20-Quote e addizioni.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "011d3dfa",
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils import set_pyplot_params\n",
    "set_pyplot_params()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82d34757",
   "metadata": {},
   "source": [
    "# Quote e addizioni\n",
    "\n",
    "Questo capitolo prensenta un nuovo modo di rappresentare un grado di incertezza, quote e una nuova forma del teorema di Bayes chiamata regola di bayes. La regola di bayes è conveniente se vuoi l'aggiornamento di bayes sulla carta a mano. \n",
    "\n",
    "La seconda parte di questo capitolo è relativa agli \"addendi\", quantità aggiunte, e come calcolare le loro distribuzioni.\n",
    "Costruiremo funzioni che calcolano la distribuzione delle somme, differenze, prodotti e altre operazioni. \n",
    "Poi useremo queste distribuzioni come parte dell'aggiornamento Bayesiano.\n",
    "\n",
    "## Quote\n",
    "Un modo per rapprestare una probabilità è con un numero tra 0 e 1, ma questa non è il solo modo.\n",
    "Se hai mai scommesso su una partita di calcio o ad una corsa ai cavalli avrai probabilmente incontrato un'altra rappresentazione di probabilità chiamata **quote**. \n",
    "\n",
    "Avrai certamente sentito l'espressione tièp \"le quote sono tree a uno\", ma potresti non sapere cosa significhi.\n",
    "Le **quote a favore** di un evento sono il rapporto di una probabilità, che occorre con la probabilità positive e negative.\n",
    "\n",
    "Qui la funzione per effettuare il calcolo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "429d8847",
   "metadata": {},
   "outputs": [],
   "source": [
    "def odds(p):\n",
    "    return p / (1-p)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe59016d",
   "metadata": {},
   "source": [
    "Per esempio, se la mia squadra ha il 75% di probabilità di vincere, le quote in favore saranno tre a uno, perchè le possibilità di vincere sono tre volte superiori alle possibilità di perdere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0f143462",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "odds(0.75)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf54332c",
   "metadata": {},
   "source": [
    "Possiamo scrivere le quote in forme decimale ma è anche comune scriverle come un rapporto tra interi.\n",
    "Dunque \"tre a uno\" è spesso scritto come $3:1$\n",
    "\n",
    "Quando le probabilità sono basse è più facile scrivere questo come **quote a sfavore** piuttosto che come quote a favore.\n",
    "Per esempio se il mio cavallo ha il 10% di possibilità di vittoria la quota a favore è $1:9$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fecab9cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11111111111111112"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "odds(0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19f28232",
   "metadata": {},
   "source": [
    "Ma nel caso sarebbe più facile usare le quote a sfavore che sono $9:1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "467e0d7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.000000000000002"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "odds(0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bde1341",
   "metadata": {},
   "source": [
    "Date le quote a favore, nella forma decimale possiamo convertila in probabilità come:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bd89b150",
   "metadata": {},
   "outputs": [],
   "source": [
    "def prob(o):\n",
    "    return o / (o+1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5fca6a9",
   "metadata": {},
   "source": [
    "Se per esempio abbiamo una quota pari a $3:2$ la corrispondente probabilità sarà:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bc7bb9bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob(3/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f7f51d6",
   "metadata": {},
   "source": [
    "Oppure se presentiamo le quote con un numeratore e denominatore, possiamo convertire le probabilità in questo modo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "536589f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def prob2(yes, no):\n",
    "    return yes / (yes + no)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "33dccf03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.75"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob2(3, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "600c7398",
   "metadata": {},
   "source": [
    "Probabilità e quote sono rappresentazioni differenti della stessa informazione; data una rappresentazione possiamo calcolare l'altra.\n",
    "\n",
    "Ma alcuni calcoli sono semplici quando lavoriamo con le quote, come vedremo nella prossima sezione e alcuni calcoli sono ancora più semplici con le quote logaritmiche, come vedremo in seguito.\n",
    "\n",
    "## Regola di Bayes\n",
    "\n",
    "Abbiamo lavorato con il teorema di bayes nella forma probabilistica:\n",
    "\n",
    "$$P(H|D) = \\frac{P(H)~P(D|H)}{P(D)}$$\n",
    "\n",
    "Scrivendo $\\mathrm{odds}(A)$ per le quote in favore di $A$, possiamo esprimere il teorema di bayes nella forma delle quote:\n",
    "\n",
    "$$\\mathrm{odds}(A|D) = \\mathrm{odds}(A)~\\frac{P(D|A)}{P(D|B)}$$\n",
    "\n",
    "Questa è la regola di Bayes, che ci dice che la quota a posteriori è la quota a priori moltiplicato per il rapporto della verosomiglianza.\n",
    "\n",
    "La regola di Bayes è conveniente per calcolare l'aggiornamento Bayesiano su carta o a mente. Per esempio torniamo sul problema dei biscotti:\n",
    "\n",
    "> Supponiamo di avere due ciotole di biscotti. La ciotola 1 contiene 30 biscotti alla vaniglia e 10 al cioccoloato. La ciotola 2 contiene 20 di ciascuno. Supponiamo di scegliere una ciotola a caso e senza guardare di prendere un biscotto.\n",
    "Il biscotto è alla vaniglia. Qual è la probabilità che venga dalla ciotola 1?\n",
    "\n",
    "La probabilità a priori è del 50%, dunque la quota a priori è 1. Il rapporto della verosomiglianza è \n",
    "\n",
