "    ps = np.mean((shrunk - rate_future) ** 2)\n",
    "    pred_mle_all.append(pm); pred_shrunk_all.append(ps)\n",
    "    wins += ps < pm\n",
    "print(f\"MSE vs future years (avg of 200) — MLE: {np.mean(pred_mle_all):.2e}   \"\n",
    "      f\"shrunk: {np.mean(pred_shrunk_all):.2e}\")\n",
    "print(f\"shrinkage beats MLE in {wins/200:.0%} of simulated future years\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b5ca707",
   "metadata": {},
   "source": [
    "Shrinkage wins against the unobservable truth and, on average, against future realized rates —\n",
    "though note the honest wrinkle the simulation forces on you: **in any single future year the\n",
    "binomial noise is large enough that raw MLE occasionally 'wins' by luck**. That's exactly why the\n",
    "comparison needs many replications, and why one good year proves nothing about an estimator.\n",
    "This is Stein's paradox doing honest work in a credit portfolio.\n",
    "\n",
    "## Exercises\n",
    "\n",
    "1. **Conservatism buffer.** Price a PD add-on as the gap between the posterior 90th percentile and\n",
    "   the mean, per segment. Which segments pay the biggest uncertainty premium, and is that fair?\n",
    "2. **Sequential updating.** Feed the zero-default portfolio's loans in month by month, plotting the\n",
    "   95% upper bound as it walks down. When would you have approved a limit increase?\n",
    "3. **Prior from transitions.** Build the prior for a BBB-rated segment from the transition-matrix\n",
    "   workbook of [credit Module 6](https://rodoslay.com/credit-models/06-ratings-and-transition-matrices)\n",
    "   instead of guessing. How strong (in pseudo-loans) should a rating-based prior be?\n",
    "4. **Break the hierarchy.** Make two segments genuinely different (true PD 10x the rest) and rerun.\n",
    "   Does shrinkage hide them? How would you detect exchangeability failing?"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
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    "name": "ipython",
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