{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "DzPgKBitkwE4" }, "source": [ "# Inferência Bayesiana\n", "\n", "\n", "por **Cibele Russo**\n", "\n", "**ICMC/USP - São Carlos SP**\n", "\n", "\n", "\n", "## Programa\n", "\n", "\n", "- O paradigma Bayesiano.\n", "\n", "- Os diferentes tipos de prioris. \n", "\n", "- Distribuições conjugadas. \n", "\n", "- Estimação Bayesiana. \n", "\n", "- Densidade preditiva.\n", "\n", "- Computação Bayesiana.\n", "\n", "- Exemplos com PyMC3.\n", "\n", "\n", "**Referências e leituras recomendadas:**\n", "\n", "1. Migon, H. S., Gamerman, D. and Louzada, F. (2014). Statistical Inference: An Integrated Approach, Second Edition, CRC Press.\n", "\n", "2. Ehlers, R. (2011) Inferência Bayesiana. \n", "Disponível em https://sites.icmc.usp.br/ehlers/bayes/bayes.pdf . Acesso em 31/03/2021.\n", "\n", "2. Caffo, B. (2016). Statistical Inference for Data Science. Leanpub. \n", "Disponível em https://leanpub.com/LittleInferenceBook \n", "\n", "3. https://pt.wikipedia.org/wiki/Infer%C3%AAncia_bayesiana\n", "\n", "4. https://github.com/datawookie/talks/tree/master/2018-10-12-pycon-johannesburg\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "UxiXTy-IkwFD" }, "source": [ "## O paradigma Bayesiano\n", "\n", "Seja uma amostra aleatória $X_1,\\ldots, X_n$ que vem de um modelo $p(x|\\theta)$, $\\theta \\in \\Theta$ e sejam $x_1,\\ldots,x_n$ os dados observados.\n", "\n", "\n", "Sob o **paradigma clássico ou frequentista**, $\\theta$ é um **parâmetro fixo e desconhecido**.\n", "\n", "Sob o **paradigma Bayesiano**, consideramos modelos probabilísticos para **representar a incerteza** a respeito de $\\theta$.\n", "\n", "Se temos informação **a priori** sobre o parâmetro $\\theta$, antes de observar os dados, por que não usá-la?\n" ] }, { "cell_type": "markdown", "metadata": { "id": "5DaNE9OFkwFF" }, "source": [ "### Exemplo:\n", "\n", "Na aplicação de dados bancários que vimos na Aula 1, suponha que antes de observar os dados, exista um conhecimento prévio de que a proporção p de inadimplentes esteja em torno de 20\\%. Como incorporar esse conhecimento prévio? Uma possibilidade seria considerar uma distribuição a priori beta para a proporção p." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 225 }, "id": "IQG8LwifkwFH", "outputId": "59eca112-4048-437c-ebf5-6914b7266f25" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Mais sobre a distribuição beta: https://pt.wikipedia.org/wiki/Distribui%C3%A7%C3%A3o_beta\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy import stats\n", "from scipy.stats import beta\n", "\n", "# Conjuntos de parâmetros da distribuição a priori para a proporção de inadimplentes\n", "a_b_params = ((0.1, 0.1), (1, 1), (2, 8), (10, 5))\n", "p = np.linspace(0, 1, 100)\n", "\n", "# Plota as densidades da beta para cada conjunto de parâmetros\n", "plt.figure(figsize=(13,3))\n", "for i, (a, b) in enumerate(a_b_params):\n", " plt.subplot(1, len(a_b_params), i+1)\n", "\n", " prior = beta(a, b)\n", "\n", " plt.plot(p, prior.pdf(p)) \n", " plt.xlabel(r'$p$')\n", " plt.title(\"a = {:.1f}, b = {:.1f}\".format(a, b))\n", " plt.tight_layout()\n" ] }, { "cell_type": "markdown", "metadata": { "id": "R4VahvazkwFN" }, "source": [ "\n", "\n", "### Teorema de Bayes\n", "\n", "Ver, por exemplo: https://pt.wikipedia.org/wiki/Teorema_de_Bayes\n", "\n", "\n", "Sejam\n", "\n", "- $p(\\theta)$ a **distribuição a priori** para $\\theta$.\n", "\n", "- $l(\\theta,x) = p(x|\\theta)$ a **verossimilhança** de $\\theta$.\n", "\n", "- $p(\\theta|x)$ a **distribuição a posteriori** de $\\theta$.\n", "\n", "O Teorema de Bayes ilustra o aumento de informação com a introdução do conhecimento a priori\n", "\n", "$$p(\\theta|x) = \\displaystyle \\frac{p(x,\\theta)}{p(x)} = \\frac{p(x|\\theta)p(\\theta)}{p(x)} = \\frac{p(x|\\theta) p(\\theta)}{\\displaystyle\\int p(\\theta,x) d\\theta}.$$\n", "\n", "\n", "\n", "\n", "\n", "\n", "Em outras palavras:\n", "\n", "distribuição a posteriori $\\propto$ verossimilhança $\\times$ distribuição a priori\n", "\n", "\n", "\n", "\n", "\n", "Para um valor fixo de $x$, as duas fontes de informação para $\\theta$ são\n", "\n", "- a função $l(\\theta;x)=p(x|\\theta)$ fornece a plausibilidade ou verossimilhança de cada um dos possíveis valores de $\\theta$ e\n", "\n", "- $p(\\theta)$ é chamada distribuição a priori de $\\theta$,\n", "\n", "que, combinadas, levam à distribuição a posteriori de $\\theta$, $p(\\theta|x)$.\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Assim, a forma usual do teorema de Bayes é\n", "$p(\\theta|x) \\propto l(\\theta;x)p(\\theta).$ \n", "\n", "\n", "O termo omitido $p(x)$ é apenas uma constante normalizadora e não depende de $\\theta$. \n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "KgOaqB1WkwFP" }, "source": [ "Para $x$ fixo, a **verossimilhança** fornece a **plausibilidade** de cada um dos possíveis valores de $\\theta$.\n", "\n", "Já a **distribuição a priori** $p(\\theta)$ incorpora o **conhecimento do pesquisador**.\n", "\n", "Essas duas quantidades combinadas são levadas à **distribuição a posteriori** de $\\theta$.\n", "\n", "A **distribuição a posteriori** de $\\theta$ dados $x_1,\\ldots,x_n$ observados é dada por:\n", "\n", "$$p(\\theta|x_1,\\ldots,x_n) = \\displaystyle\\frac{p(x_1,\\ldots,x_n|\\theta)p(\\theta)}{\\int_{\\Theta} p(x_1,\\ldots,x_n|\\theta)p(\\theta)d\\theta}$$\n", "\n", "\n", "\n", "\n", "- $p(x_1,\\ldots,x_n|\\theta) = \\displaystyle\\prod_{i=1}^n p(x_i|\\theta) = L(\\theta|x_1,\\ldots,x_n)$ é a **função de verossimilhança** de $\\theta$.\n", "\n", "\n", "- O denominador $$\\int_{\\Theta} p(x_1,\\ldots,x_n|\\theta)p(\\theta)d\\theta = C(x_1,\\ldots,x_n).