    "$$\\frac{3}{4} / \\frac{1}{2}$$\n",
    "\n",
    "\n",
    "Dunque le quote a posteriori darà come risultato $3/2$ che corrisponde alla probabilità di $3/5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "337f2425",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prior_odds = 1\n",
    "likelihood_ratio = (3/4) / (1/2)\n",
    "post_odds = prior_odds * likelihood_ratio\n",
    "post_odds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "14f1a4d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_prob = prob(post_odds)\n",
    "post_prob"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "531fa47d",
   "metadata": {},
   "source": [
    "Se estraiamo un altro biscotto e otteniamo cioccolata possiamo eseguire l'aggiornamento:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "769ece9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.75"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihood_ratio = (1/4) / (1/2)\n",
    "post_odds *= likelihood_ratio\n",
    "post_odds"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9eac6a0c",
   "metadata": {},
   "source": [
    "e lo convertiamo in probabilità otteniamo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f7ecfc82",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.42857142857142855"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_prob = prob(post_odds)\n",
    "post_prob"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e63560e1",
   "metadata": {},
   "source": [
    "## Il sangue di Oliver\n",
    "\n",
    "Useremo la regola di bayes per risolvere un'altro problema proposto da MacKay nel libro [*Information Theory, Inference, and Learning Algorithms*](https://www.inference.org.uk/mackay/itila/):\n",
    "\n",
    ">Due persone hanno lasciato tracce del loro sangue sulla scena di un crimine. Un sospettato Oliver viene fermato e si verifica che il suo gruppo sanguinio è '0'. I due gruppi sanguinei trovati nelle tracce sono di tipo '0' (un tipo comune nella popolazione locale, che ha una frequenza del 60%) e un tipo 'AB' (un raro tipo con la frequenza dell 1%). Questi dati \\[le tracce trovate sulla scena\\] danno l'evidenza in favore  della proposta che Oliver fosse una delle persone \\[che hanno lasciato il sangue sulla scena\\]?\n",
    "\n",
    "\n",
    "Per rispondere alla questione, dobbiamo pensare circa il significato dei dati di dare evidenza in favore o contro l'ipotesi.\n",
    "Intuitivamente, possiamo dire che il dato è a favore delle ipotesi se le ipotesi sono più probabili alla luce dei dati rispetto a prima. \n",
    "\n",
    "Nel problema dei biscotti visto prima, le quote a priori sono 1. che corrisponde ad una probabilità del 50%. Le quote a posteriori sono $3/2$, o la probabilità è del 60%. Dunque il biscotto alla vaniglia è una evidenza in favore alla ciotola 1.\n",
    "\n",
    "La regola di Bayes ci da una vita per rendere questa intuizione più precisi. Ancora \n",
    "$$\\mathrm{odds}(A|D) = \\mathrm{odds}(A)~\\frac{P(D|A)}{P(D|B)}$$\n",
    "\n",
    "Dividere per $\\mathrm{odds}(A)$ otteniamo:\n",
    "$$\\frac{\\mathrm{odds}(A|D)}{\\mathrm{odds}(A)} = \\frac{P(D|A)}{P(D|B)}$$\n",
    "\n",
    "Il termine sulla sinistra è il rapporto tra le quote a posteriori e priori. Il termine sulla destra è il rapporto tra le verosomiglianze anche chiamato **Fattore di Bayes**.\n",
    "\n",
    "Se il fattore di Bayes è minore di 1 significa che il dato è meno probabile sotto $A$ piuttosto che sotto $B$, dunque le quote in favore di $A$ scendono.\n",
    "\n",
    "\n",
    "Finalmente, se il fattore di Bayes è esattamente 1 il dato è egualmente probabile sotto ogni ipotesi, dunque la quota non cambia.\n",
    "\n",
    "Applichiamolo al problema appena visto. Se Oliver è una delle persone che ha lasciato il sangue sulla scena del crimine, rappresenta il campione '0', in questo caso la probabilità del dato è la probabilità che un membro della popolazione scelto a caso abbia il tipo ‘AB’ che rappresenta l'1%.\n",
    "\n",
    "Se Oliver non ha lasciato il sangue sulla scena abbiamo due campioni di cui tener conto.\n",
    "\n",
    "Se scegliamo due persone a caso dalla popolazione, qual'è la probabilità di trovarne uan con il tipo '0' e una con il tipo 'AB'?\n",
    "\n",
    "Bene ci sono sue cose che possono accadere:\n",
    "\n",
    "* La prima persona può avere il gruppo '0' e il secondo 'AB',\n",
    "* Oppure la prima persona può avere il gruppo 'AB' e il secondo '0'.\n",
    "\n",
    "La probabilità di entrambe le combinazioni sono $(0.6) (0.01)$, che rappresenta il 0.6%, perciò la probabilità è doppia 1.2%.\n",
    "Quindi i dati sono un pò più probabilit se Oliver *non* è una delle persone che hanno lasciato il sangue sulla scena.\n",
    "\n",
    "Possiamo usare queste probabilità per calcolare il rapporto delle verosomiglianze:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a309b572",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8333333333333334"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "like1 = 0.01\n",
    "like2 = 2 * 0.6 * 0.01\n",
    "\n",
    "likelihood_ratio = like1 / like2\n",
    "likelihood_ratio"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93a28185",
   "metadata": {},
   "source": [
    "Visto che il rapporto delle verosomiglianze è minore di 1, il test del sangue contro le ipotesi contro le opitesi che Oliver abbia lasciato traccie del suo sangue sulla scena.\n",
    "\n",
    "Ma questa è una evidenza debole. Per esempio se il rapporto a priori era 1 (che rappresenta il 50% della probabilità) la probabilità a posteriori sarà 0.83 che corrisponde al 45%:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4a2cf6cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.45454545454545453"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_odds = 1 * likelihood_ratio\n",
    "prob(post_odds)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92e14c2b",
   "metadata": {},
   "source": [
    "Dunque questa evidenza non muove la bilancia dalla nostra parte.\n",
    "\n",
