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技术 2022年11月11日
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第1章 从随机变量采样

  研究者提出的概率模型对于分析方法来说通常比较复杂,研究者处理复杂概率模型时越来越依赖计算、数值方法,通过使用计算方法,研究者就不用对一些分析技术做一些不现实的假设(如正态性和独立性)。

  大多数近似技术的关键是能够从分布中采样。需要采样来预测一个特别的模型在一些情景下是什么样的,找到在实验数据上应用模型的隐变量(参数)的合适值。大部分计算采样方法把从复杂分布采样的问题转化为简单采样分布的子问题。本章我们将介绍两种采样方法:逆变换方法和拒绝采样。这些方法适用于大多数单变量单值输出,下一章我们将讨论马尔科夫链蒙特卡罗方法,能够有效处理多变量分布。

1.1 标准分布

  一些常用的分布就成了matlab支持的分布标准集的一部分。matlab统计工具箱支持大量的概率分布,使用matlab可以很容易计算概率密度、分布的累积密度以及从这些分布中采样,Table 1.1列举了matlab支持的一些标准分布,Matlab文档列举了更多可以用matlab模拟的分布。使用在线文档,很容易找到对其它常见分布的支持。

《Computational Statistics with Matlab》硬译

  为了演示如何使用这些函数,Listing1.1展示了Matlab代码可视化Normal(µ,σ)分布,其中 µ = 100,σ = 15。为了帮助理解,想象这个分布代表人口的智商分布,代码演示了如何显示概率密度和累积密度,也演示了如何从分布中提取随机值,以及如何使用hist函数可视化这些随机采样的分布,代码产生的输出显示在Figure 1.1。

Listing1.1:可视化正态分布的Matlab代码

mu = ;
sigma = ;
xmin = ;
xmax = ;
n = ;
k = ;x = linspace( xmin , xmax , n );
p = normpdf( x , mu , sigma );
c = normcdf( x , mu , sigma );figure( ); clf;subplot( ,, );
plot(x,p,'k-')
xlabel( 'x' ); ylabel( 'pdf' );
title( 'Probability Density Function' );subplot( ,, );
plot(x,c,'k-')
xlabel( 'x' ); ylabel( 'cdf' );
title( 'Cumulative Density Function' );y = normrnd( mu , sigma , k , );subplot( ,, );
hist( y , );
xlabel( 'x' ); ylabel( 'frequency' );
title( 'Histogram of random values' );