$$\n", "\n", "\n", "É comum escrever que \n", "\n", "\n", "$p(\\theta|x_1,\\ldots,x_n) = \\displaystyle\\frac{ L(\\theta|x_1,\\ldots,x_n) p(\\theta)}{ C(x_1,\\ldots,x_n)}\\propto L(\\theta|x_1,\\ldots,x_n) p(\\theta)$,\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "DP2kJ5mSkwFR" }, "source": [ "## Distribuição preditiva\n", "\n", "A constante normalizadora da posteriori pode ser facilmente recuperada pois $p(\\theta|x)=kp(x|\\theta)p(\\theta)$ onde\n", "\n", "$k^{-1}= \\int p(x|\\theta)p(\\theta)d\\theta=E_\\theta[p(X|\\theta)]= p(x)$\n", "\n", "chamada **distribuição preditiva** (ou marginal) de $X$. \n", "\n", "\n", "Esta é a distribuição esperada para a observação $x$ dado $\\theta$. Assim,\n", "\n", "- Antes de observar $X$ podemos checar a adequação da priori fazendo predições via $p(x)$.\n", "\n", "- Se $X$ observado recebia pouca probabilidade preditiva então o modelo deve ser questionado, revisado, ou existe observação aberrante.\n", "\n", "\n", "\n", "\n", "Se, após observar $X=x$, estamos interessados na previsão de uma quantidade $Y$, também relacionada com $\\theta$, e descrita probabilisticamente por $p(y|\\theta)$ então\n", "\n", "$$p(y|x)=\\int p(y,\\theta| x)d\\theta =\\displaystyle \\int p(y|\\theta,x)p(\\theta| x)d\\theta$$\n", "\n", "Os conceitos de priori e posteriori são relativos àquela observação que está sendo considerada no momento. Assim, $p(\\theta| x)$ é a posteriori de $\\theta$ em relação a $X$ (que já foi observado) mas é a priori de $\\theta$ em relação a $Y$ (que não foi observado ainda).\n", "\n", "Após observar $Y=y$ uma nova posteriori (relativa a $X=x$ e $Y=y$) é obtida aplicando-se novamente o teorema de Bayes. \n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "L1Gr8nrfkwFX" }, "source": [ "## Os diferentes tipos de prioris\n", "\n", "\n", "Destacamos as distribuições a priori \n", "\n", "- **Priori não-informativa**\n", " - Uniforme\n", " - Priori vaga (às vezes imprópria)\n", "\n", "- **Priori informativa**\n", " - Conhecimento do pesquisador dá informação sobre os parâmetros\n", "\n", "- **Priori conjugada**\n", " - Priori e posteriori tem a mesma distribuição, a menos dos parâmetros (em geral facilita os cálculos)" ] }, { "cell_type": "markdown", "metadata": { "id": "QiApEE6GkwFY" }, "source": [ "### Distribuições conjugadas\n", "\n", "Leituras recomendadas:\n", "\n", "- Notas Ricardo Ehlers e Paulo Justiniano: http://www.leg.ufpr.br/~paulojus/CE227/ce227/node1.html\n", "\n", "- Conjugate Prior Explained, with examples & proofs: https://towardsdatascience.com/conjugate-prior-explained-75957dc80bfb\n", "\n", "\n", "\n", "Vantagem de usar distribuições a priori conjugadas: principalmente **ganho de custo computacional.**\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
PrioriNúcleo da VerossimilhançaPosteriori
$\\theta$ proporçãoBetaBernoulli Beta
$\\theta$ média Normal Normal Normal
taxa de falha Gama Poisson Gama
Dirichlet Multinomial Dirichlet
" ] }, { "cell_type": "markdown", "metadata": { "id": "a0qWN-BSkwFZ" }, "source": [ "### Exemplo de priori conjugada beta-Bernoulli\n", "\n", "Ver https://towardsdatascience.com/conjugate-prior-explained-75957dc80bfb\n", "\n", "\n", "\n", "No exemplo do banco, se considerarmos que\n", "\n", "\n", "- $X=\\left\\{ \\begin{array}{lll} 1, &\\mbox{se o cliente é classificado como inadimplente,} \\\\ 0, &\\mbox{caso contrário.} \\end{array}\\right.$\n", "\n", "\n", "- $X \\sim Bernoulli(p)$\n", "\n", "\n", "- Verossimilhança:\n", "\n", "Para $n$ suficientemente grande, pelo TLC sabemos que a distribuição amostral de $\\bar{X}$ se aproxima da normal $$\\bar{X} \\sim N\\left(p, \\displaystyle{\\frac{p(1-p)}{n}}\\right)$$\n", "\n", "\n", "Além disso, $Y = \\sum_{i=1}^{n} X_i \\sim binomial(n, p)$. \n", "\n", "\n", "\n", "\n", "- Priori: $p \\sim beta(2, 8)$\n", "\n", "\n", "- Posteriori: $p|k \\sim beta(k+a, n-k+b)$\n", "\n", "onde $k$ é o número de sucessos observados na amostra.\n", "\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "id": "d8b1TdEOkwFa", "outputId": "4bbe63cd-afdb-47ae-f17e-329e7db6b4d0", "colab": { "base_uri": "https://localhost:8080/", "height": 270 } }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ " Cliente Sexo Idade Empresa Salario Saldo_cc Saldo_poupança \\\n", "33227 33227 M 38 Privada 6467 993.18 0.0 \n", "64805 64805 M 33 Privada 5764 1167.27 0.0 \n", "39764 39764 F 35 Privada 5417 667.3 0.0 \n", "51271 51271 M 36 Privada 5858 846.53 0.0 \n", "9699 9699 M 32 Privada 5579 768.9 16801.57 \n", "\n", " Saldo_investimento Devedor_cartao Inadimplente \n", "33227 0.0 2038.32 1 \n", "64805 0.0 4617.05 1 \n", "39764 0.0 5726.83 1 \n", "51271 0.0 1723.74 1 \n", "9699 8138.71 0.0 0 " ], "text/html": [ "\n", "
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ClienteSexoIdadeEmpresaSalarioSaldo_ccSaldo_poupançaSaldo_investimentoDevedor_cartaoInadimplente
3322733227M38Privada6467993.180.00.02038.321
6480564805M33Privada57641167.270.00.04617.051
3976439764F35Privada5417667.30.00.05726.831
5127151271M36Privada5858846.530.00.01723.741
96999699M32Privada5579768.916801.578138.710.00
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\n", " " ] }, "metadata": {}, "execution_count": 10 } ], "source": [ "import pandas as pd\n", "\n", "\n", "# Dados banco - Leitura dos dados\n", "dados = pd.read_csv('amostra_banco.csv', index_col=0, decimal=',')\n", "\n", "dados.head()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "id": "7YhJJXIhkwFc", "outputId": "35f83545-f7b7-4837-a62b-67befa570ec4", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "0.242" ] }, "metadata": {}, "execution_count": 18 } ], "source": [ "import random\n", "from scipy.stats import beta\n", "\n", "a = 2\n", "b = 8\n", "\n", "n = len(dados)\n", "k = dados['Inadimplente'].sum()\n", "posteriori = beta(a + k, n - k + b) \n", "\n", "k/n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "id": "WMjMFn1QkwFd", "outputId": "a32eacf1-d1cf-44ad-a40e-5208796f89da", "colab": { "base_uri": "https://localhost:8080/", "height": 262 } }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "" ] }, "metadata": {}, "execution_count": 19 }, { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "from scipy.stats import norm\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Eixo x entre 0 e 1 de .002 em .002.