    "Questo esempio è un pochino forzato, ma ci dimostra che il risultato controintuitivo del dato *consistente* con ipotesi che non sono a *favore* delle ipotesi.\n",
    "\n",
    "Se questo risultato non ti soddisfa, questo modo di pensare potrebbe aiutarti:\n",
    "\n",
    "Il dato consiste in un evento comune gruppo '0' e un raro evento gruppo 'AB'.\n",
    "Se Oliver spiega l'evento comune , questo lascia l'evento raro non spiegato.\n",
    "\n",
    "Se Oliver non spiega il gruppo '0', abbiamo due possibilità di trovare nella popolazione il gruppo 'AB'.\n",
    "E' quel fattore due a fare la differenza.\n",
    "\n",
    "**Esercizio:** Supponiamo che basandosi sulla nostra evidenza, la nostra credenza a priori che Oliver sia colpevole è del 90%.\n",
    "Quanto la nostra evidenza relativa al gruppo sanguineo può cambiare le nostre credenze? Ese inizialmente pensassi che c'è solo il 10% di possibilità che sia colpevole?."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5a3570cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8823529411764706"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_odds = odds(0.9) * likelihood_ratio\n",
    "prob(post_odds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "73dbde23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08474576271186442"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_odds = odds(0.1) * likelihood_ratio\n",
    "prob(post_odds)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb0a5a4e",
   "metadata": {},
   "source": [
    "# Addizioni\n",
    "\n",
    "La seconda metà di questo capitolo è relativa alle distribuzioni di somme e i risultati di altre operazioni.\n",
    "Partiremo con un problema in cui dati gli input calcoleremo la distribuzione del risultato.\n",
    "Passeremo poi al problema inversom dato l'output calcoleremo la distribuzione degli input.\n",
    "\n",
    "Come primo esempio, supponiamo di lanciare due dadi e di sommare il risultato. Quale sarà la distribuzione della somma?\n",
    "Usiamo la seguente funzione per creare un `Pmf` che rappresenti i possibili risultati dei dadi:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f3dbd02b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from distribution import Pmf\n",
    "\n",
    "def make_die(sides):\n",
    "    outcomes = np.arange(1, sides+1)\n",
    "    die = Pmf(1/sides, outcomes)\n",
    "    return die"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3afea3d",
   "metadata": {},
   "source": [
    "In un dado a sei facce i risultati possono avere un valore tra 1 e 6 tutti con la stessa probabilità."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "cb9fffd4",
   "metadata": {},
   "outputs": [],
   "source": [
    "die = make_die(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "af167d1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from utils import decorate\n",
    "\n",
    "die.bar(alpha=0.4)\n",
    "decorate(xlabel='Outcome',\n",
    "         ylabel='PMF')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49cce77e",
   "metadata": {},
   "source": [
    "Se lanciamo due volte il dado e sommiamo il risultato otterremo 11 risultati possibili che vanno dal 2 al 12 ma non tutti con la stessa probabilità.\n",
    "\n",
    "Per calcolare la distribuzione della somma dobbiamo enumerare tutti i possibili risultati.\n",
    "Ed è quello che fa la seguente funzione:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "cd7ed27c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_dist(pmf1, pmf2):\n",
    "    \"\"\"Compute the distribution of a sum.\"\"\"\n",
    "    res = Pmf()\n",
    "    for q1, p1 in pmf1.items():\n",
    "        for q2, p2 in pmf2.items():\n",
    "            q = q1 + q2\n",
    "            p = p1 * p2\n",
    "            res[q] = res(q) + p\n",
    "    return res"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b97dddd",
   "metadata": {},
   "source": [
    "la parte più interessante della funzione è il pezzo di codice:\n",
    "\n",
    "```\n",
    "            res[q] = res(q) + p\n",
    "```\n",
    "\n",
    "`res(q)` restituisce 0 se l'elemento `q` non esiste nella distribuzione, `res[q]` poi viene usato nella parte a sinistra per aggiornare la distribuzione.\n",
    "\n",
    "L'oggetto `Pmf` ha anche la funzione `add_dist` che fa esattamente la stessa cosa possiamo usarla in questo modo:\n",
    "\n",
    "\n",
    "```\n",
    "            twice = die.add_dist(die)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3399824c",
   "metadata": {},
   "source": [
    "vediamo invece il risultato della somma dei due dadi:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "dfe1d9b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils import decorate\n",
    "\n",
    "def decorate_dice(title=''):\n",
    "    decorate(xlabel='Outcome',\n",
    "             ylabel='PMF',\n",
    "             title=title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c9593e57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "twice = add_dist(die, die)\n",
    "twice.bar(color='C1', alpha=0.5)\n",
    "decorate_dice()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "931fe329",
   "metadata": {},
   "source": [
    "Se hai una sequenza di `Pmf` che rappresentano un dado possiamo calcolare la somma della distristribuzione in questo modo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "fb8cf1da",
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_dist_seq(seq):\n",
    "    \"\"\"Compute Pmf of the sum of values from seq.\"\"\"\n",
    "    total = seq[0]\n",
    "    for other in seq[1:]:\n",
    "        total = total.add_dist(other)\n",
    "    return total"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b70498cc",
   "metadata": {},
   "source": [
    "ad esempio se i dadi sono 3 possiamo calcola la distribuzione della somma come:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "58d80e69",
   "metadata": {},
   "outputs": [],
   "source": [
    "dice = [die] * 3\n",
