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    \n", + "
  • 对每一个对话(i)观测计数数据(y)\n", + "
  • 数据由一个随机过程产生,我们认为可以用泊松分布模拟\n", + "
  • 泊松分布只有一个参数,介于 0 到 60 之间\n", + "
  • 均匀分布的原因在于并没有提及任何条件" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**马尔可夫链蒙特卡洛方法MCMC**\n", + "\n", + "贝叶斯公式的只是一个参数,但如果我们的问题涉及到多个参数呢?分布的积分就应该改成多重积分,但是难点在于我们该怎么算,MCMC采样器从先验分布中选取参数值,计算从这些参数值决定的某个分布中得到观测数据的可能性。这个计算可以作为MCMC采样器的导引。从参数的先验分布中选取值,然后计算给定数据条件下这些参数值可能性——导引采样器到更高概率的区域。与上面讨论的频率论优化技术在概念上有相似之处,MCMC采样器向可能性最高的区域运动。但是,贝叶斯方法不关心寻找绝对最大值,而是遍历和收集概率最高区域附近的样本。所有收集到的样本都可认为是一个可信的参数\n", + "\n", + "**蒙特卡洛方法**\n", + "\n", + "是一系列应用非常广泛的算法,其思想是通过随机采样来计算或模拟给定过程。尽管很多问题都难以求解甚至没办法用公式表达,但我们可以通过采样或者模拟来有效地研究\n", + "\n", + "统计模拟中有一个重要的问题就是给定一个概率分布p(x),如何在计算机中生成它的样本。其基本思想是通过大量取近似得到想要的答案。有一个经典的试验就是计算圆周率,在一个边上为1的正方形中画一个内切圆,现在在正方形内产生大量随机数,最后我们只需要计算圆内点的个数比上总体的个数,便得到了圆周率的值。" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# 每次结果会不一样,样本越多必然也会越准确,可以尝试把N值改小改大\n", + "N = 10000\n", + "\n", + "x, y = np.random.uniform(-1,1,size=(2,N))\n", + "inside = (x**2 + y**2) <= 1\n", + "pi = inside.sum()* 4 / N\n", + "error = abs((pi - np.pi) / pi) * 100\n", + "\n", + "outside = np.invert(inside)\n", + "\n", + "plt.plot(x[inside], y[inside], 'b.')\n", + "plt.plot(x[outside], y[outside], 'r.')\n", + "plt.plot(0,0,label='$\\hat \\pi$ = {:4.3f}\\nerror = {:4.3f}%'.format(pi, error), alpha=0)\n", + "plt.axis('square')\n", + "plt.legend(frameon=True, framealpha=0.9,fontsize=16)" + ] + }, { "cell_type": "code", "execution_count": null,