\n", "x_axis = np.arange(0, 1, 0.002)\n", "\n", "# Plota as densidades da beta para cada conjunto de parâmetros\n", "plt.figure(figsize=(20,6))\n", " \n", "prior = beta(a, b)\n", "\n", "p_chapeu = dados['Inadimplente'].mean()\n", "dp = np.sqrt(p_chapeu*(1-p_chapeu)/n)\n", "\n", "media = p_chapeu\n", "dp = np.sqrt(media*(1-media)/n)\n", "\n", "plt.s = 0\n", "plt.rcParams.update({'font.size': 22})\n", "\n", "plt.plot(x_axis, norm.pdf(x_axis, media, dp), label='verossimilhança')\n", "plt.plot(x_axis, prior.pdf(x_axis), label='priori')\n", "plt.plot(x_axis, posteriori.pdf(x_axis), label='posteriori') \n", "plt.xlabel(r'$p$')\n", "plt.legend()\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "_laDm83-kwFf" }, "outputs": [], "source": [ "" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "id": "WcVtKminkwFf", "outputId": "eb5ae773-b86f-413d-a48c-aca6ee5f0b30", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Média: 0.24\n", "Intervalo com 95% de credibilidade: (0.205, 0.279)\n" ] } ], "source": [ "# Estimador bayesiano EAP (Esperança a posteriori)\n", "print('Média: %.2f' % posteriori.mean())\n", "\n", "\n", "# E para calcular um intervalo de credibilidade, decidimos uma probabilidade \n", "# Por exemplo 95% para a credibilidade\n", "# Uma maneira seria definir que 2,5% de cada cauda como os limites do intervalo (chamado intervalo simétrico)\n", "# Este método é válido quando a posteriori se aproxima de uma distribuição simétrica, pois nesse caso tende a gerar o intervalo com menor amplitude\n", "# A seguir, apresentamos outra solução com um intervalo de credibilidade de menor amplitude.\n", "\n", "LI = posteriori.ppf(.025)\n", "LS = posteriori.ppf(.975)\n", "print(\"Intervalo com 95% de credibilidade: ({:.3f}, {:.3f})\".format(LI,LS))\n" ] }, { "cell_type": "markdown", "metadata": { "id": "G4PWnA1akwFg" }, "source": [ "## Estimação Bayesiana\n", "\n", "\n", "Leituras recomendadas:\n", "\n", "- Notas Ricardo Ehlers e Paulo Justiniano: http://www.leg.ufpr.br/~paulojus/CE227/ce227/node1.html\n", "\n", "- Migon, H. S., Gamerman, D. and Louzada, F. (2014). Statistical Inference: An Integrated Approach, Second Edition, CRC Press.\n", "\n", "\n", "### Introdução à Teoria da Decisão\n", "\n", "Um problema de decisão fica completamente especificado pela descrição dos seguintes espaços:\n", "\n", "(i) Espaço do parâmetro ou estados da natureza, $\\Theta$. \n", " \n", "(ii) Espaço dos resultados possíveis de um experimento, $\\Omega$. \n", " \n", "(iii) Espaço de possíveis ações, $A$. \n", "\n", "Uma regra de decisão $\\delta$ é uma função definida em $\\Omega$ que assume valores em $A$, i.e. $\\delta:\\Omega\\rightarrow A$. A cada decisão $\\delta$ e a cada possível valor do parâmetro $\\theta$ podemos associar uma **perda** $L(\\delta,\\theta)$ assumindo valores positivos. Definimos assim uma **função de perda**.\n", "\n", "**Definição:** O **risco de uma regra de decisão**, denotado por $R(\\delta)$, é a **perda esperada a posteriori**, i.e. $$R(\\delta)=E_{\\theta\\vert\\mathbf{x}} [L(\\delta,\\theta)].$$\n", "\n", "Uma regra de decisão $\\delta^*$ é **ótima** se tem risco mínimo, i.e. $R(\\delta^*)\n", " \n", " \t\n", " eficiente ($\\theta=1$) \t\n", " não eficiente ($\\theta=0$)\n", " \n", " \n", " lança ($\\delta=1$) \t\n", " -500 \t\n", " 600\n", " \n", " \n", " não lança ($\\delta=0$) \t\n", " 1500 \t\n", " 100\n", " \n", " \n", " \n", "\n", "Vale notar que estas perdas traduzem uma **avaliação subjetiva** em relação à gravidade dos erros cometidos.\n", "\n", "Suponha agora que a incerteza sobre os estados da natureza é descrita por\n", "\n", "$P(\\theta=1)=\\pi$, $0<\\pi<1$ \n", "\n", "avaliada na distribuição atualizada de $\\theta$ (seja a priori ou a posteriori). \n", "\n", "\n", "Note que, para $\\delta$ fixo, $L(\\delta,\\theta)$ é uma variável aleatória discreta assumindo apenas dois valores com probabilidades $\\pi$ e $1-\\pi$. \n", "\n", "Assim, usando a definição de risco obtemos que\n", "\n", "\n", "$\\displaystyle R(\\delta=0) = \\displaystyle E(L(0,\\theta))=\\pi 1500 +(1-\\pi) 100 = 1400\\pi + 100$ \t\n", "\n", "$\\displaystyle R(\\delta=1) = \\displaystyle E(L(1,\\theta))=\\pi(-500)+(1-\\pi) 600 =-1100\\pi + 600$ \t \n", "\n", "Uma questão que se coloca aqui é, para que valores de $\\pi$ a regra de Bayes será de lançar a droga. \n", "\n", "Não é difícil verificar que as duas ações levarão ao mesmo risco, i.e.\n", "\n", "$R(\\delta=0)=R(\\delta=1)$ se somente se $\\pi=0.20$. \n", "\n", "Além disso, para $\\pi<0.20$ temos que $R(\\delta=0)0.20$ implica em $R(\\delta=0)>R(\\delta=1)$ e a regra de Bayes deve ser de **lançar a droga**. " ] }, { "cell_type": "markdown", "metadata": { "id": "pNO3CxOEkwFh" }, "source": [ "\n", "### Estimadores de Bayes\n", "\n", "Considere uma amostra aleatória $X_1,\\dots,X_n$, tomada de uma distribuição com função de (densidade) de probabilidade $p(x\\vert\\theta)$, onde o valor do parâmetro $\\theta$ é desconhecido. \n", "\n", "Em um problema de inferência como este o valor de $\\theta$ deve ser estimado a partir dos valores observados na amostra.\n", "\n", "Se $\\theta\\in\\Theta$ então é razoável que os possíveis valores de um estimador $\\delta(\\mathbf{x})$ também devam pertencer ao espaço $\\Theta$. \n", "\n", "Além disso, um bom estimador é aquele para o qual, com alta probabilidade, apresenta o seguinte erro $$\\delta(\\mathbf{x})-\\theta$$ próximo de zero.\n", "\n", "\n", "\n", "\n", "### Funções de perda\n", "\n", "\n", "\n", "Para cada possível valor de $\\theta$ e cada possível estimativa $a\\in\\Theta$ vamos associar **uma perda** $L(a,\\theta)$ de modo que quanto maior a distância entre $a$ e $\\theta$ maior o valor da perda. A perda esperada a posteriori é dada por\n", "\n", "$$E[L(a,\\theta)\\vert\\mathbf{x}] = \\int L(a,\\theta)p(\\theta\\vert\\mathbf{x}) d\\theta$$\n", "\n", "O **estimador de Bayes** será aquele que minimiza a perda esperada.\n", "\n", "\n", "#### Função de perda quadrática\n", "\n", "$$L(a,\\theta)=(a-\\theta)^2$$ \n", "\n", "O estimador de Bayes para $\\theta$ será a **média de sua distribuição atualizada** (EAP: expected a posteriori).