    "thrice = add_dist_seq(dice)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "21df8efb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "die.plot(label='once')\n",
    "twice.plot(label='twice', style='--')\n",
    "thrice.plot(label='thrice', style=':')\n",
    "\n",
    "plt.xticks([0,3,6,9,12,15,18])\n",
    "decorate_dice(title='Distributions of sums')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c41616ba",
   "metadata": {},
   "source": [
    "Come precisazione, questo dimostra anche il teorema del limite centrale, che dice che sotto alcune condizioni la somma delle destribuzioni converge verso una distribuzione normale. \n",
    "\n",
    "## Sensibilità al glutine\n",
    "\n",
    "Nel 2015 è uscito uno studio dove si testava se le persone a cui veniva diagnosticata una sensibilità al glutine (ma non una celiachia) fossero capaci di distinguere la farina con il glutine da quella senza glutine in un test cieco ([qui lo studio](https://onlinelibrary.wiley.com/doi/full/10.1111/apt.13372)).\n",
    "\n",
    "Su 35 soggetti, 12 hanno identificato correttamente la farina con il glutine basandosi sui sintomi mentre la stavano mangiando.\n",
    "Gli altri 17 hanno sbagliato l'identificazione basandosi sui loro sintomi e 6 non furono in grado di distunguerle.\n",
    "\n",
    "Gli autori conclusero: \"Il test in doppio cieco induce i sintomi ricorrenti solo in un terzo dei pazienti\".\n",
    "\n",
    "Questa conclusione sembra strana, perchè se nessuno dei pazienti era sensibile al glutine ci aspetteremmo che qualcuno di essi identifichi la farina con il glutine correttamente per caso.\n",
    "\n",
    "E qui parte la domanda: basandosi su questo dato, quanti soggetti sono sensibili al glutine e quanti hanno solo indovinato?\n",
    "\n",
    "Possiamo usare il teorema di Bayes per rispondere a questa domanda, ma prima dobbiamo fare alcuno decisioni di modellazione.\n",
    "Assumeremo che:\n",
    "\n",
    "* Le persone che sono sensibili al glutine hanno il 95% di possibilità di identificare correttamente la farina con il glutine sotto le condizioni del test e\n",
    "\n",
    "* Le persone che non sono sensibili al glutine hanno il 40% di possibilità di identificare la farina con il glutine per caso ( e il 60% di possibilità di scegliere l'altra farina e di fallire).\n",
    "\n",
    "Questi valori sono arbitrari, ma i risultati non sono sensibili a questa scelta.\n",
    "\n",
    "Risolveremo questo problema in due passi, Primo assumendo di conoscere quanti soggetti sono sensibili, calcoleremo la distribuzione del dato.\n",
    "\n",
    "Poi usando la verosomiglianza del dato, calcoleremo la distribuzione a posteriori del numero dei pazienti sensibili.\n",
    "\n",
    "Il primo è il problema in **avanti**, il secondo è il **problema inverso**.\n",
    "\n",
    "## Problema in avanti\n",
    "\n",
    "Supponiamo di conoscere che 10 delle 35 persone sono sensibili al glutine. Questo significa che 25 non lo sono:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "3b1bfd5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 35\n",
    "num_sensitive = 10\n",
    "num_insensitive = n - num_sensitive"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f21c8347",
   "metadata": {},
   "source": [
    "Ogni soggetto sensibile ha il 95% di possibilità di identificare la farina con il glutine, dunque il numero di classificazioni corrette segue la distrbuzione binomiale.\n",
    "\n",
    "Usiamo la funzione `make_binomial` per creare un oggetto `Pmf` corretto."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "a15ed948",
   "metadata": {},
   "outputs": [],
   "source": [
    "from distribution import make_binomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "f73a3d0a",
   "metadata": {},
   "outputs": [],
   "source": [
    "dist_sensitive = make_binomial(num_sensitive, 0.95)\n",
    "dist_insensitive = make_binomial(num_insensitive, 0.40)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e02218ad",
   "metadata": {},
   "source": [
    "I risultati sono le distribuzioni del numero delle corrette identificazioni in ogni gruppo.\n",
    "Ora possiamo usare `add_dist` per calcolare la distribuzione del numero totale delle identificazioni corrette:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "355b056d",
   "metadata": {},
   "outputs": [],
   "source": [
    "dist_total = Pmf.add_dist(dist_sensitive, dist_insensitive)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb89b3a6",
   "metadata": {},
   "source": [
    "Qui i risultati"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "0c96d2f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dist_sensitive.plot(label='sensitive', style=':')\n",
    "dist_insensitive.plot(label='insensitive', style='--')\n",
    "dist_total.plot(label='total')\n",
    "\n",
    "decorate(xlabel='Number of correct identifications',\n",
    "         ylabel='PMF',\n",
    "         title='Gluten sensitivity')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b9fce39",
   "metadata": {},
   "source": [
    "Ci aspettiamo che molte delle persone sensibili al glutine identifichino correttamente la farina con il glutine.\n",
    "Su 25 soggetti non sensibili, ci aspettiamo che 10 riescano ad identificare la farina con il glutine per caso.\n",
    "Dunque ci aspettiamo 20 identificazioni corrette nel totale.\n",
    "\n",
    "Questa è la risposta del problema in avanti: dato il numero delle persone sensibili al glutine possiamo calcolare la distribuzione del dato.\n",
    "\n",
    "## Il problema inverso\n",
    "\n",
    "Risolviamo ora il problema inverso: dato il dato, calcoliamo la distribuzione a posteriori del numero delle persone sensibili al glutine.\n",
    "\n",
    "Ecco qui come. Analizzeremo i possibili valori di `num_sensitive` e calcoleremo la distribuzione del dato per ognuno di essi:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "5f695a06",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "table = pd.DataFrame()\n",
    "for num_sensitive in range(0, n+1):\n",
    "    num_insensitive = n - num_sensitive\n",