Figure 1.1 正态分布µ=100,σ=15

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gVuPpEmpBUGjek+RM1Lnchold7ZaLXr4UO81L8v6++6v1j67zbZNvqbOvpzdUn0oHk0bsbzZ+od8WrEL3aax69Xr1G9Mog4T4nXFJjrj6RDiSP3t1o/kS9K16F6NXeitHrz2fWeffIuc85V9WSq0+k/UiifSuaP1H7opcgerW3aPR68w96/TN97pJzn3OuqiVXn0j7kUT7VjR/ovZFL0H0am+h6PXqTxsOX/nL7DI1lHlXM6+trnisXH0ivUcGK/Sh+ROtUPeJhn8TfEH06myV6PXmOYffanZd+su8yZnX1omrT6T3yGCFPjR/ohXqPtHm/CN6NbdE9Hr/kKLX/fLvcP4VNuDqE2k8plukCc2faJHSzyJ68dA/eu39/dg/0+d6+Xc4/wobcPWJNB5zrdOB5k+0TvWnEL14KBO9/r3+jyO/ecHvPz07+vjwjWbXpbMq21tlnXW5+kS6jrnW6UDzJ1qn+lOIXjxUil630XmXqrK9VdZZl6tPpOuYaKn2M3+ipRrgfqIXD6LXgM67VJXtrbLOulx9Il3HREu1n/kTLdUA9xO9eBC9BnTedWrtba3VluPqE2k5Zlmt98yfaLUeuJnoxYPoNaDzrlNrb2utthxXn0jLMctqvWf+RKv1wM1ELx5ErwGdd5GKG1txzVW4+kT6jSkWbDzzJ1qwDe4kevEgeg3ovItU3NiKa67C1SfSb0yxYOOZP9GCbXAn0YsH0WtA512h7q7WXXlyrj6RZuN+a3ad+ROt2Qm3Eb14EL0GdN4V6u5q3ZUn5+oTaTbut2bXmT/Rmp1wG9GLB9FrQOddoe6u1l15ci2vPl8/HHiBZuNmy7Zcy/nzoWWb4R6iFw+i14DOO131La2+/pz6XX1+PVF8wC0vmF0W1rJsy/WbP59bthnuIXrxIHoN6LzTVd/S6uvPqd/VR/SilpX7rd/8+dzK/XAD0YsH0WtA552rwX42eISE+l19RC9qWbnf+s2fz63cDzcQvXgQvQZ03rl67GePp0il39Xnz2T1zz/rRRqLN1u/+fO5xVviaqIXD6LXgM47V4/97PEUqfS7+pzyW69fZleJtpbqrniy+s2fzy3VEvcTvXgQvQZ03ok6bWanZ8mg39XHHzikCp3Wb/58TldcSvTiQfQa0Hkn6rSZnZ4lg35XH9GLKnRav/nzOV1xKdGLB9FrQOedqNNmdnqWDPpdfUQvStBm3x3nz+c0xqVELx5ErwGdd5Z+O9nviSZqefUZ/pMkv/76zT9qosG4gTb7bjp/PqQxLiV68SB6Dei8s/TbyX5PNJGrT6TBuJoeezB/Ir1xKdGLB9FrQOedouU2tnyoWVx9Ig3G1fTYg/kT6Y1LiV48iF4DOu8UXbex63Pdz9Un0l1cSoM9mT+R9riU6MWD6DWg807RdRu7Ptf9XH0i3cWlNNiT+RNpj0uJXjyIXgM673O997D3093G1SfSWlxHd/1k/kQ65FKiFw+i14DO+1zvPez9dLdx9Ym0FtfRXT+ZP5EOuZToxYPoNaDzPtd7D3s/3W1cfSKtxUW01i/mT6RJLiV68SB6Dei8D62wgSs849VcfSJ9xUW01i/mT6RJLiV68SB6Dei8D62wgSs849VcfSJ9xRX0VWT+RPrkUqIXD6LXgM770AobuMIzXs3VJ9JXXEFfReZPpE8uJXrxIHoN6LxPrLN76zzpRVx9Ik3FFfRVZP5E+uRSohcPoteAzvvEOru3zpNexNUn0lScTlMNmT+RVrmU6MWD6DWg8z6xzu6t86QXcfWJNBWn01RD5k+kVS4levEgeg3ovMNW27rVnvdcrj6RjuJcOuoV8yfSLZcSvXgQvQZ03mGrbd1qz3suV59IR3EuHfWK+RPplkuJXjyIXgM677DVtm615z2Xq0+koziRdnrD/Ik0zKVELx5ErwGdd8ya+7bmU5/C1SfSTpxIO71h/kQa5lKiFw+i14DOO2bNfVvzqU/h6hNpJ06knd4wfyINcynRiwfRa0DnHbPmvq351Kdw9Ym0E2fRS++ZP5GeuZToxYPoNaDzDlh501Z+9k+4+kR6ibPopffMn0jPXEr04kH0GtB5B6y8aSs/+ydcfSK9xCk00p/Mn0jbXEr04kH0GtB5B6y8aSs/+ydcfSK9xCk00p/Mn0jbXEr04kH0GtB5e9kxO3CAq0+kkficLtrC/Il0zqVELx5ErwGdt5cdswMHuPpEGonP6aItzJ9I51xK9OJB9BrQeXvZMTtwgKtPpJH4nC7awvyJdM6lRC8eRK8BnbeL7XqwD3u5+kS6iA9poY3Mn0jzXEr04kH0GtB5u9iuB/uwl6tPpIv4kBbayPyJNM+lRC8eRK8BnbeL7XqwD3u5+kS6iE/on+3Mn0j/XEr04kH0GtB529mrJ1uxl6tPpIv4hP7ZzvyJ9M+lRC8eRK8BnbedvfrJbuzi6hNpIQ7TPLuYP5EWupToxYPoNaDztrNXP9mNXVx9Ii3EYZpnF/Mn0kKXEr14EL0GdN529uonu7GLq0+khThM8+xi/kRa6FKiFw+i14DO28hGRfZkO1efSP9wjM7Zy/yJdNGlRC8eRK8BnbeRjYrsyXauPpH+4Rids5f5E+miS4lePIheAzpvIxsV2ZPtXH0i/cMB2uYA8yfSSJcSvXgQvQZ03kY2asi2bOTqE2keDtA2B5g/kUa6lOjFg+g1oPO2sEuv2JmNXH0izcNeeuYY8yfSS5cSvXgQvQZ03hZ26RU7s5GrT6R52EvPHGP+RHrpUqIXD6LXgM7bwi69Ymc2cvWJNA976ZljzJ9IL11K9OJB9BrQeVvYpTdszhauPpHOYRcNc5j5E2mnS4lePIheAzpvC7v0hs3ZwtUn0jnsomEOM38i7XQp0YsH0WtA5/3JFr1nf7Zw9Yl0Dtvplk+YP5GOupToxYPoNaDz/mSL/mSL/uTqE2kbttMtnzB/Ih11KdGLB9FrQOf9yRb9yRb9qeXV5+uH958dvkbbsJ1u+UTL+fMhHXUp0YsH0WtA5/3JFv3JFv2p39Xn1xO9f8BX2Wx2WahBq3yo3/z5nKa6lOjFg+g1oPPesz9b2KU/9bv6iF7cRqt8qN/8+ZymupToxYPoNaDz3rM/G9mo9/pdfbZHr1ef0jNspFU+1G/+fE5TXUr04kH0GtB579mfjWzUe/2uPqIX99Ann+s3fz6nry4levEgeg3ovPfsz0Y26r1+V5+N0et9JPtldpXISGPsFU9Wv/nzOX11KdGLB9FrQOe9YXO2s1fv9bv6nBK9ZpeF7DTJKfrNn89prUuJXjyIXgM67w2bs529eq/f1WdL9Hr/1HqGP2mSU/SbP5/TWpcSvXgQvQZ03hs2Zzt79V6/q4/oxdV0yFn6zZ/P6a5LiV48iF4DOu8Nm7OL7Xqj5dVn+E+SvPrr4ZfPLgup6ZCztJw/H9JdlxK9eBC9BnTeK3ZmLzv2hqtPpGF4T4ecxfyJdNelRC8eRK8BnfeKndnLjr3h6hNpGN7QHicyfyINdinRiwfRa0DnvWJn9rJjb7j6RBqGN7THicyfSINdSvTiQfQa0HlDtuUY+/aKq0+kW3hFb5zL/In02KVELx5ErwGdN2RbjrFvr7j6RLqFV/TGucyfSI9dSvTiQfQa0HlDtuUY+/aKq0+kW3hFb5zL/In02KVELx5ErwGdF9mTw2zdK64+kW5hSGOczvyJtNmlRC8eRK8BnRfZk0/YvSFXn0irMKQxTmf+RNrsUqIXD+Wj19cP21/w/qt0XmRPPmH3hlx9Iq3CkMY4nfkTabNLiV481I5ev1YfH2b4gi1fNbsu6diTT9i9IVefSKsQ6YorlJ4/8Rqz8UfMfu48kejFw4rR6/1r/pk+gQ35nD2MSl99LqJPiHTFFerOn5imfn121wd/fWR2WToTvXgQvUyfv9mQz9nDqO7V5zr6hF+0xEWKzp8YokSvKkQvHkQv0+dvNuRz9jAqevW5lD7hFy1xkdLzR/SqSPTiYfXo9SqM/TK7TDMt/vhnsY3xWJW++lxEn/CLlrhI6fkjelUkevGwdPR69fA67ye7cRY7+Uvpq89FNAk/6YfrlJ4/10UvP3e+jui1pkt/7lwser15cp33k904i538pfTV5yKahJ/0w3VKzx+/9apI9OJh0ej1/rF13k924yx28pfSV5+LaBJ+0g/XKT1/RK+KRC8eakevf6//yxVvXvDnL/503pOtOJHN/KX01ecimoQnzXCp0vNH9KpI9OKhfPS6gs57shXnsp8/lb76XESH8KQZLlV6/sQQNfwZ9MYP/vzs7LJ0JnrxIHoN6LwnW3Eu+/lT6avPRXQIT5rhUuZPpOUuJXrxIHoN6LwnW3Eu+/mTq0+kQ3jSDJcyfyItd6kq0Wuj2dtZmOg1oKUe7MPpbOlPrj6RDuFBJ1zN/Il03aXqRC+/HLuW6DWgpR7swxXs6pOrT6Q9eNAJVzN/Il13KdGLB9FrQEs92Icr2NUnV59Ie/CgE65m/kS67lKiFw+i14CWerAPV7CrT64+kfbgQSdczfyJdN2lRC8eRK8BLfXtb/xXsrcPrj6R3uDbiLiF+RNpvEuJXjyIXgNa6tvf+69kbx9cfSK9wbcRcQvzJ9J4lxK9eBC9BrTUt7/3X8nePrj6RHoDPXAP8yfSe5cSvXgQvQa01Le//V/J3j64+kR6Az1wD/Mn0nuXEr14EL0GtJQduJod/nb1GdEY6IF7mD+R3ruU6MWD6DWgpezA1ezwt6vPiMZYnAa4jfkTab9LiV48iF4DWsoOXM0Of7v6jGiMxWmA25g/kfa7lOjFg+g1oKXswNXs8Lerz4jGWJwGuI35E2m/S4lePIheA4u31OKPfxv77OoT6YqVqf6dzJ9IB15K9OJB9BpYvKUWf/zb2GdXn0hXrEz172T+RDrwUqIXD6LXwOIttfjj38Y+u/pEumJZSn8z8yfShJcSvXgQvQZWbqmVn/1+i++2q0+0eEusTOlvZv5EmvBSohcPotfAyi218rPfb/HddvWJFm+JlSn9zcyfSBNeSvTiQfQaWLmlVn72+y2+264+0eItsSx1v5/5E+nDS4lePIheAyu31MrPfr/Fd9vVJ1q8JZal7vczfyJ9eCnRiwfRa2DZllr2wSdaec9dfaKV+2Fl6n4/8yfSh5cSvXgQvQaWballH3yilffc1SdauR+WpehTmD+RVryU6MWD6DWwbEst++ATrbznrj7Ryv2wLEWfwvyJtOIBX/skD1Si1x1Er4FlW2rZB59o5T139YlW7odlKfoU5k+kFQ+4ItWIXr2JXgNrttSaT53Bsjvf8urz88ebB16wbDMsS8VnaTl/PqQbDxC92Ev0GlizpdZ86gyW3fl+V59fTxQfcMsLZpeFW6n4LP3mz+d04wGiF3uJXgNrttSaT53Bsjvf7+qzN3oNv8PssnArFZ+l3/z5nG48QPRiL9FrYMGWWvCR81h28/tdfUQvdlHuifrNn89pyANEL/YSvQYWbKkFHzmVNfe/39VnY/T6+p/hd5hdFu6j3BP1mz+f05AHiF7