\n", "\n", "\n", "\n", "#### Função de perda absoluta\n", "(introduz punições que crescem linearmente com o erro de estimação)\n", "\n", "$$L(a,\\theta)=\\vert a-\\theta\\vert$$\n", "\n", "O estimador de Bayes para $\\theta$ é a **mediana de sua distribuição atualizada**.\n", "\n", "\n", "\n", "#### Função de perda 0-1\n", "\n", "(associam uma perda fixa a um erro cometido, não importando sua magnitude)\n", "\n", "$$L(a,\\theta)=\\left\\{ \\begin{array}{ccc} 1 &\\mbox{se}& |a-\\theta|>\\epsilon \\\\ 0 &\\mbox{se}& |a-\\theta|<\\epsilon \\end{array}\\right.$$\n", "\n", "para todo $\\epsilon>0$. \n", "\n", "Neste caso, o estimador de Bayes é a **moda da distribuição atualizada de $\\theta$** (MAP: maximum a posteriori). \n", "\n", "A moda da posteriori de $\\theta$ também é chamado de estimador de máxima verossimilhança generalizado (EMVG) e é o mais fácil de ser obtido dentre os estimadores vistos até agora.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "hR0rOUJYkwFi" }, "source": [ "**Exemplo:**\n", "\n", "Suponha que queremos estimar a proporção $\\theta$ de itens defeituosos em um grande lote. Para isto será tomada uma amostra aleatória $X_1,\\dots,X_n$ de uma distribuição de Bernoulli com parâmetro $\\theta$. Usando uma priori conjugada beta($a,b$), após observar a amostra a distribuição a posteriori é beta($a+k,b+n-k$) onde $k=\\sum_{i=1}^n x_i$. \n", "\n", "A média desta distribuição beta é dada por $(a+k)/(a+b+n)$ e portanto o estimador de Bayes de $\\theta$ usando perda quadrática é\n", "\n", "$\\delta(\\mathbf{x})= \\displaystyle\\frac{a+\\sum_{i=1}^n X_i}{a+b+n}.$\n" ] }, { "cell_type": "markdown", "metadata": { "id": "PZIFOYaikwFj" }, "source": [ "### Estimação por Intervalos\n", "\n", "Pode-se desenvolver a estimação por intervalos por meio do **intervalo de credibilidade (ou intervalo de confiança Bayesiano)** baseado no distribuição a posteriori.\n", "\n", "\n", "\n", "**Definição:**\n", "\n", "C é um **intervalo de credibilidade** de 100(1-$\\alpha$)$\\%$, ou nível de credibilidade (ou confiança) $1-\\alpha$, para $\\theta$ se $P(\\theta\\in C)\\ge 1-\\alpha$.\n", "\n", "\n", "\n", "Obs: Quanto menor for o tamanho do intervalo, mais concentrada é a distribuição do parâmetro, ou seja o tamanho do intervalo informa sobre a dispersão de $\\theta$. \n", "\n", "\n", "O **intervalo com o menor comprimento possível** é obtido tomando-se os valores de $\\theta$ com maior densidade a posteriori, e esta idéia é expressa matematicamente na definição abaixo.\n", "\n", "\n", "**Definição:**\n", "\n", "Um intervalo de credibilidade $C$ de 100(1-$\\alpha$)% para $\\theta$ é de **máxima densidade a posteriori (MDP)** se $C=\\{\\theta\\in\\Theta:p(\\theta\\vert\\mathbf{x})\\ge k(\\alpha)\\}$ onde $k(\\alpha)$ é a maior constante tal que $P(\\theta\\in C)\\ge 1-\\alpha$.\n", "\n", "Usando esta definição, todos os pontos dentro do intervalo MDP terão densidade maior do que qualquer ponto fora do intervalo. \n", "\n", "Um problema com os intervalos MDP é que eles não são invariantes a transformações 1 a 1, a não ser para transformações lineares. O mesmo problema ocorre com intervalos de comprimento mínimo na inferência clássica. " ] }, { "cell_type": "markdown", "metadata": { "id": "Y4CV55ARkwFj" }, "source": [ "## Computação Bayesiana\n", "\n", "Leituras recomendadas:\n", "\n", "- Métodos de Monte Carlo: https://pt.wikipedia.org/wiki/M%C3%A9todo_de_Monte_Carlo\n", "\n", "- Notas Ricardo Ehlers e Paulo Justiniano: http://www.leg.ufpr.br/~paulojus/CE227/ce227/node1.html\n", "\n", "- Salvatier, John; Wiecki, Thomas V.; Fonnesbeck, Christopher. Probabilistic programming in Python using PyMC3. PeerJ Computer Science, v. 2, p. e55, 2016. Disponível em https://peerj.com/articles/cs-55/. Acessado em 06/04/2021.\n", "\n", "\n", "A obtenção de informações a partir da distribuição a posteriori dos parâmetros pode envolver a avaliação de probabilidades ou esperanças, que exigem métodos computacionais baseados em simulações, como \n", "\n", "- Método de Monte Carlo simples\n", "\n", "- Monte Carlo com função de importância, \n", "\n", "- Algoritmo de Metropolis-Hastings,\n", "\n", "- Amostrador de Gibbs,\n", "\n", "- Método do Bootstrap Bayesiano, \n", "\n", "- Monte Carlo via cadeias de Markov (MCMC), \n", "\n", "- Monte Carlo Hamiltoniano (HMC),\n", "\n", "- No-U-Turn Sampler (NUTS).\n", "\n", "\n", "HMC e NUTS aproveitam as informações de gradiente da probabilidade e alcançam uma convergência muito mais rápida do que os métodos de amostragem tradicionais, especialmente para modelos mais complexos. \n", "\n", "O pacote PyMC3 do Python usam a programação probabilística para executar os métodos de HMC como o NUTS. Esse tipo de programação permite a especificação flexível e ajuste de modelos estatísticos bayesianos com sintaxe intuitiva e legível, embora poderosa, que é próxima da sintaxe natural que os estatísticos usam para descrever modelos.\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "jqAf5HDdkwFk" }, "source": [ "## Exemplos\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "9iJhuKmzkwFk" }, "outputs": [], "source": [ "#!pip install pymc3==3.11.1\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "qqRkY6qSkwFl" }, "outputs": [], "source": [ "#!pip install arviz==0.11.2" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "id": "ECBRrmj0kwFl" }, "outputs": [], "source": [ "import warnings\n", "\n", "import arviz as az\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pymc3 as pm\n", "import theano.tensor as tt\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "SI4y97_zkwFm" }, "outputs": [], "source": [ "!pip show pymc3" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "pTwZpB-YkwFm" }, "outputs": [], "source": [ "!pip show arviz" ] }, { "cell_type": "markdown", "metadata": { "id": "rkeg8ht0kwFn" }, "source": [ "## Exemplo beta-Bernoulli: clientes do banco" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "id": "Q2RwxOuYkwFn", "outputId": "ef5aca18-8bab-4a92-b10b-bf1e7dc7a7a0", "colab": { "base_uri": "https://localhost:8080/", "height": 198 } }, "outputs": [ { "output_type": "stream", "name": "stderr", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Sequential sampling (2 chains in 1 job)\n", "NUTS: [p]\n" ] }, { "output_type": "display_data", "data": { "text/plain": [ "" ], "text/html": [ "\n", "\n" ] }, "metadata": {} }, { "output_type": "display_data", "data": { "text/plain": [ "" ], "text/html": [ "\n", "