    "    dist_sensitive = make_binomial(num_sensitive, 0.95)\n",
    "    dist_insensitive = make_binomial(num_insensitive, 0.4)\n",
    "    dist_total = Pmf.add_dist(dist_sensitive, dist_insensitive)    \n",
    "    table[num_sensitive] = dist_total"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb9296d0",
   "metadata": {},
   "source": [
    "Il ciclo enumera i possibili valori di `num_sensitive`.\n",
    "Per ogni valore, calcoliamo la distribuzione del numero totale delle identificazione corrette e salva il risultato nella colonna del `DataFrame`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "20efc667",
   "metadata": {},
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>26</th>\n",
       "      <th>27</th>\n",
       "      <th>28</th>\n",
       "      <th>29</th>\n",
       "      <th>30</th>\n",
       "      <th>31</th>\n",
       "      <th>32</th>\n",
       "      <th>33</th>\n",
       "      <th>34</th>\n",
       "      <th>35</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.719071e-08</td>\n",
       "      <td>1.432559e-09</td>\n",
       "      <td>1.193799e-10</td>\n",
       "      <td>9.948326e-12</td>\n",
       "      <td>8.290272e-13</td>\n",
       "      <td>6.908560e-14</td>\n",
       "      <td>5.757133e-15</td>\n",
       "      <td>4.797611e-16</td>\n",
       "      <td>3.998009e-17</td>\n",
       "      <td>3.331674e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>1.501694e-36</td>\n",
       "      <td>1.251411e-37</td>\n",
       "      <td>1.042843e-38</td>\n",
       "      <td>8.690357e-40</td>\n",
       "      <td>7.241964e-41</td>\n",
       "      <td>6.034970e-42</td>\n",
       "      <td>5.029142e-43</td>\n",
       "      <td>4.190952e-44</td>\n",
       "      <td>3.492460e-45</td>\n",
       "      <td>2.910383e-46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.011165e-07</td>\n",
       "      <td>5.968996e-08</td>\n",
       "      <td>7.162795e-09</td>\n",
       "      <td>7.792856e-10</td>\n",
       "      <td>8.013930e-11</td>\n",
       "      <td>7.944844e-12</td>\n",
       "      <td>7.676178e-13</td>\n",
       "      <td>7.276377e-14</td>\n",
       "      <td>6.796616e-15</td>\n",
       "      <td>6.274653e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>7.508469e-34</td>\n",
       "      <td>6.486483e-35</td>\n",
       "      <td>5.596590e-36</td>\n",
       "      <td>4.823148e-37</td>\n",
       "      <td>4.152060e-38</td>\n",
       "      <td>3.570691e-39</td>\n",
       "      <td>3.067777e-40</td>\n",
       "      <td>2.633315e-41</td>\n",
       "      <td>2.258457e-42</td>\n",
       "      <td>1.935405e-43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.545987e-06</td>\n",
       "      <td>9.741401e-07</td>\n",
       "      <td>1.709122e-07</td>\n",
       "      <td>2.506426e-08</td>\n",
       "      <td>3.269131e-09</td>\n",
       "      <td>3.940182e-10</td>\n",
       "      <td>4.490244e-11</td>\n",
       "      <td>4.908756e-12</td>\n",
       "      <td>5.197412e-13</td>\n",
       "      <td>5.365476e-14</td>\n",
       "      <td>...</td>\n",
       "      <td>1.806613e-31</td>\n",
       "      <td>1.620070e-32</td>\n",
       "      <td>1.449030e-33</td>\n",
       "      <td>1.292922e-34</td>\n",
       "      <td>1.151034e-35</td>\n",
       "      <td>1.022555e-36</td>\n",
       "      <td>9.066202e-38</td>\n",
       "      <td>8.023344e-39</td>\n",
       "      <td>7.088005e-40</td>\n",
       "      <td>6.251357e-41</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3 rows × 36 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             0             1             2             3             4   \\\n",
       "0  1.719071e-08  1.432559e-09  1.193799e-10  9.948326e-12  8.290272e-13   \n",
       "1  4.011165e-07  5.968996e-08  7.162795e-09  7.792856e-10  8.013930e-11   \n",
       "2  4.545987e-06  9.741401e-07  1.709122e-07  2.506426e-08  3.269131e-09   \n",
       "\n",
       "             5             6             7             8             9   ...  \\\n",
       "0  6.908560e-14  5.757133e-15  4.797611e-16  3.998009e-17  3.331674e-18  ...   \n",
       "1  7.944844e-12  7.676178e-13  7.276377e-14  6.796616e-15  6.274653e-16  ...   \n",
       "2  3.940182e-10  4.490244e-11  4.908756e-12  5.197412e-13  5.365476e-14  ...   \n",
       "\n",
       "             26            27            28            29            30  \\\n",
       "0  1.501694e-36  1.251411e-37  1.042843e-38  8.690357e-40  7.241964e-41   \n",
       "1  7.508469e-34  6.486483e-35  5.596590e-36  4.823148e-37  4.152060e-38   \n",
       "2  1.806613e-31  1.620070e-32  1.449030e-33  1.292922e-34  1.151034e-35   \n",
       "\n",
       "             31            32            33            34            35  \n",
       "0  6.034970e-42  5.029142e-43  4.190952e-44  3.492460e-45  2.910383e-46  \n",
       "1  3.570691e-39  3.067777e-40  2.633315e-41  2.258457e-42  1.935405e-43  \n",
       "2  1.022555e-36  9.066202e-38  8.023344e-39  7.088005e-40  6.251357e-41  \n",
       "\n",
       "[3 rows x 36 columns]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c77af271",
   "metadata": {},
   "source": [
    "La figura seguente mostra le colonne selezionate dal `DataFrame`, corrispondenti alle differenti ipotesi del valore `num_sensitive`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "a43d30a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "table[0].plot(label='num_sensitive = 0')\n",
    "table[10].plot(label='num_sensitive = 10')\n",
    "table[20].plot(label='num_sensitive = 20', style='--')\n",
    "table[30].plot(label='num_sensitive = 30', style=':')\n",
    "    \n",
    "decorate(xlabel='Number of correct identifications',\n",
    "         ylabel='PMF',\n",
    "         title='Gluten sensitivity')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be264c62",
   "metadata": {},
   "source": [
    "Possiamo usare questa tabella per calcolare la verosomiglianza del dato:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "ec6443da",