sJXoNLNhSCz5yKmvuf7+rz5bo9fODr17w0+wqcSH1vU08Wf3mz+c05AGiF3uJXgMLttSCj5zKmvvf7+qz8bde718wuyzcRK3n6jd/PqcnDxC92Ev0GlitpVZ73oTWLEG/q4/oxXZqPVe/+fM5PXmA6MVeotfAai212vPmtGAV+l19RC82Uujp+s2fz2nLA0Qv9hK9BlZrqdWeN6cFq9Dy6vP1w88Pvn/Bz8/OLgt3UOjpWs6fD2nLA0Qv9hK9BlZrqdWeN6cFq+DqEy3YBmtS6OnMn0hbHiB6sZfoNbBUSy31sJktWAhXn2jBNliQKmdg/kQ68wDRi71Er4GlWmqph01utVq4+kSr9cCaVDkD8yfSmQeIXuwleg0s1VJLPWxyq9XC1SdarQfWpMoZmD+RzjxA9GIv0WtgqZZa6mGTW60Wrj7Raj2wICVOwvyJNOcBohd7iV4D67TUOk9axVIVcfWJlmqANSlxEvpms8oAACAASURBVOZPpDkPEL3YS/QaWKel1nnSKpaqiKtPtFQDrEmJkzB/Is15gOjFXqLXwDottc6TVrFURVx9oqUaYEHqm4f5E+nPA0Qv9hK9BtZpqXWetIqlKuLqEy3VAAtS3zzMn0h/HiB6sZfoNbBISy3ymOWsUxdXn2id6q9JffMwfyL9eYDoxV6i18AiLbXIY5azTl1cfaJ1qr8gxU3F/Im06AGiF3uJXgOLtNQij1nOOnVx9YnWqf6CFDcV8yfSogeIXuwleg0s0lKLPGY569TF1Sdap/oLUtxUzJ9Iix4gerGX6DWwQkut8Ix1LVIdV59okdIvSGWzMX8iXXqA6MVeotfACi21wjPWtUh1XH2iRUq/IJXNxvyJdOkBohd7iV4DK7TUCs9Y1yLVcfWJFin9apQ1IfMn0qgHiF7sJXoNtG+p9g9Y3SIFcvWJFin9apQ1IfMn0qgHiF7sJXoNtG+p9g/YwAo1cvWJVqj7gpQ1IfMn0qgHiF7sJXoNtG+p9g/YwAo1cvWJVqj7atQ0J/Mn0qsHiF7sJXoNtG+p9g/YwAo1cvWJVqj7atQ0J/Mn0qsHiF7sJXoN9G6p3k/XxgplcvWJVqj7atQ0J/Mn0qsHiF7sJXoN9G6p3k/XSftKufpE7Yu+GgVNy/yJtOsBohd7iV4DvVuq99N10r5Srj5R+6KvRkHTMn8i7XqA6MVeotdA75bq/XSdtK+Uq0/UvuirUdC05s6fr6+vhANQux4gerGX6DXQuKUaP1o/7YuV8OYxXfuiL0U1M8swf77+Z/ZC/h8de4DoxV6i10Djlmr8aC31rleeC0cevSu+GtXMLNX8+fph7jJml6Ue0Yu9RK+Bxi3V+NFa6l2vVFefJHpXfDWqmVmG+TOMWxMXpmMPEL3YS/QaaNxSjR+tpd71ynD1yaZ3xZeilMlN//3SqwWIXrWIXuwleg10bamuz9VY75KJXlHvii9FKZMzfyJNe4DoxV6i10DXlur6XL01rpqrT9S43KtRyuTMn0jTHiB6sZfoNdC1pbo+V2+Nq+bqEzUu91LUMb/p8+fnAqYv5kHfHiB6sZfoNdC1pbo+V2+Nq5bktpFK43IvRR3zm/7Pev35kfvp2wNEL/YSvQZatlTLh1pB48JluGpk07jc61DEEkSvSOseIHqxl+g10LKlWj7UIrrWLsNVI5uutV6KIpYgekVa9wDRi71Er4GWLdXyoRbRtXYZrhrZdK31UhSxhOnz5+u/5i7mQeseIHqxl+g10LKlWj7UIrrWLsltI5WutV6HClZh/kS69wDRi71Er4F+LdXviZbStXyuPlHXWq9DBaswfyLde4DoxV6i10C/lur3RKtpWUFXn6hloZeiglVMnz9fwdz1/DN/DhG92Ev0GujXUv2eaDUtK5jhqpFNy0KvQ/kKmTt/ck4/DXyA6MVeotdAv5bq90SraVnBnJePuVoWeh3KV4joFWngA0Qv9hK9Bpq1VLPHWVPLIua8fMzVstDrUL5CRK9IAx8gerGX6DXQrKWaPc6y+tUx5+Vjrn5VXofa1TI9ekUT1/Nc1eyy1CN6sdd90SvDWNmoWUs1e5xl9atjwpkwfUn9qrwOtatl+mFPSA8fIHqx14TolX/eNWupZo+zrH51TDgKpo+pflVeh9rVknD+TKeHDxC92OvWP3A4/A17kt+z/9SppTo9y+L6lTLbwX+YO6b6VXkRClfO9Pnzc7BMX8yDNj5A9GKvW6PX82wffIO/7kBvXvDrI+9vVJ1aqtOz0KyaSW4bQ/eMqd7DZykKV87c+fMVfsGeYR5q4wNEL/aaEL0OfveQnba/IF5x3j92p5bq9Cw0q2aGq8a5tsyZdYbPUhSuHNEr0sYHiF7sdV/0+nrr7+9+NHp9jX6bv87tp9Oz0KyaGa4av1w9pl598OdnZ5eF3VStItEr0skHiF7sdV/0+nW8h3+98UuGX/X+BbvesU1LtXkQHpoVNMNV440bxtTwO8wuC7upWkXT58/en+zcQCcfIHqx14TodeA6El/zYfR6P+/atFSbB+GpU02T3DaGrhtTiwyfpahaRZnnzyw6+QDRi70WjV5/fqtfZpfpoLor55W6NY3HKvPVZ8qY+tdo+KxDjUqoNX9m0cwHiF7sNSF6/Tv0e/YTo9f7L/zXaPq0eRCeOtU0+dXnijH1/vX/Gg2fdShZUXPnT84oqJkPEL3Ya070OvLdRa+dejwFUZvKZrhqnEv0WpCSFZVq/iRZjGY+QPRirxWj15ZvNbsuJ+jxFERtKpvktnGiD8fUvy7DZx3qVVe2+ZNhPfr5ANGLveZEr2O/ZB9+ya+/fvU9443nzbv3aKkeT0HUprIZrhpvvPl5zfuvOjym/nUZPutQr7qyzZ8M69HPB4he7DUhev2Zi6br0VI9noKoTWWzHfyfZo2pNsVdhHrVNXf+fAUTF/Oknw8QvdhL9Bpo0FINHoE3etQ328H/SfTiT4pVWub5M4uWPkD0Yq8J0evf0T/Jc5sGLdXgEXijR30Tnv0n0Ys/KVZpmefPLFr6ANGLveb81uuNs1bziQYt1eAReKNHfZOc91emjKYelV2EYpU2d/7kvAhp6QNEL/aaEL3ya9BSDR6BN3rUN3n0mqJHZVegUtVNnz9f+f74j64+QPRiL9FroHpLVV8/WzSocpLbRioNyroIlapu+m+9/vzI/XT1AaIXe4leA9Vbqvr62aJBlTNcNbJpUNZFqFR1olekqw8QvdhL9Bqo3lLV188WDaqc4aqRTYOyrkCZGpg+f77+a+5iHjT2AaIXe4leA6VbqvTi2a5BoZPcNlJpUNYVKFMD5k+ksQ8QvdhL9Boo3VKlF88u1Wvt6hNVr+kilKkB8yfS2AeIXuwleg2UbqnSi2eX6rV29Ymq13QFatTD9Pnz848aTl/Mg94+QPRiL9FroHRLlV48u1SvdZLbRirVa7oCNeph7vx5vnv8i4n09gGiF3uJXgN1W6ruyjmgerkzXDWyqV7T9hSoDdEr0t4HiF7sJXoN1G2puivnmNIVz3DVyKZ0QVegQG2IXpH2PkD0Yi/Ra6BuS9VdOceUrniGq0Y2pQu6AgVqY/r8+fqvuYt50N4HiF7sJXoN1G2puivnmNIVT3LbSKV0QdtTnU7Mn0iHHyB6sZfoNVC0pYoum0+ULrqrT1S6oO2pTidJ/sBhKjr8ANGLvUSvgaItVXTZfKhu3XNePuaqW80VqE4nolekww8QvdhL9Boo2lJFl82H6tY95+VjrrrVbE9pmpkevaKJ63muanZZ6hG92Ev0GijaUkWXzYfq1j3DVSObutVsT2maMX8iTX6A6MVeotdAxZaquGbOUrT6rj5R0VKuQGmamTJ/kg89TX6A6MVeotdAxZaquGbOUrT6yW8hUxQtZXvq0s/c6JVz+unzA0Qv9hK9Biq2VMU1c5ai1c95+ZiraCnbU5d+Zs2fr9emrOfX2maXpR7Ri71Er4GKLVVxzZylaPUzXDWyKVrK9tSln7nzJ+f00+cHiF7sJXoNlGupcgvmdBV7IOflY66KdWxPUVoyfyKtfoDoxV6i10C5liq3YE5XsQdcfaKKdWxPUVoyfyKtfoDoxV6i10C5liq3YE5XsQdcfaKKdWxPUVoyfyKtfoDoxV6i10C5liq3YE5XsQdcfaKKdexNRboyfyLdfoDoxV6i10Ctlqq1Wq5TrhNcfaJyRWxPRboyfyLdfoDoxV6i10Ctlqq1Wq5TrhNcfaJyRexNORozfyINf4DoxV6i10Ctlqq1Wq5TrhNcfaJyRexNORozfyINf4DoxV6i10Chliq0VG5Qqx9cfaJaFWxPORozfyINf4DoxV6i10Chliq0VG5Qqx9cfaJaFexNLXozfyI9f4DoxV6i10Chliq0VG5Qqx9cfaJaFexNLXozfyI9f4DoxV6i10Chliq0VG5Qqx9cfaJaFexNLXozfyI9f4DoxV6i10CVlqqyTu5UqCtcfaJC5etNIdozfyJtf8Cy0Wu72SVKR/QaqNIoVdbJnQp1hatPVKh8vSlEe+ZPpO0PWDh6bf2Gs0uUjug1UKVRqqyTOxXqClefqFD5elOI9syfSNsfIHqJXnuJXgNVGqXKOrlToa5w9YkKla8xVViB+RPp/ANEL9FrL9FroESjlFgkU1TpDVefqErtelOFFZg/kc4/QPQSvfYSvQZKNEqJRTJFld5w9Ymq1K43VViB+RPp/ANEL9FrL9FroESjlFgkU1TpDVefqErtGlOCRZg/keY/QPQSvfYSvQbyN0r+FTJRlfZw9Ymq1K4xJViE+RNp/gNEL9FrL9FrIH+j5F8hc5XoEFefqEThelOCRZg/keY/QPQSvfYSvQbyN0r+FTJXiQ5pefX5+uHPVw4/OLssS7P/62g5fz6k/w8QvUSvvUSvgfyNkn+FzFWiQ/pdfX490ZsHfJXNShSuMfu/jn7z53P6/wDRS/TaS/QaSN4oyZdHBiWapN/VR/QqzeYvpd/8+ZwjcIDoJXrtJXoNJG+U5Msjifx90u/qszF6PT4uemVj85fSb/58zhE4QPQSvfYSvQaSN0ry5ZFE/j7pd/URvUqz+UvpN38+5wgcIHqJXnuJXgPJGyX58kgif5/0u/psiV7PD7767C+zq7QKW91bPFn95s/nnIIDRC/Ray/RayBzo2ReG6nkb5V+V59TotfssizKzq+m3/z5nFNwgOgleu0leg1kbpTMayOb5N3S7+rzZ/T68+fuyUvWmJ1fTb/58zmn4ADRS/TaS/QayNwomddGNsm7pd/VZ8tvvd5/NnnJurLtC+o3fz7nIBwgeolee4leA5kbJfPayCZ5t7S8+gx/o/X+Tx7++uDssqzIti+o5fz5kINwgOgleu0leg2kbZS0CyOtzD3j6hNlrldjtn1B5k/kIBwgeolee4leA2kbJe3CSCtzz7j6RJnr1ZU9X5P5EzkLB4heotdeotdA2kZJuzDSytwzrj5R5np1Zc/XZP5EzsIBopfotZfoNZCzUXKuiuQyt42rT5S5Xl3Z8zWZP5GzcIDoJXrtJXoN5GyUnKsiv7Sd4+oTpS1WVzZ8WeZP5DgcIHqJXnuJXgM5GyXnqsgvbee4+kRpi9WVDV+W+RM5DgeIXqLXXqLXQM5Gybkq8kvbOa4+UdpidWXDl2X+RI7D09c+opfotYPoNZCwURIuiUJy9o+rT5SzUl3Z7ZWZP5ET8VQl1ZRY5OxipiN6DSRslIRLopCc/ePqE+WsVFd2e2XmT+REPFVJNSUWObuY6YheAwkbJeGSKCRn/7j6RDkr1ZKtXpz5EzkUT1VSTYlFzi5mOqLXQMJGSbgkCsnZP64+Uc5KtWSrF2f+RA7FU5VUU2KRs4uZjug1kK1Rsq2HihJ2katPlLBMXdnqxZk/kUPxVCXVlFjk7GKmI3oNZGuUbOuhooRd5OoTJSxTS/YZ8ydyLp6qpJoSi5xdzHREr4FsjZJtPVSUsItcfaKEZWrJPmP+RM7FU5VUU2KRs4uZjug1kK1Rsq2HihJ2katPlLBMLdlnzJ/IuXiqkmpKLHJ2MdMRvQayNUq29VBRwi5y9YkSlqkfm8y3+TPiaDxVSTUlFjm7mOmIXgPZGiXbeqgoYRe5+kQJy9SPTebb/BlxNJ6qpJoSi5xdzHREr4FUjZJqMZSWrZdcfaJsNerHDvNg/kROx1OVVFNikbOLmY7oNZCqUVIthtKy9ZKrT5StRv3YYR7Mn8jpeKqSakoscnYx0xG9BlI1SqrFUFq2XnL1ibLVqB87zIP5EzkdT1VSTYlFzi5mOqLXQKpGSbUYSsvWS64+UbYaNWN7eTJ/IgfkqUqqKbHI2cVMR/QayNMoeVZCD6k6ytUnSlWgfmwvT+ZP5IA8VUk1JRY5u5jpiF4DeRolz0roIVVHufpEqQrUj+3lyfyJHJCnKqmmxCJnFzMd0WsgT6PkWQk9pOooV58oVYGasbf8ZP5EzshTlVRTYpGzi5mO6DWQpFGSLINOUjWVq0+UqkDN2Ft+Mn8iZ+SpSqopscjZxUxH9BpI0ihJlkEzefrK1SfKU51+7C0/mT+RM/JUJdWUWOTsYqZTPnp9/bD3BW++ZHZdvr9dFLhGnr5y9YnyVKcfe8tPnebP13/FDw5fOfw+s8uSRZVUU2KRs4uZTu3o9Wv1f4arOIBefdvZdfn+dlHgGnn6qtPV5yx5qtOMjeWXTvNn4+Vny5VpdlmyqJJqSixydjHTWTR6DcfQz5fNrouLAhdK0l2drj5nSVKafmwsv3SaP6LX6aqkmhKLnF3MdBaNXq9e//z47Lq4KHChJN3V6epzliSl6cfG8kub+TN8ENHrQ1VSTYlFzi5mOqLX+NvOrouLAhdK0l1trj4nSlKafmwsv7SZP1//9fzgr9e8+uCvj8wuSxZVUk2JRc4uZjqi1/jb/nJ/VW5+R1YzpaujM8ZAK87+FewqUZv5sz1lbbkyzb385FEl1ZRY5OxiTnbp5adV9Jpep7kLoL0MPdbm6nOiDHXpx64SdZ0/H0av2WXJokqqKbHI2cVMR/Qaf9vpVZm7ANrL0GNdrz6fyFCXZmwpQ13nj+h1iiqppsQiZxczHdFr/G3nlmTiu7OIDG3W9erziQx1acaWMtRm/mxPWaLXdlVSTYlFzi5mOrWj17/X/9HA9y+IL/v18bklmfjurGN6p7W5+pxoelH6saUMdZo/ry5CGz/487Ozy5JFlVRTYpGzi5lO+eh1BdGLFUzvtE5Xn7NML0oz9pNXzJ/IeXmqkmpKLHJ2MdMRvQZEL1YwvdNcfaLpRWnGfvKK+RM5L09VUk2JRc4uZjqi18DERtGj3Gn6Txlmn/V0TIBz2U9eMX8i5+WpSqopscjZxUxH9BoQvViE6JWNCXAim8kb5k/kyDxVSTUlFjm7mOmIXgOiF4sQvbIxAU5kM3nD/IkcmacqqabEImcXMx3Ra2BWo2hQ7jf3Bw2zz3o6hsBZ7CTvmT+RU/NUJdWUWOTsYqYjeg2IXqxD9ErFEDiLneQ98ydyap6qpJoSi5xdzHRErwHRi3WIXqkYAmexk7xn/kROzVOVVFNikbOLmY7oNTClUXQnU4he5/r64cALzIFT2Eb+1HL+fMjBeaqSakoscnYx0xG9BkQvljLx17yzz/rJfj1RfMAtL5hSi2ZsI3/qN38+5+A8VUk1JRY5u5jpiF4DohdLEb3O8meyev/6f64+J7GN/Knf/Pmcg/NUJdWUWOTsYqYjeg2IXixF9DqL6JWBPWSLfvPnc87OU5VUU2KRs4uZjug1cH+jaE3mmvXjhtln/WQbo9fX/ww/dX8hmrGHbNFv/nzO2XmqkmpKLHJ2MdMRvQZEL1Yjep3ilN96/XJ/XUqzYwzFk9Vv/nzO8XmqkmpKLHJ2MdMRvQZEL1Yjep3ilOh1fyE6sYFs1G/+fM7xeaqSakoscnYx0xG9Bm5uFH1JBlN+4jD7rJ9M9JrL7rFdv/nzOSfoqUqqKbHI2cVMR/QaEL1YkOj1uT+j15YX3FyFTuwe2/WbP59zgp6qpJoSi5xdzHRErwHRiwWJXqf4+uHnB9+/4Odnb65CJ3aP7VrOnw85QU9VUk2JRc4uZjqi18CdjaIpSUL0ysBAOMzWsYv5EzlET1VSTYlFzi5mOqLXgOjFmu7/fe/ss56OgXCYrWMX8ydyiJ6qpJoSi5xdzHRErwHRizWJXtMZCMfYN/YyfyLn6KlKqimxyNnFTEf0GhC9WJPoNZ2BcIx9Yy/zJ3KOnqqkmhKLnF3MdESvgdsaRUeSzc0/d5h91tMxE46xb+xl/kTO0VOVVFNikbOLmY7oNSB6sSzRay4z4QCbxgHmT+QoPVVJNSUWObuY6YheA6IXyxK95jITDrBpHGD+RI7SU5VUU2KRs4uZjug1cE+jaEdyuvNHD7PPejrGwgE2jQPMn8hReqqSakoscnYx0xG9BkQvViZ6TWQs7GXHOMb8iZympyqppsQiZxczHdFrQPRiZaLXRMbCXnaMY8yfyGl6qpJqSixydjHTEb0GbmgUvUhmt/30YfZZT8dk2MV2cZj5EzlQT1VSTYlFzi5mOqLXgOjF4kSvWUyGXWwXh5k/kQP1VCXVlFjk7GKmI3oNiF4sTvSaxWTYzl7xCfMncqaeqqSaEoucXcx0RK+BqxtFI5LfPT+AmH3W0zEctrNXfML8iZyppyqppsQiZxczHdFrQPQC0WsKw2E7e8UnzJ/ImXqqkmpKLHJ2MdMRvQZELxC9pjAcNrJRfMj8iRyrpyqppsQiZxczHdFr4NJG0YVUccPPIGaf9XTMh41sFB8yfyLH6qlKqimxyNnFTEf0GhC94Fv0msF82MIu8TnzJ3KynqqkmhKLnF3MdESvAdELvkWvGcyHLewSnzN/IifrqUqqKbHI2cVMR/QauK5RtCC1XP1jiNlnPR0j4k+2iFOYP5HD9VQl1ZRY5OxipiN6DYhe8CB63cyI+JMt4hTmT+RwPVVJNSUWObuY6YheA6IXPIheNzMi/mSLOIX5EzlcT1VSTYlFzi5mOqLXwEWNov+o6NKfRMw+6+mYEu/ZH85i/kTO11OVVFNikbOLmY7oNSB6wZPodSdT4j37w1nMn8j5eqqSakoscnYx0xG9BkQveBK97mRKvGFzOJH5EzliT1VSTYlFzi5mOqLXwBWNovmo67ofRsw+6+kYFG/YHE5k/kTtj9jXPgVSTZFFbjW7QW4ieg2IXvCT6HUbg+IVO8O5zJ+o/SnrmGpaLXJ2g9xE9Bo4vfzr9BMtiV63MStesTOcy/yJ2p+ylVNNiUXObpCbiF4Dohf8ctGvgmef9XTMilfsDOcyf6L2p2zlVFNikbMb5Cai14DoBb+IXvcwK4ZsC6czf6L2B23lVFNikbMb5Cai18C55V+nmejtih9JzD7r6RgXQ7aF05k/UfuDtnKqKbHI2Q1yE9FrQPSCSPS6gXER2ROuYP5E7c/ayqmmxCJnN8hNRK8B0Qsi0esGxkVkT7iC+RO1P2srp5oSi5zdIDcRvQZOLP86ncQKTv+pxOyzno6J8YsN4SLmT9T+uK2cakoscnaD3ET0GhC9YEj0upqJ8YsN4SLmT9T+uK2cakoscnaD3ET0Gjir/Ou0EYsQva5maPxkN7iO+RO1P3Erp5oSi5zdIDcRvQZEL3jl3N8Jzz7r6RgaP9kNrmP+RO1P3MqppsQiZzfITUSvAdELXhG9LmVoPNkKLmX+RO0P3cqppsQiZzfITUSvgVPKv04PsZoTfzYx+6ynY2482QouZf5E7Q/dyqmmxCJnN8hNRK8B0QveEL2uY2482AeuZv5E7c/dyqmmxCJnN8hNRK8B0QveEL2uY2482AeuZv5E7c/dyqmmxCJnN8hNRK+Bz8u/TgOxprN+PDH7rKdjdHybn9zC/InaH72VU02JRc5ukJuIXgOiF7wnel3E6Pg2P7mF+RO1P3orp5oSi5zdIDcRvQY+LP863cOyRK+LmB52gHuYP1H707dyqimxyNkNchPRa0D0gj+d8svh2Wf9fF8/HHiB6WEHuEfL+fOh9qdv5VRTYpGzG+QmoteA6AV/Er2iX08UH3DLC06pTlGLPz536jd/Ptf+AK6cakoscnaD3ET0Gvik/Ou0Dnz+Q4rZZ/1kfyar96//t8DV573FH5879Zs/n2t/AFdONSUWObtBbiJ6DYhesIXo9Yvo9aHFH5879Zs/n2t/AFdONSUWObtBbiJ6DYhesIXo9Yvo9YmVn5379Zs/n2t/BldONSUWObtBbiJ6DRwu/zp9Aw8f/pxi9lk/2a7oNfzsV3BisZJb6mG5WTxZ/ebP59qfwZVTTYlFzm6Qm4heA6IXbCR6/bQ9er361LIzZNkHZ5Z+8+dz7Y/hyqmmxCJnN8hNRK+BY+Vfp2ngp09+VDH7rJ9sY/R6H8nOrU4Vyz44s/SbP59rfwxXTjUlFjm7QW4ieg2IXrCd6PW0JXq9f+o1x8iaT81c/ebP59qfxJVTTYlFzm6Qm4heAwfKv07HQHT4pxWzz/r5vn74+cH42V+veb7g9Orkt+ZTM1fL+fOh9idx5VRTYpGzG+QmoteA6AW7iF5nWXCSLPjIZGD+RO0P48qppsQiZzfITUSvAdELdhG9zrLgJFnwkcnA/InaH8aVU02JRc5ukJuIXgN7y79Ou8Arx35gMfusp7PaMFntecnD/Inan8eVU02JRc5ukJuIXgOiF+wlep1itWGy2vOSh/kTtT+PK6eaEouc3SA3Eb0GdpV/nV6B9w78zGL2WU9nqXmy1MOSjfkTtT+SK6eaEouc3SA3Eb0GRC84QPT63DrzZJ0nJSfzJ2p/KldONSUWObtBbiJ6DWwv/zqNAlvs/bHF7LOezjojZZ0nJSfzJ2p/KldONSUWObtBbiJ6DYhecIzo9aFFRsoij0lm5k/U/mCunGpKLHJ2g9ykUvT6+mH7C/78YPxuohccI3p9aJGRsshjkpn5E7U/mCunmhKLnN0gNykTvX4tdJiX4v999VXvH3tj+dfpEthu108uDg+ErlaYKis8I/mZP1H7s7lyqimxyNkNchPRa/xeG/fu6vJAOaLXJ1aYKis8I/mZP1H7s7lyqimxyNkNcpMVo9efz7yl/Ou0COy1/YcXhwdCV+0HS/sHpArzJ2p/PFdONSUWObtBbrJo9Ppp+F5bNu6G8kBFotdh7QdL+wekCvMnan88V041JRY5u0Fusmj0+vNb/RJ3bUq1oIrhqYk+mwoN9Z4tvZ+OWsyfqP0JXTnVlFjk7Aa5yYrR6/0X/tswfdbpDzhmyxlx9Yl6z5beT0ct5k/U/oSunGpKLHJ2g9xE9BK94Hyi1zGNZ0vjR6Mi8ydqf0hXTjUlFjm7QW6yYvTa8q3eb9lt5YG6tvwI47Op0FDX8dL1uajL/Inan9OVU02JRc5ukJuUiV7/Xv/Hkf98wcYP/vzs+y27rTxQl+h1QNfx0vW5qMv8idqf05VTQXuzQwAAD4FJREFUTYlFzm6Qm1SKXrd5U/51OgM+9+dPMWaf9XRaTpiWD0V15k/U/qiunGpKLHJ2g9xE9BoQveAUotdeLSdMy4eiOvMnan9UV041JRY5u0FuInoNvCr/Om0BZ3n/g4zZZz2dfkOm3xPRg/kTtT+tK6eaEouc3SA3Eb0GRC84i+i1S78h0++J6MH8idqf1pVTTYlFzm6Qm4heA8Pyr9MTcCLRa5dmc6bZ49CJ+RO1P7Arp5oSi5zdIDcRvQZELzjRm18jzz7r6TSbM80eh07Mn6j9gV051ZRY5OwGuYnoNRDLv05DwOlEr+06jZpOz0I/5k/U/syunGpKLHJ2g9xE9BoQveBcr36TPPusp9Np1HR6Fvoxf6L2Z3blVFNikbMb5Cai18Cv8q/TDXAR0WujNtOmzYPQlfkTtT+2K6eaEouc3SA3Eb0GRC843fCXybPPejo9pk2Pp6A38ydqf3JXTjUlFjm7QW4ieg38LP86rQBXiz/UmH3W0+kxcHo8Bb2ZP1H7k7tyqimxyNkNchPRa0D0giuIXn9qMHAaPAIrMH+i9od35VRTYpGzG+QmotfAs/zr9AHc49fPNWaf9XQazJwGj8AKzJ+o/eFdOdWUWOTsBrmJ6DUgesFFRK/3qs+c6utnHeZP1P78rpxqSixydoPcRPQaeJR/nSaAO/380cbss55O6bFTevGsxvyJ2h/hlVNNiUXObpCbiF4DohdcR/R6o+7Yqbty1mT+RO1P8cqppsQiZzfITUSvga+vr3U6AO73/OnG7LOeTt3JU3flrMn8idqf4pVTTYlFzm6Qm4heA6IXXEr0eqXo5Cm6bFZm/kTtD/LKqabIIjeZ3UefEr0GepQWMnucstlnPZ2Kk6fimsH8idqf5bVTTZtFlu9S0WugQV0hOdFrqOLwqbhmMH+i9mdZqmmxyPJdKnoNNKgr5OfqE5UbPuUWDA/mT9T+OEs1LRZZvktFr4EGdYX8XH2icsOn3ILhwfyJ2h9nqabFIst3qeg10KCukJ+rT1Rr+NRaLfxk/kTtT7RU02KR5btU9BpoUFfIz9UnKjR8Ci0VIvMnqnuov3aQaqovsmqXPoleAw3qCvm5+kSFhk+hpUJk/kR1D3WFwFAi1ZRYZNUufRK9BhrUFfJz9YmqDJ8q64RXzJ+o7rmuEBhKpJoSi6zapU+i10CDukJ+La8+Xz+8f9mrj88uyyZV1gmvtJw/H6p7risEhhKppsQiq3bpk+g10KCukF+/q8+vJ3qTr0pHrxKLhPf6zZ/P1T3aFQJDiVRTYpFVu/RJ9BpoUFfIr9/VZ0v0enywbvTKv0LYot/8+Vzd010hMJRINSUWWbVLn0SvgQZ1hfz6XX02/tbrzafyD5/8K4Qt+s2fz9U93RUCQ4lUU2KRVbv0SfQaaFBXyK/f1ad99Eq+PNiu3/z5XN0DXiEwlEg1JRZZtUufRK+BBnWF/PpdfU6JXr/MrtL/l2oxsEs8Wf3mz+fqnvEKgaFEqimxyKpd+iR6DTSoK+TX7+rT+LdeaRcGx/SbP5+re8wrBIYSqabEIqt26ZPoNdCgrpBfv6tP1+iVc1XwiX7z53N1T3qFwFAi1ZRYZNUufRK9BhrUFfLrd/VpGb0SLgk+12/+fK7uYa8QGEqkmhKLrNqlT6LXQIO6Qn4trz5fP/z8YHzZqy+fXZb/yLYeOEvL+fOhuue9QmAokWpKLLJqlz6JXgMN6gr5ufpE2YZPtvXAWcyfqO55rxAYSqSaEous2qVPotdAg7pCfq4+Uarhk2oxcC7zJ6p75CsEhhKppsQiq3bpk+g10KCukJ+rT5Rn+ORZCVzB/InqnvoKgaFEqimxyKpd+iR6DTSoK+Tn6hMlGT5JlgHXMX+iuge/QmAokWpKLLJqlz6JXgMN6gr5ufpEGYZPhjXA1cyfqO7ZrxAYSqSaEous2qVPotdAg7pCfq4+0fThM30BcA/zJ6p7/CsEhhKppsQiq3bpk+g10KCukJ+rTzR3+Bh9rMP8iepOgAqBoUSqKbHIql36JHoNNKgr5OfqE4lecA/zJ6o7ASoEhhKppsQiq3bpk+g10KCukJ+rTzRx+Jh7LMX8ieoOgQqBoUSqKbHIql36JHoNNKgr5OfqE80aPoYeqzF/orpzoEJgKJFqSiyyapc+iV4DDeoK+bn6RFOGj4nHgsyfqO4oqBAYSqSaEous2qVPotdAg7pCfq4+0f3Dx7hjTeZPVHcaVAgMJVJNiUVW7dIn0WugQV0hP1ef6M7h8/X1ZdaxLPMnqjsQKgSGEqmmxCKrdumT6DXQoK6Qn6tPdNvwMeVYnPkT1R0LFQJDiVRTYpFVu/RJ9BpoUFfIz9Unumf4GHFg/kR1J0OFwFAi1ZRYZNUufRK9BhrUFfJz9YluGD7mG3ybPyN1h0OFwFAi1ZRYZNUufRK9BhrUFfJz9YmuHj6GGzyYP1Hd+VAhMJRINSUWWbVLn0SvgQZ1hfxcfaJLh4/JBk/mT1R3RFQIDCVSTYlFVu3SJ9FroEFdIT9Xn+i64WOswU/mT1R3SlQIDCVSTYlFVu3SJ9FroEFdIT9Xn+ii4WOmwS/mT1R3UFQIDCVSTYlFVu3SJ9FroEFdIT9Xn+j04fP19WWgQWT+RNlmxdc+yQNDiVRTYpE7zG7hsROHT58plrZa0ImrT3Tu8DHK4BXzJ8o2MXoFBouc8NazW3hM9BpIWy3oxNUnOmv4ZP6BH2Rg/kTZhkavwGCRE956dguPiV4DaasFnbj6RKcMHxMM/mT+RNlGR6/AYJET3np2C4+JXgNpqwWduPpEHw4fv+yCjcyfKNv06BUYLHLCW89u4THRayBttaATV5/ok+FjcMF25k+UbYb0CgwWOeGtZ7fwmOg1kLZa0ImrT3Rs+PhlF+xl/kTZxkivwGCRE956dguPiV4DaasFnbj6RAeGj3kFB5g/UbZh0iswWOSEt57dwmOi10DaakEnrj7RruHjl11wmPkTZZsnvQKDRU5469ktPCZ6DaStFnTi6hNtHz7GFHzC/ImyTZVegcEiJ7z17BYeE70G0lYLOnH1ibYMH7/sgs+ZP1G2wdIrMFjkhLee3cJjotdA2mpBJ64+0fvhI3TBWcyfKNt46RUYLHLCW89u4THRayBttaATV5/o1fARuuBc5k+Ubcj0CgwWOeGtZ7fwmOg1kLZa0ImrTxSHj9AFVzB/omyjpldgsMgJbz27hcdEr4G01YJOXH2in8NH6ILrmD9RtoHTKzBY5IS3nt3CY6LXQNpqQSeuPtHXD7PrA52ZP1G2sdMrMFjkhLee3cJjotdA2mpBJ64+keED9zB/omzzp1dgsMgpb73VzY192pk96xtNl236QEuuPpHhA/cwf6Js82f2rb1EtFhwkZe89c2NfdqZPesbTZdt+kBLrj6R4QP3MH+ibPOnyq3dIhu89c2NfdqZPesbTZdt+kBLrj6R4QP3MH+ibPOnyq3dIhu89c2NfdqZPesbTZdt+kBLrj6R4QP3MH+ie+bP1z4Fbu0W2eCtb+j8n0fgtDN71jeazu0HbuDqExk+cA/zJ7oxerW6tVtkg7e+ofN/HoHTzuxZ32g6tx+4gatPZPjAPcyfSPTK8UqLnPDWN3T+zyNw2pk96xtNl+32k2093/mWlG093/mWlG09364+I9nKlG0935a0Qbb1fGdd0uzjno7oleOVFjnhrW/o/J9H4LQze9Y3usHXD8PP3lmDP2Vbz3e+JWVbz3e+JWVbz/eqVx/D50OW9Kds6/nOuqT7j/90GeZPv1u7RTZ46xs6/+cROO1En/WNrvbrmeMWZPubRLb1fOdbUrb1fOdbUrb1fC959TF8PmdJf8q2nu+sS7rx6Kdw9fz52qHVrd0iW7z1VqmGT5kp9uX287FsS8q2nu98S8q2nm9XH8PnEEv6U7b1fGdd0o1HP4Wr58/sq3Pyt7bIBm/9f05JaKKX288R2ZaUbT3f+ZaUbT3frj6GzyGW9Kds6/nOuqQbj34Kx+bP9rtmhavz9Ft78rcuscga+3PP8Ckzxdx+PpdtSdnW851vSdnW8+3qY/gcYkl/yrae76xLuvHop/BB9Gpzda5xa7fIrG+9Y5H3DJ8yU2zL9AFucOO5T+HL8IE0bjz6KXyZP5DDaYf6rG90ta+/pg/AFQwfYBbzB5opc4ZNH2AKwweYxfyBZsqcYdMHmMLwAWYxf6CZSmf4ij9wCfAnwweYxfyBThxjAACAy5WMXq/+rSMTfzI0fOu5P6lKtaT4Ryamr234LlvWec96Em5RhiVN9xXEj09c0vsPLrukbJ08fIsti7xtSdO3KOeSUkmyDwnrkmpJCds425JevUXjLSo/rZ7PHHfq/jX8/L8T15NtSbFfp69teFq2rPOe9STcogxLysbwKbGkbJ2cbfhsfHdLSuXn/pg/aZeUsI2zLelVdJnY4TdsUflRZfokX1J86+lre/OOU24/w/X8+YL7t2jukhIyfPIvKdv8yTZ8Xi3pzxestqRsckav4QeXnT/Zhs+rd5y4pDfrmdXhf1btlCXVHlWz/l71Zhn/ph71tEtKNX3evMXEjsozDTMvKQ/Dp+iSMiwv2/B5/xbmTza/Hj/P/Bl+cPH5k234vH+LJPNweoeLXu8kuf38+19AnxXTh+v5tba5S6oyfUSv92+RqsnnMnzerOfX2rItKX4qw2EXvf5cUqo+n2j6xTSuJFVdUo3EbMPn/VskmYfTOzxW7dyOKjyq3j/5rKP1b95x+uVno0xfUpXpM/H28+r7J5k+w09Nb/JZDJ/3Ug2ff/nmT7bh8+YtzJ9sYkXmzp/hJXXWel69e5IRnWRt2Q77q7dLMnyuaPLCo8rtZ7vpS6oyfbJFr5y3sX8JOmouw2e7DEvKNn+qHPaES/r5qVR9fpsMF9NX75WhLtmWlG34vHqLPJefDB1+ddWqjqr4nEmO1r8ERz2aviTT58B6pt/vXX2GDJ9dMiwp2/zJNnyGb2H+JPQV/DN/ci8p2/AZvsXcw/5rizJ0uOg15vazfUnPv06yRUm2K9vt58+36zd9ispQmvdvbfhsWdLP/yt6mT/lZDhcCeuSbUkJ2zjbYX/1/Sd2uOg19upvXT+D8s3riW89cT0/3334wenTcPp2/Xn7uXlJr7bi57vP3aIMVcvgVefM2oeEdRm+9dwt+nMlsw77rkXes6QwfsyfjJLsQ8K6pFpSwjbOdthfvUWSLXr17p8sablpBQAAcD/RCwAA4HKiFwAAwOVELwAAgMuJXgAAAJcTvQAAAC4negEAAFxO9AIAALic6AUAAHA50QsAAOBy/xcHYvhRV/ES/QAAAABJRU5ErkJggg==” alt=”” width=”860″ height=”450″ />