\n", " \n", " 100.00% [3500/3500 00:03<00:00 Sampling chain 0, 0 divergences]\n", "
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meansdhdi_3%hdi_97%mcse_meanmcse_sdess_bulkess_tailr_hat
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\n", " " ] }, "metadata": {}, "execution_count": 25 } ], "source": [ "az.summary(idata)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "id": "1Kkj3gWBkwFp", "outputId": "05e9ed26-632a-4c7d-e01d-25d552028ccd", "colab": { "base_uri": "https://localhost:8080/", "height": 287 } }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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hmzc3HOeGrl7cEd5W7ziNRtM0xof5sv9cJmfT8vSOI5oRKcbiMgaD4oWVh3F1sGbe+K5N9ge7mozr4Q0gfY5Fo5JiLC7z3b449p/L5PmxnXB1sNE7TqPzcbWndzt3Vh6Ilz7HotFIMRZVZOWXMP/naHoHuDPhuvoNCN8U3NLDm9MX8ohKyNY7imgmpBiLKj7dfprM/BIixoU2u+aJi93YtQ3WlhqrDsTrHUU0E1KMRaWUnEI+3xHLuO7edPZ20TuOrlwdbBgQ5MG6w0nSVCEahRRjUemjzacpLjMwdWRHvaOYhLFd2xCfWcDh+Cy9o4hmQIqxACAtt4j/7TnHbdf50M7D8eorNAOjOntiZaGx7nCS3lFEMyDFWADwze/nKC418PAg831qR0NzdbChb2BL1h9JlKYKYXRSjAWFJWV8/XssQ4NbEdS66YxR3BBu7NqGs2n5HE2UXhXCuKQYC1YfSCA1t5gHB8pV8aVGhXphaaGx7rCMVSGMS4qx4JvdZwn2dKZfYEu9o5gcd0cb+rR3l14VwuikGDdz0UnZHDqfxZ292jbrfsVXMrZLG2JS8zienKN3FNGESTFu5pbvO4+1pcatYc33brurGR3qhYUG62RYTWFEUoybseJSAz/uj2dEJ0/cHZvfGBS11crZll4B7qw/Il3chPFIMW7GfotOIT2vmNvDffWOYvJu6NqGkym5nEqRpgphHFKMm7Hl++Jo7WzLoA6t9I5i8sZ08QJgvdwAIoxEinEzlZpbxJYTF5hwnS9WlvI1uBpPFzvC/d1YJ00VwkjkLGym1h9JosyguKViIHVxdWO6eHEsMZvYVHkCiGh4UoybqTUHEwhs5UiIl9xxV1tju7YBkB/yhFFIMW6GkrML2RObzk3dvKVvcR34uNrTva0r649IFzfR8KQYN0PrDieiFNzcvY3eUczODV28OHQ+i7j0fL2jiCZGinEztOZQIiFezjIoUD2M7VL+F9jP0lQhGpgU42YmIbOAP85mcFM3uSquD7+WDoR6u0hThWhwUoybmb9GH7uxm/SiqK8burbhz3OZJGYV6B1FNCFSjJuZjVHJhHg5y9M8rsFfN4BIU4VoSFKMm5HU3CL2nk1nVKiX3lHMWmArJ4I9naWLm2hQUoybkV+PJqMUjA711DuK2Rvb1Yu9semk5BTqHUU0EVKMm5GNR5PxdbOncxsXvaOYvRu6tkEp2BCVrHcU0URIMW4mcotK2XEyldGhXnKjRwPo0NqJ9q0cWS+PYxINRIpxM7HleArFZQZGS3txg9A0jZu6tuH3M2kkZ0tThbh2UoybiQ1RybR0tKGnv5veUZqMW8J8MCj46WCC3lFEEyDFuBkoKi1jc3QKIzp5YmkhTRQNJbCVE919W/Dj/ni9o4gmQIpxM7DrdBq5RaWM7iK9KBrarWE+RCVkc1IeViqukRTjZmBDVDKONpb0C/TQO0qTc1M3bywtNFYekKtjcW2kGDdxZQbFL0eTGRLSGjtrS73jNDmtnG0Z2MGDlfsTMBiU3nGEGZNi3MQdiMsgNbeIUZ2licJYxof5EJ9ZwJ7YdL2jCDMmxbiJ2xiVjLWlxtCQ1npHabJGdfbC2c6KZXvj9I4izJgU4yZMKcXGo8n0DfTAxc5a7zhNlr2NJbf28GHd4USy8kv0jiPMlBTjJuz0hVxiUvMYKU0URjexd1uKSg38uP+83lGEmZJi3IT9NW7CyE5SjI0t1LsF3XxbsHRvHErJD3mi7qQYN2EbjybTva0rXi3s9I7SLEzs5Ud0Ug4H4jL1jiLMkBTjJiopq5CDcZnSi6IR3dy9DfbWlvxv9zm9owgzJMW4ifrlWHkThYxd3Hic7ay5NcyH1QcTyMgr1juOMDNSjJuojVFJtPdwJLCVk95RmpXJ/QIoKjWwVLq5iTqSYtwEZRWUsOt0GiNDPWXs4kYW7OVM3/Yt+eb3s5SWGfSOI8yIFOMmaMvxFEoNilGdZexiPUzqF0B8ZgG/HpOngIjak2LcBG08moyHky1hbV31jtIsjejUGh9XexbvjNU7ijAjUoybmKLSMrYev8DIzq2xkLGLdWFlacE/+/rz+5l0Dp/P0juOMBNSjJuYv8YuliYKfd11vR/Otlb8d9tpvaMIMyHFuInZeLR87OK+gS31jtKsudhZc08ff9YfTiQ2NU/vOMIMSDFuQsoMio1RSTJ2sYmY0j8AKwsLPt1+Ru8owgxIMW5CdsekkZpbzI1d2+gdRQCtXey4racP3/9xnpQceYK0uDIpxk3IusOJ2FtbMjRYxi42FQ8PCqSkzMAXkbF6RxEmTopxE1FmUPx8JJlhIa2xt5EmClPRzsORsV28+GbXWbIKZKxjUTMpxk3Enph0UnOLuEGaKEzO40ODyCkq5fMdMXpHESZMinETUdlEEdJK7yjiEqHeLRjV2ZPPI2Pk6ljUSIpxE1BmUKw/ksSwkNY42FjpHUdU46kRHcgpLOUzuToWNZBi3ARIE4XpC/VuwehQT77YESPPyRPVkmLcBKw7nIidtYU0UZi4p4Z3JKeolM8i5epYXE6KsZkrKTOw7nAiwzt5ShOFievs7cKYUC+5OhbVkmJs5rafvEBaXjHje/joHUXUwlMjOpBTVMpCuStPXEKKsZn7cX8Cbg7WDOooTRTmoFMbF27s1obPdsTIXXmiCinGZiynsISNUUnc3N0bGyv5ozQXz4wKpqTMwIJNJ/WOIkyInMFm7OcjSRSVGrg1TJoozEk7D0fu6u3H0j1xxMiIbqKCFGMztvJAPP4tHeSJHmboieFBWFta8ObG43pHESZCirGZSsgsYOfpNG7p4SMPHTVDrZ3teGhgO9YeSuTQ+Uy94wgTIMXYTH3/x3mUgtt7+uodRdTTQ4Pa4+5ow2s/R+sdRZgAKcZmyGBQLNsbR/+glrR1d9A7jqgnZztr/m9oEJGn0th+8oLecYTOpBibocjTqcRnFnBnLz+9o4hrdE8fP3zd7Jm/PhqDQekdR+hIirEZWro3DlcHa0Z19tQ7irhGtlaWTB/VkaiEbH46lKB3HKEjKcZmJj2vmI1RSYwP85Hn3DURt3T3oVMbF97aeILiUoPecYROpBibmRV/nqekTHFnr7Z6RxENxMJC49kxwZxLz2fJnnN6xxE6kWJsRgwGxde/n6WnvxshXi56xxENaEjHVvRp786CTSfJLSrVO47QgRRjM7L15AXOpuUzqV+A3lFEA9M0jefHdiItr5gPN5/SO47QgRRjM/LVzlhaOdsyJtRL7yjCCLq3dWXCdT58tj2Gc2n5escRjUyKsZmITc1jy4kL3N3bTwYFasJmjgnBylLjP+uO6h1FNDI5q83EN7+fxVLTuPt66VvclHm62PHYkEA2RCWz83Sq3nFEI5JibAZyi0pZti+O0V288HSx0zuOMLIHB7bH182el386SmmZdHVrLqQYm4Gle86RU1jKwwPb6x2FlStX0q1bN2xtbWnXrh1vv/32FZefOnUqmqbxzDPPVJkeHR3N9ddfT4sWLZg4cSK5ublV5m/btg0fH5/Lpldn8eLFaJpW7bIRERF4eHhUvo+NjUXTtMqXo6MjgYGB3HPPPWzfvv2y9SdPnkx4ePhVMzQkO2tL/n1DJ6KTcli6N65R9y30I8XYxJWUGfh8RwzXt3Onu85DZUZGRjJhwgR69+7NTz/9xJQpU5g5cybvvvtutcsfPXqUzz77DBeXy7vhTZ48maCgIL777juOHj3KvHnzKucZDAaeeuopXn31VZycnIxyLG+++Sa7du1i3bp1zJo1i7S0NAYNGsScOXOMsr+6GtvFi97t3Hn7lxNkFcjz8poFpVR9XqKRrPgzTvnPXKM2HUvSO4oaNWqUGjBgQJVp06ZNU25ubqqoqOiy5YcNG6ZefPFF5e/vr6ZPn145PScnRwEqJSVFKaXU0qVLVXh4eOX8hQsXql69eimDwVCrXF988YUCVE5OzmXzZs+erVq2bFn5PiYmRgHqp59+umzZWbNmKUBt3ry5ctqkSZNUz549a5WjoR2Jz1QBz61RL/8Upcv+hVHUWFflytiEKaX4ZOsZOrR2YkjH1nrH4cCBA4wcObLKtFGjRpGRkcGuXbuqTP/++++Jjo7mueeeu2w7xcXFANjb2wPg4OBQOS07O5sXX3yR9957r9HHaZ49ezbe3t7897//bdT91iTUuwUTe7Xly52xnEq5enONMG9SjE3Y9pOpRCfl8NCg9lhY6D+AfGFhITY2NlWm/fX+2LFjldMKCgqYPn068+fPx9HR8bLtuLu7ExAQwPvvv096ejqffvppZbvsK6+8wogRI+jbt2+d85WVlVFaWlrlZTDU/gcwS0tLhg0bxu+//17nfRvL9FHB2Ftb8p+10tWtqbPSO4Co2SfbTuPpYsstPbz1jgJAUFAQe/furTJtz549AKSnp1dOe/XVV2nTpg333ntvjdv66KOPuP322/n3v/9Nhw4d+PDDDzl16hSLFi3i8OHD9crn6lp9m3rLli1rvQ1fX1+Sk5PrtX9j8HCy5cnhHfjPumNsiEpitNzw02TJlbGJ+uNsBpGn0nhgQDtsrUxjdLZHHnmElStXsnDhQjIyMtiwYUNlbwoLi/KvUkxMDG+++eZVmxnGjh1LSkoKx48f59ixY/j5+TFt2jSmTp2Kr68vH374IX5+fvj5+fHRRx/VKt+2bdvYu3dvlddDDz1Up2NUyvTGFJ7cP4AQL2ciVkfJuBVNmFwZm6gFm07i7mjDvX389Y5SacqUKRw8eJBHH32Uhx9+GAcHB1577TWeeOIJvLzKr9iee+45xo4dS3BwMJmZ5c92MxgMFBUVkZmZSYsWLSqLtIODAx07dgTgl19+4eDBgyxbtoyDBw8ya9Ysdu7cCUDfvn0ZMGAA3bp1u2K+sLCwy3pfrFmzpk7HGB8fj6enaY0TbW1pwbwJXbnt4528tfE4s28O1TuSMAK5MjZBB+Iy2XriAg8NbI+Djen8fWlpackHH3zAhQsXOHToEMnJyfTp0weg8r/Hjx9nxYoVuLm5Vb7i4uL44IMPcHNzIz4+/rLtlpWVMXXqVF5//XXs7e3ZsmULw4YNIyQkhJCQEIYPH87WrVuNfnylpaX89ttv9WqvNrbr/Ny493p/vtwZKw8wbaJM50wXlRZsOomrgzX39TWdq+KL/VVkobztt1+/foSEhACwaNGiy26+mDhxIoMHD+bRRx+lVatWl23v448/xs3NjTvvvLNyWn7+3wPl5OXlNUrzwcsvv0xCQgKPPPKI0fdVHzPGBLMhKonnVxxm1eP9sbKUa6mmRIqxiTl8PovfolOYMToYJ1vT+uP5/fff2bFjBz169CA7O5slS5awYcMGduzYUblMdXer2dnZ0bZtW4YMGXLZvPT0dObMmcOGDRsqpw0aNIhnn32Wzz//HKUUv/32G/Pnz2/QYzl+/DgeHh4UFxcTExPD0qVL+fnnn4mIiGDw4MENuq+G4mJnTcS4UB779k8W74zlQRO4I1M0HNM62wXvbTqJi50V/zTBq2Jra2uWLVtGREQEFhYWDBw4kMjISLp27VrvbUZERDBu3Diuu+66ymlhYWG8/vrrvPDCC0D53XLdu3e/5vwX++v2bDs7O9q0aUPfvn3Ztm0bAwcObND9NLSxXbwYFtKat385wZguXvi6ydPBmwqtnv/8M72fnJuAI/FZ3PT+DqaO6MhTIzroHUeYqPMZ+Yx+ZxvX+bvx1ZTejX5zjLgmNf5hSaOTCXn/t5M421kxuX+A3lGECfN1c+C5Gzqx/WQqy2QgoSZDirGJOBKfxYaoZO7v344W9tZ6xxEm7p7efvRt35K5a4+RkFmgdxzRAKQYm4g3Nx6nhb01Dwxop3cUYQYsLDRe/0c3DErx/IrDJnmziqgbKcYmYE9MOluOX+DRIYFyVSxqra27AzPHhLD1xAWW/3Fe7zjiGkkx1plSijc2RNPK2ZZJfQP0jiPMzH19/Ondzp1X1hwlKatQ7zjiGkgx1tnWExfYG5vBk8OCsLcxjTEohPmwsNB44x/dKCkz8PyKQ9JcYcakGOvIYFC8seE4vm723NlLHjQq6se/pSMzx4Sw+fgFftx/+e3mwjxIMdbR+iNJRCVkM3VER2ys5I9C1N+kvgH09JQWN/0AABWhSURBVHfj5TVHuZBTpHccUQ9SAXRSWmbgrV+O06G1E7eG+egdR5g5CwuN127rRn5xGbNXH9E7jqgHKcY6+W7fec5cyGP6qGAsTeApHsL8BbV24ukRHVh3OIn1hxP1jiPqSIqxDnKLSnn7lxP0CnBjdKhpjZ0rzNvDA9vTxceFWauiyMgr1juOqAMpxjr4ZOtpUnOL+PcNnWRcAdGgrCwteP227mTmFzN37bGrryBMhhTjRpaYVcDC7We4ubs3YX5uescRTVBnbxceHtSeH/48z67TaXrHEbUkxbiRvbHhOAYFz44O1juKaMKeGNaBtu72vLjyMEWlZXrHEbUgxbgRHYnP4sf98dzfP4C27jIOrTAeextLXh7XhdMX8li47YzecUQtSDFuJEop/rP2GG4ONjw+NEjvOKIZGBrSmhu6evH+b6c4m5andxxxFVKMG8mmYynsOpPG0yM64GIngwGJxvHSTaFYW1rw4sojcqu0iZNi3AiKSw3MW3+M9q0cuau33PYsGo9XCzumj+rI9pOprJW+xyZNinEj+CIyhjMX8njxxk5YyxN9RSO7r48/ndu48Mqao+QWleodR9RAKoORJWYV8N6mk4zo1JphIXKDh2h8VpYWvHJrF5Kzi3jv1xN6xxE1kGJsZP9Ze4wyg2L2zaF6RxHNWE9/N+4Mb8vnkbEcT8rRO46ohhRjI4o8lcqaQ4k8OiRQurIJ3c0cG4KznRWzVsmPeaZIirGRFJcamL06irbu9jwyOFDvOELg7mjDzDEh7IlJl3GPTZAUYyP5bEcMp1Jyibg5FDtreYKHMA13hrelR1tX5q07RlZBid5xxEWkGBtBbGoe7/56gpGdPRneSX60E6bDwkJj7q1dSM8r5u2Nx/WOIy4ixbiBqYpHp9tYWvDKLV30jiPEZbr4tODePv58/ftZjsRn6R1HVJBi3MCW7zvPrjNpPHdDCF4t7PSOI0S1po8Kxt3RhhdXHsFgkB/zTIEU4waUklPI3LVH6d3OnbvkAaPChLWwt+b5sZ04EJfJd/vi9I4jkGLcoCJWR1FYauDVCV2xkEcpCRM34Tofege4M//naNLlqSC6k2LcQH46mMC6w0k8NbwDga2c9I4jxFVpmsYrt3Yhp7CU13+O1jtOsyfFuAEkZRXy4soj9Gjryr8Gtdc7jhC1FuzlzJT+ASzdG8ef5zL0jtOsSTG+RgaDYsb3BykuNfDOnT2wkoGAhJl5akRHPF1smbXyCKVlBr3jNFtSOa7RV7ti2X4ylRdv6kQ7D0e94whRZ062Vsy+OZSohGw+3nJa7zjNlhTja3A0IZtX10czLKQ1d8s4xcKM3dC1DeO6e/PeppMcPi99j/UgxbiesgpKePTbP3B1sOa127qhadJ7Qpi3V27pgoeTLU8v209hiTzEtLE1iWJ89OhRhg8fjoODA97e3rz00kuUlV35y7R3717uv/9+goKCcHBwIDg4mDlz5lBYWFhluX379jF58mSCg4OxsLBg8uTJKKV4ZvlB4jMK+PDu62jlbGvMwxOiUbRwsObN27tz+kIeEaujWLVqFV27dsXOzo7OnTuzbNmyq25j+fLljBs3Dh8fH5ycnOjZsydLliy5bLns7GyefvppAgICcHBwoFOnTrz77rvNejQ5K70DXKuMjAxGjBhB586dWbVqFadPn2b69OkYDAbmzp1b43rLli3j9OnTzJw5kw4dOnDo0CFmzZrFoUOH+OGHHyqXi4yMZMeOHfTp04ecnPJxYN//7RS/HE3mpZs6Ex7gbvRjFKKxDOjgwWNDAnn7m9W8sfTfPP7YYyxYsIB169Zx11134ebmxqhRo2pc/+2336Zdu3a88847eHh4sG7dOu6++25SU1N54oknKpebPHky27ZtY968eQQFBbF582amTZuGUoqpU6c2xqGaHqVUfV4mY968ecrV1VVlZWVVTnvttdeUvb19lWmXunDhwmXTPvnkEwWo2NjYymllZWWV/9+zZ0815KZ/KP+Za9TUpfuVwWBooKMQwnSUlhlUm9Drlb1/N/Xn2fTK6WPHjlX9+/e/4rrVnVd33XWXCggIqHyfl5enLCws1IIFC6osN378eNW7d+9rTG/yaqyrZt9MsX79ekaPHo2Li0vltIkTJ1JQUMDWrVtrXM/Dw+OyaWFhYQAkJCRUTrOw+Psjyi0q5Y+zGfQPasl8aScWTVRpSTGpJ/6kTdgw/vX1H8Sl5wPl59WuXbvIyqr5B76azquLz6mysjIMBgMtWrSospyrq2uzbqYw+2IcHR1NSEhIlWl+fn44ODgQHV23u4p27dqFhYUFgYGXDwa/83QqZ9Pycbaz5uN7e2JjZfYfnRDVOn36NCUlJUTcN5LiMgP3LNpNSnYhnTp1wmAwcOJE3Z6jt2vXLjp27Fj53tnZmTvuuIPXX3+dAwcOkJOTw5o1a/juu+94/PHHG/pwzIbZV5SMjAxcXV0vm+7m5kZGRu3vKEpKSmLu3Lncd999tG7dusq8LcdTuP+LvVhbagzs4IGLnfU15xbCVP113nRt780Xk3uRmlvExIW/U2RpX2V+bWzatImVK1cyffr0KtO/+uorQkJCCAsLw8XFhXHjxjFr1iwmTZrUcAdiZsz+B7yGUFxczB133IGTkxPvvPNO5XSlFF/ujOWVtccI9nTGvpWTPLVDNCthfm58OaU3Uxbv5Yn//VmndWNjY7n77ru55ZZbmDx5cpV5U6dOZffu3XzxxRe0b9+eHTt2EBERgYeHBw888EADHoH5MPti7ObmVm0bVkZGBm5ublddXynFP//5T6KiooiMjKxcJyu/hJdWH2HVgQRGdPLk3Yk9GPK1tBGLpq/yHKg4r3oFuPPdv/py28tfA7AvsZiRSl3xN5P09HTGjh2Lv78/3377bZV5hw4d4uOPP2bjxo2MHDkSgEGDBpGTk8MzzzzD/fffX+W3mubC7I84JCTksrbhuLg48vPzL2tLrs7TTz/NqlWrWLVqFSEhIRgMih/3n2fUu1tZeyiRaSM78ul9PXGyNfu/t4SolcDAQKytraucV53auPB4mD2aZsF/D+QzZfFezqXlV7t+fn4+N910E8XFxaxZswYHh6pPRv9ruz169KgyPSwsjMzMTNLS0hr4iMyD2RfjsWPHsmHDhso+wFDeh9je3p7Bgwdfcd1XX32VDz74gG+++Yb+/fuz9cQFbv0okqnLDtLK2ZYfH+vPk8M7yNjEolmxtbVl6NChLF++vMr09atX0LdfX16aEM6emHRGvrOV+eujScn5+0ap0tJSbr/9dk6ePMnPP/982e8vAP7+/gD8+WfVZo8//vgDR0fHantkNAtX6vd2hZfJSE9PV15eXmrEiBHql19+UZ988olydHRUL7zwQpXlAgMD1ZQpUyrff/vttwpQ9/7zn2r2whUq/MkPlde9b6rQRxaoz389oMrKyvsQp6SkqOXLl6vly5er9u3bqyFDhlS+F6Kp2r59u7K0tFRPPfWU2rx5s5oxY4bSNE1t2LBBKaVUYmaBun/BGoVmoTxvnq6e++GgOnAuQz344IMKUO+9957atWtXlVdhYaFSSqnS0lIVHh6uvL291aJFi9SmTZvUnDlzlI2NjZoxY4aeh90YaqyrZl+MlVIqKipKDR06VNnZ2SkvLy/14osvqtLS0irL+Pv7q0mTJlW+v23iPQqo9vXFF19ULrd58+YalxOiKfvxxx9VaGiosrGxUcHBwWrJkiVV5sfExChA3fD4Kyr4xXXKf+YaZefmVeP5EhMTU7luYmKieuCBB5Sfn5+yt7dXISEhat68eaqoqKiRj7LR1VhXNVW/TtZm2TPbYFBsPXmBr3bGsuXEBSw1jdGhXtzfP4Ce/m5yE4cQ9ZRdWMKag4l8ty+OA3GZWFtqjAr14p7efvRp31Ka+v5W4wfRbIrxztOpzF8fzaHzWbRytuXu3n7cfb0fni7yBGchGtKJ5ByW7oljxf7zZOaXENDSgYm9/bgzvC1ujjZ6x9Nb8y3GxxKzmb8+mq0nLuDdwo6pIztySw8fuYNOCCMrLCnj5yNJ/G/POfbEpGNvbcnt4b48MKAd/i2b7YMYml8xjs8s4K2Nx/lxfzzOtlY8PjSISf0C5KYNIXRwPCmHRdvPsOpAAiUGA6M6e/LwoPb09G92ox42n2KcmV/MR1tOs3hnLAD39wvgsSFBtHCQW5iF0FtKTiFf7TzLN7vPkplfQpifKw8MaMeYUK/m8vzIpl+MC0vKWLwzlo82nyKnqJQJYb5MG9URH1d7vaMJIS6RX1zKD3+c57MdMcSm5ePjas/9/QO4o1fbpj72S9MtxiVlBlb8eZ73fj1JQlYhQ4JbMXNMCJ3auFx9ZSGErsoMit+iU1i0/Qy7Y9JxsrVifJgPd/ZqSxefFlffgPlpesW4pMzAyv3xvP/bKc6l59PdtwUzx4bQL7CZ3r0jhJk7fD6LLyJjWHs4kaJSA6HeLtze05exXds0pV5PTacYp2QX8r8951iy5xzJ2UV08XFh6oiODAtpLf2EhWgCsvJLWHUwniV74jiWmA1AmJ8ro0O9GBrcmg6tncy537J5F+P0vGJ+OZrE+iNJ7DiZSqlBMbhjKyb182dosOkV4YiICObMmaN3DCGuavbs2UREROgdo1pKKU6m5LLhSBIbjiZxJL68MLs72tA7wJ3e7dzp7O1CsKezOfVfrrFYmdxQZEopUnOLOZKQxe4z6fx+Jo3D8VmUGRS+bvY8MKAdE3v70c6j2fZTFKJZ0DSNjp7OdPR05onhHYjPLGDnqVR+P5PO7pg0fo5Kqly2tbMtwV7O+Ld0wNfNAV83e9pW/Nfd0cbkLtiq06jFODW3iJTsIopKyygqNZBXVEpKThHJ2YUkZxdx5kIuJ5JzyMgvAcDaUqO7ryuPDQlkdKgXod4uZvGhCiEano+rPbeHt+X28LYAJGUVcjw5h+NJ2UQn5XAyOZfD8YlkVtSPvzjYWOLtao+Xix2tXWzxcrHDq4Udni7lLy8XOzycbHTvWteozRTv/nqCd389We28lo42BHg40tHTiQ6tnQnxcqaHnysONiZ38S6EMGHZhSXEZxRwPqOAuPR8zmcUEJ+ZT3J2+YVfSk4RZYaqJcxCAw8nW9wcbHC2s6p4WeNsZ4WDjSVWlhZYWWhYWmiM6uxFZ+9699YyjTbjk8k5nL6Qh621BbaWFjjYWuHpYouHky3WzaPDtxBCZ2UGRVpeEclZ5cU5Kbuw4l/nhWQVlJBTWEp2Yfl/cwpLKSguo8ygKDEYUAreur07t/X0re/uTaMYCyGEOTNUXFFfQ28OKcZCCGECaizG0jYghBAmQIqxEEKYACnGQghhAqQYCyGECZBiLIQQJkCKsRBCmAApxkIIYQKkGAshhAmo100fc+bM+RmozSju3kBCnXdgOiS/viS/viR/w0udPXv2mGrnKKWM9oqIiFDG3L6xX5Jf8kt+/XM0l/zSTCGEECbA2MXY3B93Ifn1Jfn1JfkbUX0HChJCCNGApJlCCCFMgBRjIYQwAVKMhRDCBNS6GGua9pimaTGaphVqmvaHpmkDr7BsG03T/qdpWrSmaWWapi2uYbmnKpYp0DTtvKZpH2qa5lSP42jo/BM0TduoadoFTdNyNE3brWnauGqWu03TtKOaphVV/He8MbIbI7+maQ9pmrZd07QMTdMyNU3brGnaAHPJf8nyd2mapjRNW2Oc9Eb7/rhomrZA07SEiu/QKU3T7jCj/KZ6/g7WNG2npmlpFdmiNU17pprlGu38rZXa9H8D7gRKgIeATsD7QC7gV8PyAcACYDKwE1hczTJ3A0XAfRXLDwNigM8auv9ePfK/BzwH9AaCgNlAGTDwomX6AqXACxXbfKHi/fVmkv9b4P+AMCAY+C+QB3Qwh/wXLdseOA9sA9YYo/+nkT5/a2A3sB4YUHEODAB6mUl+Uz5/ewITgVCgHXBvxXf7sYuWabTzt9bHWcsPYzew8JJpJ4FXa7HuGqovxh8AWy+ZNgc4YoQ/zHrnv2j5PcBbF71fBvxyyTK/AkvMIX818zUgCXjCXPJfVNAmAYsxXjE2xvfnYeAMYGOMzI2Q39zO3xUXn5uNef7W9nXVZgpN02wo/5tm4yWzNgL9rrb+FewAemia1qdiP37AOGDdNWzzMg2Y3xnIuOh932q2uaGO27wqI+a/lA1gd5Vl6szI+f8DxCqlvqx/wiszYv5bgUjgfU3Tkir+mRyhaZr1NQW+hBHzm835q2laWMWyWy+a3Cjnb13Ups3YA7AEki+Zngx41XfHSqmlwL+BbZqmlQBngcPAzPpuswbXnF/TtMcBX+DriyZ7Xcs268BY+S81l/J/+q2uR8YrMUp+TdNGAXcA/2qYmDUy1uffHrid8qv7G4FZwCPAq9eY91JGyW8O529FO3YRsA/4SCn134tmN9b5W2u69abQNG0w5V/Ax4DrgAnAEEzsrhlN024D3gDuVkqd1TtPXdUmv6ZpT1Fe1CYopbIbM9/VVJdf07RWlDdLTFJKZeoY76qu8PlbACnAQ0qpP5RSPwAvAY9qmlbv58A3tJrym8n5OxAIp/wvuac1TbtP5zxXZFWLZVIpb7z3vGS6J+VtjPU1l/L2mUUV7w9rmuYILNI07WWlVOk1bPti9c6vado/gK+AfyqlfrpkdlJ9tlkPxsr/1zJPA68AY5VSe6497mWMkT8UaANsuqhuWVSsUwqEKqWOX3t0wHiffyJQopQqu2jaMcCB8qvBC9cS+iLGym/y569SKuaibJ5ABH9f3TfW+VtrV70yVkoVA38AIy+ZNZLynhL15UD5h3yxMsp/SGow9c1f0cXoa2CyUur7ahbZVddt1ocR86Np2jTKC/GNSqkdDZO4KiPl3wt0BXpc9FoNbK/4/xgaiBE//0ggSNO0i8/BjkA+5QWoQRgxv0mfv9WwAGwvet8o52+d1PKXyDuBYuBByruBvEd5+6J/xfyvgK8uWeevk2Qb5SdKD6DzRfMjgGzKu6C0o/yDOAX8YIRfY+uUvyJTCfAU5W1If73cL1qmH+VdYZ4DQoDnK9YxVte2hs4/o2Kbd1yyTAtzyF/NPhZj3K5tDf35t634/r9PedfC0ZR30XvDTPJHYLrn7xPATUCHitcDFVnnX7RMo52/tT7OOnwgjwGxlPct/AMYdNG8LcCWS5ZX1bxiL5pvRXn/xZNAARAHfAS4GemEqnX+ivfV5b/0GP8BRFd8UY5R3uZqnD+oBs5fsa3qlllsDvmr2f5ijFSMjfj96UP5lVgB5VfzL2Okrm5G+P6Y8vn7NBBFed/iLODPivUtLtlmo52/tXnJqG1CCGECZGwKIYQwAVKMhRDCBEgxFkIIEyDFWAghTIAUYyGEMAFSjIUQwgRIMRZCCBMgxVgIIUyAFGMhhDAB/w/sw2eFhD223QAAAABJRU5ErkJggg==\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "az.plot_posterior(idata);\n" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "id": "qzMM2DDMkwFp", "outputId": "271ad45d-f8dc-4e61-b6a7-6545d760ce97", "colab": { "base_uri": "https://localhost:8080/", "height": 298 } }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "az.plot_forest(idata, r_hat=True);" ] }, { "cell_type": "markdown", "metadata": { "id": "q-9GLzXrkwFq" }, "source": [ "## Exemplo: normal com dados simulados\n", "\n", "Fonte: https://docs.pymc.io/pymc-examples/examples/pymc3_howto/api_quickstart.html" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "id": "V8XSZFGMkwFq" }, "outputs": [], "source": [ "with pm.Model() as model:\n", " mu = pm.Normal(\"mu\", mu=0, sigma=1)\n", " obs = pm.Normal(\"obs\", mu=mu, sigma=1, observed=np.random.randn(100))" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "id": "T5kCv7eTkwFr", "outputId": "88c5801f-b3b0-479a-9129-d987535cf162", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "[mu ~ Normal, obs ~ Normal]" ] }, "metadata": {}, "execution_count": 29 } ], "source": [ "model.basic_RVs" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "id": "-MFaJqKykwFr", "outputId": "c1c01c26-9c73-4bf4-daf8-1928efe33e29", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "[mu ~ Normal]" ] }, "metadata": {}, "execution_count": 30 } ], "source": [ "model.free_RVs\n" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "id": "5gkuBJAnkwFs", "outputId": "9d68a65e-1207-4c61-d501-d6f85d34c98d", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "[obs ~ Normal]" ] }, "metadata": {}, "execution_count": 31 } ], "source": [ "model.observed_RVs" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "id": "PQHOR4oAkwFs", "outputId": "ee1e5852-528c-44ce-9616-ff82e9f0513b", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array(-151.48535177)" ] }, "metadata": {}, "execution_count": 32 } ], "source": [ "model.logp({\"mu\": 0})\n" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "id": "NWOebzswkwFt", "outputId": "301a1975-b511-48be-f4d2-9ecdecbc1321", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "10 loops, best of 5: 98.5 ms per loop\n", "The slowest run took 4.41 times longer than the fastest. This could mean that an intermediate result is being cached.\n", "10000 loops, best of 5: 30.3 µs per loop\n" ] } ], "source": [ "%timeit model.logp({mu: 0.1})\n", "logp = model.logp\n", "%timeit logp({mu: 0.1})" ] }, { "cell_type": "markdown", "metadata": { "id": "C0q06HVHkwFt" }, "source": [ "### Variáveis aleatórias não observáveis" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "id": "Y_IH0NbVkwFu" }, "outputs": [], "source": [ "with pm.Model():\n", " x = pm.Normal(\"x\", mu=0, sigma=1)\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "QHsWTkFOkwFu" }, "source": [ "### Variáveis aleatórias observáveis" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "id": "O4DDHDaSkwFv" }, "outputs": [], "source": [ "with pm.Model():\n", " obs = pm.Normal(\"x\", mu=0, sigma=1, observed=np.random.randn(100))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "W54DCJZekwFv" }, "outputs": [], "source": [ "obs.observations" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "id": "E5ET8D-IkwFw", "outputId": "5b7900e6-35ab-4461-d94a-3e625839882d", "colab": { "base_uri": "https://localhost:8080/", "height": 347 } }, "outputs": [ { "output_type": "stream", "name": "stderr", "text": [ "/usr/local/lib/python3.7/dist-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n", " warnings.warn(msg, FutureWarning)\n" ] }, { "output_type": "execute_result", "data": { "text/plain": [ "" ] }, "metadata": {}, "execution_count": 36 }, { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "import seaborn as sns\n", "sns.distplot(obs.observations, hist=False)" ] }, { "cell_type": "markdown", "metadata": { "id": "zvfRjMXQkwFw" }, "source": [ "## Inferência" ] }, { "cell_type": "markdown", "metadata": { "id": "vxX0OUAfkwFw" }, "source": [ "### Amostragem" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "id": "AcXJhpUgkwFx", "outputId": "1e37a198-8112-45c5-db07-8dc84dbe2e46", "colab": { "base_uri": "https://localhost:8080/", "height": 198 } }, "outputs": [ { "output_type": "stream", "name": "stderr", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Sequential sampling (2 chains in 1 job)\n", "NUTS: [mu]\n" ] }, { "output_type": "display_data", "data": { "text/plain": [ "" ], "text/html": [ "\n", "\n" ] }, "metadata": {} }, { "output_type": "display_data", "data": { "text/plain": [ "" ], "text/html": [ "\n", "
\n", " \n", " 100.00% [3500/3500 00:02<00:00 Sampling chain 0, 0 divergences]\n", "
\n", " " ] }, "metadata": {} }, { "output_type": "display_data", "data": { "text/plain": [ "" ], "text/html": [ "\n", "\n" ] }, "metadata": {} }, { "output_type": "display_data", "data": { "text/plain": [ "" ], "text/html": [ "\n", "
\n", " \n", " 100.00% [3500/3500 00:02<00:00 Sampling chain 1, 0 divergences]\n", "
\n", " " ] }, "metadata": {} }, { "output_type": "stream", "name": "stderr", "text": [ "Sampling 2 chains for 1_500 tune and 2_000 draw iterations (3_000 + 4_000 draws total) took 5 seconds.\n" ] } ], "source": [ "with pm.Model() as model:\n", " mu = pm.Normal(\"mu\", mu=0, sigma=1)\n", " obs = pm.Normal(\"obs\", mu=mu, sigma=1, observed=np.random.randn(100))\n", "\n", " idata = pm.sample(2000, tune=1500, return_inferencedata=True)\n" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "id": "dqZYGF6FkwFx", "outputId": "8b462b91-a875-4d2f-f7e4-70f02ddf8f71", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "Frozen(SortedKeysDict({'chain': 2, 'draw': 2000}))" ] }, "metadata": {}, "execution_count": 38 } ], "source": [ "idata.posterior.dims" ] }, { "cell_type": "markdown", "metadata": { "id": "Knn28rZskwFy" }, "source": [ "### Amostragem com 6 cadeias em paralelo" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "id": "6Llsm0HAkwFy", "outputId": "3b98507f-419d-4a31-cdf7-be5c796dc778", "colab": { "base_uri": "https://localhost:8080/", "height": 161 } }, "outputs": [ { "output_type": "stream", "name": "stderr", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (6 chains in 4 jobs)\n", "NUTS: [mu]\n" ] }, { "output_type": "display_data", "data": { "text/plain": [ "" ], "text/html": [ "\n", "\n" ] }, "metadata": {} }, { "output_type": "display_data", "data": { "text/plain": [ "" ], "text/html": [ "\n", "
\n", " \n", " 100.00% [12000/12000 00:10<00:00 Sampling 6 chains, 0 divergences]\n", "
\n", " " ] }, "metadata": {} }, { "output_type": "stream", "name": "stderr", "text": [ "Sampling 6 chains for 1_000 tune and 1_000 draw iterations (6_000 + 6_000 draws total) took 11 seconds.\n" ] } ], "source": [ "with pm.Model() as model:\n", " mu = pm.Normal(\"mu\", mu=0, sigma=1)\n", " obs = pm.Normal(\"obs\", mu=mu, sigma=1, observed=np.random.randn(100))\n", "\n", " idata = pm.sample(cores=4, chains=6, return_inferencedata=True)\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "Gt2TULQCkwFy" }, "outputs": [], "source": [ "idata.posterior[\"mu\"].shape\n" ] }, { "cell_type": "markdown", "metadata": { "id": "rD8wf8CukwFz" }, "source": [ "### Podemos incluir passos com outros métodos " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "wFJmIbkZkwFz" }, "outputs": [], "source": [ "with pm.Model() as model:\n", " mu = pm.Normal(\"mu\", mu=0, sigma=1)\n", " obs = pm.Normal(\"obs\", mu=mu, sigma=1, observed=np.random.randn(100))\n", "\n", " step = pm.Metropolis()\n", " trace = pm.sample(1000, step=step)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "Jun2pgETkwF0" }, "outputs": [], "source": [ "with pm.Model() as model:\n", " mu = pm.Normal(\"mu\", mu=0, sigma=1)\n", " sd = pm.HalfNormal(\"sd\", sigma=1)\n", " obs = pm.Normal(\"obs\", mu=mu, sigma=sd, observed=np.random.randn(100))\n", "\n", " step1 = pm.Metropolis(vars=[mu])\n", " step2 = pm.Slice(vars=[sd])\n", " idata = pm.sample(10000, step=[step1, step2], cores=4, return_inferencedata=True)\n" ] }, { "cell_type": "markdown", "metadata": { "id": "WSdS-h2JkwF0" }, "source": [ "### Análise de resultados" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "id": "Bi1VGSOHkwF1", "outputId": "3cb53135-0a9c-4f94-e25b-ed21a59d35f0", "colab": { "base_uri": "https://localhost:8080/", "height": 169 } }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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}, "metadata": { "needs_background": "light" } } ], "source": [ "az.plot_trace(idata);\n" ] }, { "cell_type": "markdown", "metadata": { "id": "k_k21Z_ZkwF1" }, "source": [ "### Estatística de Gelman-Rubin (R chapéu)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "id": "kmZ48TEHkwF1", "outputId": "863fd4e6-a7ab-4d8f-b43b-35a6fc846da1", "colab": { "base_uri": "https://localhost:8080/", "height": 80 } }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ " mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail \\\n", "mu 0.17 0.098 -0.012 0.353 0.002 0.001 2628.0 4116.0 \n", "\n", " r_hat \n", "mu 1.0 " ], "text/html": [ "\n", "
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meansdhdi_3%hdi_97%mcse_meanmcse_sdess_bulkess_tailr_hat
mu0.170.098-0.0120.3530.0020.0012628.04116.01.0
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "az.plot_forest(idata, r_hat=True);\n", "\n", "az.plot_posterior(idata);\n" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "id": "Lx2gUcxLkwF2", "outputId": "503e7321-bce2-4eb3-fdf9-021524897024", "colab": { "base_uri": "https://localhost:8080/", "height": 287 } }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" 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