   "metadata": {},
   "outputs": [],
   "source": [
    "likelihood1 = table.loc[12]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ddbb47d",
   "metadata": {},
   "source": [
    "`loc` seleziona la riga del `DataFrame`.\n",
    "\n",
    "La riga con l'indice 12 contiene le probabilità di 12 identificazioni correte per ogni ipotetico valore di `num_sensitive`.\n",
    "E questo è quello che la verosomiglianza di cui abbiamo bisogno per eseguire l'aggiornamento Bayesiano.\n",
    "Useremo la distribuzione a priori uniforme, che implica che ogni valore di `num_sensitive` ha la stessa probabilità:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "a5051ca6",
   "metadata": {},
   "outputs": [],
   "source": [
    "hypos = np.arange(n+1)\n",
    "prior = Pmf(1, hypos)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce65dd19",
   "metadata": {},
   "source": [
    "E qui l'aggiornamento:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "cfd0a7ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4754741648615132"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior1 = prior * likelihood1\n",
    "posterior1.normalize()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a0cc5fc",
   "metadata": {},
   "source": [
    "Per comparazione, ho anche calcolato la distribuzione a posteriori per un altro possibile valore di 20 identificazioni corrette."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "aca8c759",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7818649765887375"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihood2 = table.loc[20]\n",
    "posterior2 = prior * likelihood2\n",
    "posterior2.normalize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "054c04e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "posterior1.plot(label='posterior with 12 correct', color='C4')\n",
    "posterior2.plot(label='posterior with 20 correct', color='C1')\n",
    "\n",
    "decorate(xlabel='Number of sensitive subjects',\n",
    "         ylabel='PMF',\n",
    "         title='Posterior distributions')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6c314fa",
   "metadata": {},
   "source": [
    "Con 12 corrette identificazioni, il valore più probabile è che nessuno sia sensibile al glutine.\n",
    "Mentre con 20 identificazioni corrette, la conclusione potrebbe essere che 11-12 soggetti siano sensibili."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "c0dd77c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior1.max_prob()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "ce182a87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 7.])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior1.credible_interval(0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "01033a55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior2.max_prob()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "3a6eb619",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3., 17.])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior2.credible_interval(0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b440baf9",
   "metadata": {},
   "source": [
    "## Sommario\n",
    "Questo capitolo rappresenta due argomenti che solo per lo più non correlati tra loro.\n",
    "La prima parte del capitolo è relativo alla regola di Bayes e come come quantificare la forza dell'evidenza usando il rapporto delle verosomiglianze o il fattore di Bayes.\n",
    "\n",
    "La seconda parte è relativa a `add_dist`, che calcola la distribuzione della somma.\n",
    "Possiamo usare questa funzione per risolvere il problema inverso, dati i parametri del sistema possiamo calcolare la distribuzione del dato o dato il dato possiamo calcolare la distribuzione dei parametri.\n",
    "\n",
    "Nel prossimo capitolo, calcoleremo distribuzioni per minimi e massimi e le useremo per risolvere problemi Bayesiani.\n",
    "\n",
    "\n",
    "## Esercizi\n",
    "\n",
    "**Esercizio:** Usiamo la regola di Bayes per risolvere il problema del gemello di Elvis:\n",
    "> Elvis Presley aveva un fratello gemello che è morto alla nascita.Quale è la probabilità che Elvis fosse un gemello identico ?\n",
    "\n",
    "Nel 1935 circa 2/3 dei gemelli erano eterozigoti e 1/3 erano identici.\n",
    "La domanda contiene due pezzi di informazione che possiamo usare per aggiornare i dati.\n",
    "* Primo, Il gemello di Elvis era che lui maschio che è più probabile se fossero gemelli identici con un rapporto di verosomiglianza pari a 2.\n",
    "\n",
    "* Ancora, il gemello di Elvis è morto alla nascita che è più probabile se erano gemelli identici, con un rapporto di verosomiglianza pari a 1.25.\n",
    "\n",
    "Se siete curiosi circa questi numeri leggete questo [articolo](https://www.allendowney.com/blog/2020/01/28/the-elvis-problem-revisited)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "bad2c989",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.49999999999999994"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prior = odds(1/3)\n",
    "prior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "d795e4b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihood = 1.25 * 2\n",
    "likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "78a0dc14",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2499999999999998"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_odd = prior * likelihood\n",
    "post_odd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "db000d99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5555555555555555"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob(post_odd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a8c7e1f",
   "metadata": {},
   "source": [
    "**Esercizio:** La seguente è una domanda nella [intervista che è apparsa su glassdoor.com](https://www.glassdoor.com/Interview/You-re-about-to-get-on-a-plane-to-Seattle-You-want-to-know-if-you-should-bring-an-umbrella-You-call-3-random-friends-of-y-QTN_519262.htm) attribuita a Facebook:\n",
    "\n",
    "> Stai per prendere un aereo per Seattle. Vuoi conoscere se devi prendere una ombrella. Chiamiamo 3 amici a caso che vivono li e chiediamo indipendentemente se sta piovendo. Ogni tuo amico ha 2/3 di possibilità di dirti la verità e circa un 1/3 di possibilità di prenderti in giro mentendo. Tutti e tre i tuoi amici ti dicono che sta piovendo. Quale è la probabilità che stia piovendo a Seattle ?\n",
    "\n",
    "Usa la regola di Bayes per risolvere questo problema. Come priori assumiamo che a Seattle piova circa il 10% del tempo.\n",
    "Questa domanda causa alcune confusioni circa le differenze tra l'interpretazione Bayesiana e frequentista della probabilità, se sei curioso circa questo punto possiamo leggere [questo articolo](http://allendowney.blogspot.com/2016/09/bayess-theorem-is-not-optional.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "2e7ec765",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11111111111111112"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prior_odds = odds(0.1)\n",
    "prior_odds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "11a2fc1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.999999999999997"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihood = pow(odds(2/3),3)\n",
    "likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "7441dba7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8888888888888886"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_odds = prior_odds * likelihood\n",
    "post_odds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "2f835cf3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4705882352941176"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob(post_odds)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "408cb601",
   "metadata": {},
   "source": [
    "**Esercizio:** [In accordo con il CDC](https://www.cdc.gov/tobacco/data_statistics/fact_sheets/health_effects/effects_cig_smoking) le persone che fumano hanno 25 volte in più di probabilità di sviluppare il cancro ai polmoni dei non fumatori.\n",
    "[Sempre in accordo con il CDC](https://www.cdc.gov/tobacco/data_statistics/fact_sheets/adult_data/cig_smoking/index.htm) circa il 14% degli adulti negli stati uniti sono fumatori. Se sai che una persona ha il cancro ai polmoni quale è la probabilità che sia un fumatore ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "b25fd8e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.16279069767441862"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prior_odds = odds(0.14)\n",
    "prior_odds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "5ab85f56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.069767441860465"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_odds = prior_odds * 25\n",
    "post_odds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "3b7fa3dc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8027522935779816"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob(post_odds)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ee49709",
   "metadata": {},
   "source": [
    "**Esercizio:** In *Dungeons & Dragons*, l'ammontare dei danni che un goblin può supportare è la somma di dadi a sei facce. La somma dei danni che puoi infliggere con una spada corta è determinato dal lancio di un dado a sei facce.\n",
    "Un goblin è sconfitto se il totale dei danno inflitti è maggiore o uguale alla quantità che può supportare.\n",
    "\n",
    "Supponiamo che tu stia combattendo un goblin e che tu abbia già inflitto 3 punti di danni. Quale è la probabilità di sconfiggere il goblin con l'attacco successivo?\n",
    "\n",
    "Suggerimento: possiamo usare `Pmf.add_dist` per aggiungere una quantità costante tipo 3 a `Pmf` e `Pmf.sub_dist` per calcolare la distribuzione dei punti rimanenti."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "d130dc07",
   "metadata": {},
   "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>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "1    0.166667\n",
       "2    0.166667\n",
       "3    0.166667\n",
       "4    0.166667\n",
       "5    0.166667\n",
       "6    0.166667\n",
       "Name: , dtype: float64"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d6 = make_die(6)\n",
    "d6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "edfcf252",
   "metadata": {},
   "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>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.027778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.055556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.083333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.138889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.138889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.083333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.055556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.027778</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "2     0.027778\n",
       "3     0.055556\n",
       "4     0.083333\n",
       "5     0.111111\n",
       "6     0.138889\n",
       "7     0.166667\n",
       "8     0.138889\n",
       "9     0.111111\n",
       "10    0.083333\n",
       "11    0.055556\n",
       "12    0.027778\n",
       "Name: , dtype: float64"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hp_before = Pmf.add_dist(d6, d6)\n",
    "hp_before"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "cca4b3e7",
   "metadata": {},
   "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>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-1</th>\n",
       "      <td>0.027778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.055556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.083333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.138889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.138889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.083333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.055556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.027778</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "-1    0.027778\n",
       " 0    0.055556\n",
       " 1    0.083333\n",
       " 2    0.111111\n",
       " 3    0.138889\n",
       " 4    0.166667\n",
       " 5    0.138889\n",
       " 6    0.111111\n",
       " 7    0.083333\n",
       " 8    0.055556\n",
       " 9    0.027778\n",
       "Name: , dtype: float64"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Questo è il numero dei punti dopo il primo attacco\n",
    "hp_after = Pmf.sub_dist(hp_before, 3)\n",
    "hp_after"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "60c2c8a0",
   "metadata": {},
   "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>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-1</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.090909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.121212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.151515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.181818</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.151515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.121212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.090909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.060606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.030303</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "-1    0.000000\n",
       " 0    0.000000\n",
       " 1    0.090909\n",
       " 2    0.121212\n",
       " 3    0.151515\n",
       " 4    0.181818\n",
       " 5    0.151515\n",
       " 6    0.121212\n",
       " 7    0.090909\n",
       " 8    0.060606\n",
       " 9    0.030303\n",
       "Name: , dtype: float64"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Ma i valori -1 e 0 non sono possibili, in quanto il goblin sarebbe già stato sconfitto.\n",
    "# Dunque dobbiamo azzerare questa casistica e rinormalizzare\n",
    "hp_after[hp_after.index <= 0] = 0\n",
    "hp_after.normalize()\n",
    "hp_after"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "49111420",
   "metadata": {},
   "outputs": [],
   "source": [
    "# il danno del secondo attacco sarà uno dei seguenti casi\n",
    "damage = d6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "e2936f9a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# qui come la distribuzione come sembra\n",
    "hp_after.bar(label='Hit points')\n",
    "damage.plot(label='Damage', color='C1')\n",
    "decorate_dice('The Goblin Problem')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "edd75363",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Qui la distribuzione dei punti dopo aver lasciato il goblin\n",
    "points_left = Pmf.sub_dist(hp_after, damage)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "d96ef763",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4545454545454545"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# e qui la probabilità che il ghoblin sia morto\n",
    "points_left.le_dist(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e2769e8",
   "metadata": {},
   "source": [
    "**Esercizio:** Supponiamo di avere una scatola con un dado a 6 facce, uno a 8 facce e uno a 12 facce.\n",
    "Scegliamo un dado a caso, lanciamo il dado due volte, moltiplichiamo i risultati e riportiamo che il prodotto è 12.\n",
    "\n",
    "Quale è la probabilita di aver scelto un dato a 8 facce?\n",
    "\n",
    "Suggerimento: L'oggetto `Pmf` è una funzione chiamata `mul_dist` che prende due oggetti `Pmf` e ritorna un oggetto `Pmf` che rappresenta la distribuzione del prodotto."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "d060f6a7",
   "metadata": {},
   "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>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "6     1\n",
       "8     1\n",
       "12    1\n",
       "Name: , dtype: int64"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hypos = [6, 8, 12]\n",
    "prior = Pmf(1, hypos)\n",
    "prior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "09b24ce9",
   "metadata": {},
   "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>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.1250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.1250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.1875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.1250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.1250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.0625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.1250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.0625</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "1     0.0625\n",
       "2     0.1250\n",
       "3     0.1250\n",
       "4     0.1875\n",
       "6     0.1250\n",
       "8     0.1250\n",
       "9     0.0625\n",
       "12    0.1250\n",
       "16    0.0625\n",
       "Name: , dtype: float64"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d4 = make_die(4)\n",
    "Pmf.mul_dist(d4, d4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "270a6b69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.1111111111111111, 0.0625, 0.041666666666666664]"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# qui la funzione di credibilità dopo aver fatto la moltiplicazione\n",
    "likelihood = []\n",
    "\n",
    "for sides in hypos:\n",
    "    die = make_die(sides)\n",
    "    pmf = Pmf.mul_dist(die, die)\n",
    "    likelihood.append(pmf[12])\n",
    "    \n",
    "likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "1d24a631",
   "metadata": {},
   "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>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.516129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.290323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.193548</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "6     0.516129\n",
       "8     0.290323\n",
       "12    0.193548\n",
       "Name: , dtype: float64"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# E qui l'aggiornamento\n",
    "posterior = prior * likelihood\n",
    "posterior.normalize()\n",
    "posterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "66e32a4b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}