类似的,图1.2可视化离散Binomial(N,θ)分布,其中 N=10, θ=0.7。

代码,注意Binomial是离散分布,因此绘图用的是柱状图。

n = ;
p = 0.7;
xmin = ;
xmax = ; k = linspace( xmin , xmax , );
pdf = binopdf( k , n , p );
cdf = binocdf( k , n , p );
figure( ); clf;
subplot( ,, );
bar(pdf,,'c');
set(gca,'XTickLabel',{'','','','','','','','','','',''},'FontSize',)
axis([ 0.0 0.35])
xlabel( 'k' ); ylabel( 'pdf' );
title( 'Probability Density Function' );
subplot( ,, );
bar(cdf,,'c');
set(gca,'XTickLabel',{'','','','','','','','','','',''},'FontSize',)
axis([ 0.0 1.0])
xlabel('k'); ylabel('cdf');
title( 'Cumulative Density Function' );
y = binornd( n,p,, );
subplot( ,, );
hist(y);
xlabel( 'k' ); ylabel( 'frequency' );
title( 'Histogram of random values' );

图1.2

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” alt=”” width=”717″ height=”386″ />

练习:

1、采用listing1.1的matlab程序来展示Beta(a,b)分布,a=2,b=3。类似的显示指数分布Exponential(λ),其中λ = 2。

a = ;
b = ;
xmin = ;
xmax = ;
n = ;
k = ;
x = linspace( xmin , xmax , n );
p = betapdf( x , a , b );
c = betacdf( x , a , b );
figure( ); clf;
subplot( ,, );
plot(x,p,'k-')
xlabel( 'x' ); ylabel( 'pdf' );
title( 'Probability Density Function' );
subplot( ,, );
plot(x,c,'k-')
xlabel( 'x' ); ylabel( 'cdf' );
title( 'Cumulative Density Function' );
y =betarnd( a , b , k , );
subplot( ,, );
hist( y , );
xlabel( 'x' ); ylabel( 'frequency' );
title( 'Histogram of random values' );
mu = ;
xmin = ;
xmax = ;
n = ;
k = ;
x = linspace( xmin , xmax , n );
p = exppdf( x , mu);
c = expcdf( x , mu);
figure( ); clf;
subplot( ,, );
plot(x,p,'k-')
xlabel( 'x' ); ylabel( 'pdf' );
title( 'Probability Density Function' );
subplot( ,, );
plot(x,c,'k-')
xlabel( 'x' ); ylabel( 'cdf' );
title( 'Cumulative Density Function' );
y = exprnd( mu , k , );
subplot( ,, );
hist( y , );
xlabel( 'x' ); ylabel( 'frequency' );
title( 'Histogram of random values' );

2、用以上matlab程序来展示Binomial(N,θ)分布,其中N = 10,θ = 0.7。如图1.2。

3、写程序从Bernoulli(θ)中采样10个值,θ=0.3。Bernoulli分布是最简单的离散分布,只有两个输出值,0和1,以θ的概率输出为1,1-θ的概率输出为0。这个分布能模拟一些实验结果,如猜硬币的正反面,判断题的正确与否等等。在Matlab里,你可以使用Binomial分布来模拟Bernoulli分布,只需令N=1即可。尽管如此,为了练习的目的,请写出代码来模拟Bernoulli分布值,不要使用内置的Binomial分布。

for n=:
randValue=rand()
if randValue<0.3
x(n)=
else
x(n)=
end
end

4、保证每一次仿真都给出同样结果是非常有用的,在 Matlab 里,每次重执行代码,从分布中得出随机值是不同的。有一个简单的方法保证产生同样的序列,使用随机数字生成器。写从随机分布中采样10个随机值的Matlab代码时,在两次采样间使用seeding函数可使两个随机值集合相同。Matlab代码如下:

seed=1; rand(’state’,seed); randn(’state’,seed);

使用Matlab中的RandStream方法可以有更高级的方法来生成随机数。对于本文的大部分应用,用不到该方法。

5、假设我们从以前的认可研究中知道,智商系数是均值为100,标准差为15的正态分布。从该人口中随机抽出一人,计算他/她的智商大于110但小于130的概率。你可以使用一行Matlab代码。

normcdf(,,)-normcdf(,,)

**6、Matlab当前不支持Dirichlet分布,你能使用在线资源找到一个Matlab函数,来从Dirichlet分布中采样吗?

1.1 从非标准分布中采样

如果我们要从一个Matlab没有的非标准分布中采样,在建模时,这种情况经常遇到,譬如研究者能提出一个新的噪声过程或现有分布的组合。用计算方法来解决复杂采样问题,一般要依赖现有的简单分布采样方法。从这些简单分布中的采样值能被转换或同目标分布比较。其实本章讨论的一些技术已经在Matlab中用于复杂采样,如正态分布和指数分布。

1.2.1 离散变量的反变换采样

反变换采样(也被称为反变换方法)是一种从概率分布中生成离散数字的方法,当然要给定累积分布函数的反。思想是从均匀分布随机数字(0和1之间)中采样,然后使用反累积分布函数转换这些值。这种过程的间接性是建立在基于转换均匀偏离的潜在采样的事实上。这种过程用于采样许多不同的分布。事实上,这就是Matlab执行许多分级数字生成器的方法。

很容易将这种方法用在一个我们知道单个输出概率的离散分布。在这里,反转换方法只需要一个简单的查找表。

给一个非标准离散分布的例子,我们使用一些实验数据,这个实验考察人类能够生成多均匀随机数字。在这些实验中,产生了大量的随机数字(从0到9),调查者将这些随机数字的相对频率制成表。正如你所想,人民并没有一直生成随机的分布。表1.2.1显示了一些典型数据。一些较小和较大的数代表性不足,而另一些数字则过多。由于一些原因,数字0和9从未产生(可能是对指令的解读有误)。这些数据说明人类并不擅长产生随机分布的数字。

《Computational Statistics with Matlab》硬译

如果我们要模仿这个过程,写一个采样算法,根据表1.2中的概率。所以程序应该以0.2的概率生成4,以0.175的概率生成5,等等。例如Listing1.2使用Matlab内置的函数randsample来执行这个过程。代码生成效果如图1.2.1所示。

theta=[0.000;0.100;0.090;0.095;0.200;0.175;0.190;0.050;0.100;0.000]
seed=;rand('state',seed);
K=;
digitset=:;
Y=randsample(digitset,K,true,theta);
figure();clf;
counts=hist(Y,digitset);
bar(digitset,counts,'k');
xlim([-0.5,9.5])
xlabel('Digit')
ylabel('Frequency');
title('Distribution of simulated draws of human digit generator');

《Computational Statistics with Matlab》硬译

注意上图在原文中是Figure1.3,但对该图的标题的错误的,明显不是BINOMIAL(N,θ)分布。第9页代码上面的Figure 1.2.1也是错误的,应为Figure1.4。

不用内置函数如randsample或者mnrnd,考虑如何使用反转换方法执行潜在采样函数是很有帮助的。我们首先计算累积概率分布。换句话说,我们需要知道一个结果等于或小于一个特定值得概率。如果F(X)表示累积分布函数,我们需要计算F(X=x)=p(X<=x)。对于离散分布,使用简单的求和就能完成。我们例子的累积概率显示在表1.2.1的右边一列。反转换算法的思想是从均匀离散偏离中采样,并同累积概率表中的每一个随机数比较,第一个输出的随机偏离小于采样输出相关累积概率。下图显示了一个例子,均匀随机偏离U=0.8,采样输出X=6。均匀重复采样偏离同累积分布比较,是离散变量反转换方法的基础。注意我们在使用逆函数,因为我们在做一个反查询表。

1、写一个Matlab程序对离散变量执行逆转换方法,用它来以表1.2.1的概率对随机数字采样。为了显示算法的运行,多采样些数字创建一个直方图。你的程序不能有0和9,因为它们在表中是0概率。代码如下,经测试,该代码生成的图形与上图一模一样。

cumpro=[0.000;0.100;0.190;0.285;0.485;0.660;0.850;0.900;1.000;1.000]
seed=;rand('state',seed);
K=;
digitset=:;
for n=:K
rd=rand();
for i=:
if rd>cumpro(i) & rd<=cumpro(i+)
x(n)=digitset(i+);
break;
end;
end;
end;figure();clf;
counts=hist(x,digitset);
bar(digitset,counts,'k');
xlim([-0.5,9.5])
xlabel('Digit')
ylabel('Frequency');
title('Distribution of simulated draws of human digit generator');

2、上面练习的一个解决方法是通过使用多项式的随机数生成器 mnrnd,不需循环。如何使用这个函数来实现符合表1.2.1的采样。Matlab中未发现有该函数。

3、解释下为什么以上算法在处理陡峭的概率分布时效率很低。[提示:想象一种情景,前N-1个输出概率为0,最后一个输出概率为1]。你能找出一种简单的改变来提高效率吗?

1.2.2 连续变量的逆转换采样

逆转换采样方法也能用于连续分布。一般思想是均匀随机采样,然后将累积分布的逆函数用于随机偏离。下面用F(X)表示目标变量X的累积密度函数,F-1(X)是逆函数,假定我们可以计算这个逆。我们想要采样X值,可以通过以下步骤:

aaarticlea/png;base64,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” 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让我们用一个简单的例子来说明这个方法。假设我们要从指数分布中采样随机数。 λ > 0,累积密度函数是F(x|λ) = 1 − exp(−x/λ),使用简单的代数,能够找到这个函数的逆,F−1 (u|λ) = −log(1−u)λ,这导致以下采样过程,从指数分数中采样随机数:aaarticlea/png;base64,iVBORw0KGgoAAAANSUhEUgAAAS0AAACLCAIAAAC7s1j+AAAgAElEQVR4nO2dezxV2f//30xIUtOVaZhMF9WUppmK0kijmyJK6YKKUo36uKRESo+ERCVJSMyIRnRTmFTu5N5NKtckXZDcOs45LsfZ3z/257N/+7fPxTnH4fTps55/2e+19nuts/d+7bXWe61tAYZAICQNSLoCCAQC6RCB+AJAOkQgJA/SIQIheZAOEQjJg3SIQEgepEMEQvIgHSIQkgfpEPEVcu3atYEs7t69e58/f+6LBwnokE6nN3Lj06dP3d3dA18fYenp6WlpaWEwGEwmk8lkMhiMlpYWcobW1ta2tjY8Q2tr6wBUqbW1taWlhUajMRgMGo3W0tJCfiyYTGZLS0t7ezuDwWhra2traxNj0bm5uSdOnPDx8WlsbBSj276wZ8+epKSkgSyxubl55cqVnz59EtmDoDosKiq6dOmSyMWQiYuLMzY2HjduHAAMGTJk3bp127Zt27Ztm7m5+YIFC3766ScvLy86nS6WsvqDkpISCwuLadOmAYCsrOyiRYt27drFYrHw1O7u7s2bNysrKwOAiorK+vXr29vb+7tKx44dW7JkiYKCAgAMHz582bJlZ8+eJVKTk5P19PSkpaUBYMqUKc7OzsL6P3fuXGhoKKfdyclp5cqVdDp92bJlOjo6ffoNYsLPz+/w4cOc9qdPnx47dszT09PPz6+hoUFk/1FRUfn5+Zz2wsJCfX194jEQFn46ZLFYxcXFiYmJNjY2gwYNMjMzE60Mrty7dw8AjIyMKPbq6urFixerqam9ePFCjMWJncDAQADYu3cv19SkpKTffvuto6NjIKu0b98+APDx8eGaevnyZT09vZ6eHmHdNjY2AgAAUNr2lJQUAKipqcEwzMjIaMuWLaJVW4xUVFTMnDmT8ze6u7uvXr0a77YUFxdraGhkZWUJ7pZGoxUVFUVHRxsYGADAxYsXuWbbt2/f+fPnRas5Px1+/vx5//79ISEh5eXlACBeHaanpwPA+vXrOZN6enqWL18+atSo169fi7FE8bJ+/XoAyMjI4JoaFRUVHR09wFVydXUFgDNnznBNraiocHV1Fc3z6dOnz507RzHu37//u+++E81hP7Fq1arg4GCKMT4+ftSoUQwGg7Dcvn1bSUlJ8G7k48ePXVxcrl69GhMTw0eHtbW1Y8aMaWpqEqHmAvVLmUzmQOoQw7CGhobBgwd/IV0drigpKcnJyfFq8bZv396Xzo9o8NdhZWWlyDrkytq1a2fOnClGh32koqKCojccLS2tzZs3ky0sFktRUdHb21vYIpKSkvjoEMOwDRs2nD59Wli32BerQwzDLC0tASA5OVmMhYqLsrIyANDV1eWVgbO/PQAMsA5NTEy+KB06Oztv2LCBYvz48aOUlJSHhwfFrqGhMXv2bGGL6FWHkZGR06ZNE9Yt9iXrMDIyEgCIN1lra2t5eXlmZib+wistLX348CHllCdPnkRFRd29e5ccwGSz2QwGo7u7u6enp6Ojo7Ozs7u7u6Ojo6enp7u7m8FgsNls/DfieZhMZq+VDwkJAYCjR49yTX379q2trW2vTsSOsDpsamp6+fJleno6fgXq6urS0tIqKiooJ7a2tpaVlWVmZhJXprOzk0ajGRsbz5gxg0aj0Wi0zs5O8im1tbXXr19PTk6mxGYZDMbr16/z8vLevXuHl5iZmdnV1YVhGIvFqqure/r0KX5b2Wx2WVlZSkrKhw8fyBXOzMx8/PgxfgqFGTNmkKNTONevXweAqKgoit3AwGDQoEFc/fChVx2+evWKGDMLxZerwwcPHgCAqqoqhmFNTU26urrDhw8HgNLSUkdHx+Dg4CFDhly4cAHPzGAwHB0dY2Nja2pq7ty5M3PmzLCwMDyptbV1xYoVQ4YMAYDJkyeHhobeu3dv4cKFADBo0KCVK1fi4YdNmzYBgJSU1LJly3qt/MaNG/kPDuPi4oS9IH1HKB0+e/Zs/vz58vLyAPD582c3N7eoqKi0tLSlS5cuXbqUkNz79+91dHTwq/f27VvcGBMTY2ZmpqqqqqCgYGZmZmZmRjzoDQ0NpqamZ8+eraioyMvLs7Cw8PDwIAInlpaWKioqAPDXX3/5+fkFBATMmDFj48aNGIZdvnx51qxZAKCtrV1dXe3s7JyQkBAfHz9x4sRjx45hGHb+/Plz585lZmY6ODioqalVVVWRfx2dTgeAoqIiyq8OCgoCgOvXr1Ps+PD+48ePQl3hXnWIYZiysvLly5eFcot9yTp8/vw5AEhLSxN3ER8lu7i4vH37tqmpaeTIkUQX38XFxc3NjYgaZ2RkAEBiYiLh7fz58xSLrq4upWdiYWFBqJc/3333HZ/BobW1tVCD9SdPnvj5+UVERBAPOlcKCgr4+xGhX3r06FEA8PX1JWKhb9684WxAvLy8yDrEMTExmTBhAtnS0tKioqISHx9PNm7ZssXKyoo4rK+vBwAbG5vbt29jGKarq0t+8enq6mppaXl4eOBNNIZhly5dAgBPT0/yz1dTU9u2bRu5lIqKCgBobm6m/EC85rdu3aLYzczMAKCyshITBkF0qKWlxaujxIcvV4d4kBYAiHczfhX27NmDHxK3CsMwQ0NDACgvLyeShg4dunXrViJDW1ubnJzcjh07CIu3t7eUlBT52dq9ezfZJy/wW85ncLh27dpenRC4uLgAwPjx40ePHi0nJxcQEMA1G51OX7duHX9XIujwzJkzAECJtg8ePNjGxoZsOXfunCA6tLa21tDQoBRRWloKACkpKfgh/ixNnz6dayWNjIykpKSePXtGWAoKCgBgzZo15Gz6+vqUYRj+OHHOWBw4cAAAEhISKPbNmzcDwJMnT7hWgxeC6HDFihWUqycIX64O8/LyAEBRUZGw4FchIiKCM3NlZSVlKZO6uvrKlSvJFhMTkxEjRhBDgu3btw8dOvTkyZP4YWNjo4CvsdDQUP6DQwcHB0H8YBh25coVDQ2NkpIS/DApKen77783MDDgXIWTnJx84MAB/t5E1mFOTg7ZOGzYMEprI4gOOzo6vvnmG3LTRyAvL09EUPBnifyKJGNkZCQnJ0eW05MnTwDAy8uLko3yCrh8+fKwYcM4Hbq7u3NtD/FhSFlZGddq8EIQHVpYWPT6xuTky9VhfHw8ACxevJiw4Ffh3r17vE5JSUmxt7f38vIKDg4eO3asnp4eOfXGjRsAgPeaamtrvby8Nm/e/PPPP+OpQUFBAq4csLCw4DM4jIyMJPd++aOpqfnq1Suypb6+Xltbe8qUKUTbjmEYg8H4+eefHz9+zN/boUOHhJ0/xHVI6Z4NGzbM3NycbBFEh48ePQIAru8gZWVldXV1/G/8WXJxceFaSSMjo3HjxpEtuA4pj76RkdH3339PtgQFBY0dO5bT4dmzZwHgxo0bFDs+Pnz//j3XavBCEB3u2LGD0gAIwperQycnJwAICgoiLPhVSE9P58xcXl6uoaFhaWlZX1+PW9TV1Sk67OjoGDZsGF7iqVOnqqqq7t69CwAvX77EMEzwvsSvv/4KADQajWuqvr6+gAvZ6HT6kiVLOO2dnZ329vaKior79++/efNmYGDgpEmTLC0te3V4+vRpzqaD4N69e5wS5aVDyr0WRIdZWVkAYGdnx1m0kpISMeOPP0tHjhzhWknBdUjJdu3aNVlZWU6HUVFRAMA57F+yZIm0tLSwC54E0aGpqen27duFcot9sTpkMpkqKirjxo0jzyLw0mFzc7OKisrq1avJRkKH7969I5aPW1paysvL02i0P/74A8Ow7u7uMWPGuLq61tTU+Pr6CljzadOmKSkpcU0qKSnptfdI8P79ezwSyJV79+7Nmzdv0KBBKioqBw8eFGQ9Gh6d2rlzJ9dUPz+/tLQ0ilGMOvz8+TMAWFhYUIpgsVhycnJEE9FPOsTfApxvwLdv3wIA53WePn06rzEqHwTR4ZIlS9zc3IT1LAYdirBkEetNh4cPH5aSkiIG9zi8dIjHUcnjw56eHnl5eVyHHh4exKcA+JJIV1dXYqJp9+7dP/7444kTJ968eSNgzdevX//tt99y2hkMxqpVq8T7NQNlXo4/PT09c+bMGT9+POe0WHd3t7GxMac3MeoQw7Bly5YpKytTYl24Qv766y/8sJ90iEf1uN7EOXPmUOb3GQyGvLw8pZcuyGMsiA5nzZpFTKcJjkA6bG9vBwDOxQoYhoWHhysoKIgwYZKamgoAJiYmFHtXV9fBgwfl5OSuXr1KSUpMTASA1NRUij0uLg4AIiMjCcv9+/cnTJgwd+5cDMPc3NyI56+np0dZWVlGRqaurg635OTkAIChoaGwNacsum9vb7eysnr06JHgfvqD0tJSOTk5d3d3it3d3Z3rJ3mnTp3iDFfgs4Jki7+/P+dTbmxsrKamRra8efNGUVGRMne6ZcsW8gABf5a4fhKBYZiBgQGlr/Hw4UMACAkJoWSj6LC7u1tBQYEyZYITFhamqKhIXu92/fr1oUOHkl8rW7duVVBQePr0KddaEeBPIKUyZDo6OmRkZCjthyD0osPAwEAnJ6fFixcDwNChQy0tLT09Pclr1fF4lFBL9XJzc11dXbW0tABgzJgx7u7uZ86cOXPmjLe3t7W19Q8//GBqakpZ1UGj0dzd3XV0dABg7ty5Li4uubm5RGpHR4eJicn48eNzc3MZDEZCQoK/v39iYqKsrOzp06cpIQF7e3ty7AfDMDU1NWGXyR87dkxdXT0rK4vFYn348CEqKsrIyKjXOMrAkJubO23aNEdHx7q6OhaL9fjx482bN//555+UbG/evDl8+PD06dMBYNWqVXi3/O+//961axd+X9zc3IqKit6/f+/m5qahoYFPHuDB6tzcXGdn5xEjRgDAli1bvL29iQDvixcvFi1aFBQUVFNT8/Dhw127du3cuZPoLgYHB5ubmwOAqqqqnZ1dTEwMUZ/s7GxnZ2d8qcaePXvwt4aHh8eKFSsAYNasWW5ubvX19Q8ePCCyOTg4kCfoly9f7uTkxPWabNu2bdOmTfhosKamZsKECZQI6oIFCwDg+PHjXE9vaGg4deqUra0tfrl+/PFHGxsbX1/f6upqSs6cnJzBgwcLsiSLQi86TEtLy8jIyMnJKSwszM/Pz87OTk1NJYfy2Gw2+VAQqqur07mRkZHx7Nkzrl8ednR0pKSkPHjwoLCwMDc3Nz09nXMGtri4ODg4OCAggNBDcXFxQkIC5dvi2tpayoK41NRUETqThYWFTk5Oa9as2b17d2xsrGid836CwWBERETY2NgYGRnZ2tpyfc03NTWlpaXhdzY7Oxvv7T98+DAzM7OgoCAvLy89Pb2mpqalpSU1NTUnJ6egoCArKwtfsILfwdzc3IKCguzs7JSUFPJdY7FYRUVFwcHBMTExlCc1JycnKyuroKAgPz8/MzOTvPylsrIyPT09Ly+voKAgMzMTn9lLTk7Ozs4uLCzMycnBb1NVVRVnNpzw8PB58+bxuiaJiYkHDhzw9vY+ePAg58PT1dX1+vVrT09Prue2tbWlpKRkZmbm5uYWFhbm5eVlZmampKRwLsfx8fGhTHUKCPq/GIivhPb29uHDhws7JUjQ2dnJ69NNAWGz2ZMnT+YcNwkC0iHi68HX15dXuLhX4uPj8/Ly+lJ6fHz8/PnzRTsX6RDx9dDV1TV79mwRPh/v6Ojo4ycy3d3d2traxcXFop2OdIj4qigrK9PT0xN2gv7GjRsifKxEZt++feQ1J8KCdIj42sjLy+P88Ldf+eeff/z8/PriAekQ8RUi2j+JkWBxSIcIhORBOkQgJA/SIQIheZAOEQjJg3SIQEgepEMEQvIgHSIQkgfpEIGQPEiHCITkQTpEICQP0iECIXmQDhEIyYN0iEBIHqRDBELyIB0iEJIH6RCBkDxIhwiE5EE6RCAkD9IhAiF5kA4RCMmDdIhASB6kQwRC8iAdIhCSB+kQgZA8SIcIoWEymYmJiZKuhYg8e/ZM5D2h+g9J6rCsrCwkJOTAgQPh4eH47gJ0Oj0zM3NgSm9ubm5ra2MwGEwms729nUaj8UoV71bb/QSTyayqqsrNzRVhM1qh+Pz5s4GBAWWPbknR3t7++fNn5n9oa2sj7wHa2dnZ3Nzc3t6O32JiS+AtW7bw39qppKQkKytLhO1ERaZ3HRYVFXl7e+/atcvPz+/58+fiKvjo0aMrVqzIysr68OFDfn7+nj17zp496+7uTtm1vJ9obm62sLCYNm0aAACAkpISeUvjhoaG2bNn40kzZ87csWPHAFSpj9y6dUtHR0daWpqyZ73YWb16dXJyMtekzs5ODw+PlpaWfq0AGS8vL2Nj40GDBgHAhAkT1q5de+fOHSI1Li5OT08PAKSkpBYuXBgdHY3bW1pa5s+f/+HDB15uGxsbN2zYoKqqKsLWUaLRiw6PHDni7e396tWr8vJyT09PGRkZW1vbvu99GxoaqqOjw2azycagoCAZGRlhdZienk7xIzh0Ol1ZWRkAOB+s5OTk7777Ljs7WzTPkmLZsmX9qsNLly5ZW1tTjPX19Tk5OYGBgfj23Zy77fY3o0ePlpWV5dydF0dTU5MsTpzExMR169bx8fn+/XspKam1a9eKrZZ84afDS5cu/f3332TLmTNn+GwjLjijRo26efMmp11TU1NYHZqbm1N23hYKd3d3ALC0tCQbm5qaVq9e3ceNuCSCiYlJ/+mQyWQqKSm9fPmSYr969eqRI0dSUlIcHBwGXoelpaUAoKuryyuDvr4+p5HNZk+dOhXfjZwXixYtkpGRGZjmnZ8OdXR06urqyJaOjg4FBYUhQ4awWCyRi6yqqgKA3NxczqSLFy8Kq8OffvqpLzqsr6+XkZGRk5NrbGzELe3t7Zs2bXr//r3IPiVIv+owLCxs+fLlfDIcOHBg4HUYHBwMAEePHuWa+vbtWxsbG65JISEhhoaGfDyHhYUBQHh4uBhq2Rs8dUij0QBg8ODBlCjFr7/+CgAlJSUiF4nrkGujWlVVdejQIcFd5efnA0BfdIhhmJmZGQB4eXlhGNbZ2bl169bq6uq+OJQg/apDLS2tkJAQPhkkosMNGzYAQEZGBtfUqKioa9eucU2qra2VlpbmM0psaWmRlZXV09MTT0X5wlOHbDZ7zpw5c+bMoTR9+BigLwEbNps9ZsyYoUOHZmVlcaZy3sXm5uY7d+7ExcVRYnTFxcWqqqoA0NraSqPRaDSaaILExfz99993dHTs3LlTjLGogYeXDjs6OvLy8qKjo0tLS7kOp1ks1osXL7KysvBuWF1dXURExOnTp7u6uvAMjY2NUlJS/PedlogOlZWV5eTkeG0AbG1t/enTJ17nqqioRERE8HFubGwsJSVF6RX2B8LNW9DpdHl5+WHDhhG3RzSioqLwaOTixYt9fX2Lioq4xn56enqOHj1qbGz8/Pnz8vJyU1NTOzs7XGzXr183MzObMmUKAGzatMnMzMzMzIx/d58Pc+bMAYCFCxfm5+f35XdJHK46vHz5sqmpaWpqanV19aVLlxYtWkQZ4+Xl5f3yyy/BwcG3bt1avny5tbW1v78/jUbT1tYmLuk///yjqKjIP0Q38DosLy/nPzg0MTHhc/rGjRu3b9/OJ8O1a9cA4OzZsyLXUECE02F4eDgAnDx5su8Fnzp1SkZGBv7D2LFj9+7dS8zw4OzZs2f69OmdnZ34IZ1OV1NTI08w2NnZ9b1fimFYZGQkACxYsEC009++fXvp0qW/BCM6OrrvAWdecOrw5MmTmpqa5Ev08uXLESNGlJaW4ocfPnwYOXJkcHAwftjU1CQrK/vnn39iGPbx40eiqqGhoRoaGvxLH3gdXrhwgf/g0N7ens/pzs7OfDSMYRiTyVRUVNTU1OxLJQVBCB3W19ePGTNGX1+/7889zuvXr/39/ZcsWSInJ0dM1hHhqUePHklJSRHPB86BAwdGjBhBPBzi0qGHh4eCggIAPHv2TITTX7586e7ufkQwvL29iTeL2KHosKqqavDgwZyh6fXr1xPzRoGBgQBAXmIyderUmTNnUk45cuSIjo4O/9IHXoebNm3iPzi8desWn9N9fX2nTZvGvwh8BvLVq1ei11IABNUhm83W19fX1tam0+lirwSTybx///68efMA4F//+hdu3LdvHwAUFhaSc8bExAAAMbsqFh0GBASEhYUdPHgQADgnxyRCZWVlkQA8fPiwtbWVfCJFh4cPHwaA2tpain8fHx9Ce4cOHQIAonnEMExHR+fHH3+knLJ9+3YjIyP+1RZchyL/QArjxo3jMzjcsWNHc3Mzn9PDw8NHjx7NJ4O7u7uFhQURxus/BNWhp6fn77//Tln8JRpdXV1cLxydTp86derw4cPxw6VLlwKAp6fnSRIuLi6GhoZEPLPvOoyIiDhz5gyGYe/evfvmm2/k5eX537mBYePGjQsFQFdX9+rVq+QTKTo0NDQEAM51eXh37sqVKxiGpaWlAUBcXByexGazlZWVd+7cSTnF1NR0/fr1/KstuA5F/oFkXr16xX9w2GuFo6OjhwwZwivV09PTzs6up6dHWVl5+vTpvf6oviCQDiMiIlatWsXrrSMsOTk5+PCDE3wu6M2bNxiGLV++nOszRIaiQ2Hb6ps3b5KHFuvWrRPX6FdSUHT4+++/AwDnTHRISAgAhIaG4odr1qyZO3cuvh7Fx8dn+vTpnC+j3bt3L126lH/pA9wvTUhIAIB9+/ZxTc3MzOx1DiwoKGjixIlck7y9vfX19fHJAnt7e5HHLALSuw7v3r1rZmZGbnPu3LlD7sYIS3Z2tpOTE9ek1NRU4rlxcXEBgIqKCj6uKDp0dHQUvBr379+3s7OjVAwA1NTUhI2j3L17V1VVdZxgTJ06lRKOEiMUHTo6OnId23h5eQFAUVERhmEsFuuPP/7Iz8+3tbV1dna+ePEi1+HrsWPHZs+ezb/0Adbh1atXAYDXlKaVlVV9fT1/D15eXlwHvSdPnpw2bRrRBhQWFgKAi4tLHyvMh150+OjRo127dlGmEG1sbMjvS2Gf2uzs7B9++IHrzEdYWBgxMnn8+LG0tDTnVY6NjX337h3+t6urKwC0t7fjh7xejZxkZWVZWlpy1nzWrFkAwH9w/yVD0WFubi4AUGJdGIb9/vvvkyZNwm9BWVkZ5X3ElQsXLqipqfHPM8A6xFe0+fv7cyZdu3bN19e3Vw8ODg4bN26kGP38/EaNGkV5eU2aNKnXn98X+Omwurp6xowZPj4+xPDsxIkTLi4u5Ph1eHi4goLC5cuXBS8Sb3asrKwoMujp6Zk1a1ZUVBRhcXZ2VlJSIner2tratm7dShzGxsYCwNOnTzEMY7FYzs7OglTgypUr6urqXN/6oaGhAPDbb78J/nO+KIyNjcePH0+22NnZzZ49m9ydKS8vl5WVJWKMLS0tI0aMOHv2bHx8fHJycnZ2dklJCedcf35+vpSUFP+oCR5aG7Cv+9hs9sKFCzmX2qWmptrY2AjSPCxcuJDSd/X395eRkeFcYeLm5sZrMaZY4KlDOp0+efJk4Aa5KcfXSZPn9HolOzt70qRJsbGxBgYG8fHx9fX1bDa7rKzM0NDQwcGBnLOnp+fUqVPz5s1LS0trampKSUmxs7MjL27o6urS1tY2MjKqrq4+derUkydP+JSLL5qbP38+AAwZMiQsLIyS4cKFC9OnT8d/49q1a318fMQ1QzMA5ObmOjs7jxgxQkpKytbWloi7sFis48ePr169OjMz8/3791euXNHW1k5NTSWfe+TIEcotHj16tJ2dHfkDvO7ubgUFBc4PFzAMe/Tokbe3t7W19ZgxYwBg/vz5e/fu9fPz6+NiD0F49eqVurq6k5NTU1NTV1fXw4cPd+3a5erqKogIu7u75eXlyd+74sMirsGLmpoaWVlZCwsLcdaeBE8ddnR0pPPgxYsXRDY2m11eXi5UkRUVFfi3qs3NzcHBwebm5kZGRo6OjrxWw3z8+PH27duBgYEFBQWc68tZLFZcXJy/vz+5Vrz85OXlFRUVFRYWPnjwgDN/UVFRQUEBHjEvLCzsv5dff1BdXZ2enp6Xl5efn5+ZmUlZgFZfX3/r1q1z585lZWVRRqfHjx/fsWPH69evaTQag8FobW0tKSk5e/bsqFGjKB9eWlhYcB0j1dTUpKamZmVl5eXl4dctIyMjOTm5Lx8DCA6TyQwMDNyyZcuGDRs8PDwE/2KwoKBg7Nix5FdtZWUlHkPmSnp6up+fXx9rywv0fzH+p8nPz//222+5dtFv3749cuRIsiU7O1tVVfW/qI/An+3btx8+fFjStfg3SIf/02RkZIwcOZJrw5WUlKSsrEwZKK5YsYJPi/FfRENDg5KSUkNDg6Qr8m+QDv+n6enpMTAwcHBwoAyoGhoafvnll4sXL1LyV1VVaWlp9d+6vAHDwcEhKChI0rX4fyAd/q/DYrFCQkJMTU0PHTp08eLFgIAAW1vbLVu28Fq0GR0dbWtrO8CVFC8JCQkbNmyQdC3+P5AOEf+GxWLV1tby+VqP4OLFi0Q89r+ON2/e7N69eyD/F5sgIB0iRKGpqUnSVRCRL2H9MCdIhwiE5EE6RCAkD9IhAiF5kA4RCMmDdIhASB6kQwRC8iAdIhCSB+kQgZA8SIcIhORBOkQgJA/SIQIheZAOEQjJg3SIQEgepEMEQvIgHSIQkgfpEIGQPEiHCITkQTpEICQP0iECIXmQDhEIyYN0iEBIHqRDBELyIB0iEJIH6RCBkDxIhwiE5JGADul0eiMHX+Z/WUYgBobedfjo0SMPDw97e/ujR48+ePCg70XGxcUZGxuPGzcO35fXzMzMysrK3NzcwMBAS0vLxcXl48ePfS8FgfgvohcdOjs7h4SE4I3V48ePx44du2bNGrHst3zv3j0AMDExIRuZTKadnZ28vPyXv41Jeno65ybyCIRo8NNhTEzMhg0b2traCIu/vz8AeHh49L3g9PR0AFi/fj1n0s8//ywjI5Ofn9/3UvoPc3Pzr5cMs9kAAAY+SURBVGZnXITE4afD3bt3A4C/vz9hSUlJAQBdXd2+F8xHh05OTgDwxx9/9L2U/uOnn35COkSIC346LCgosLKyevXqFWG5efMmAIhlD0c+Ojxy5AgA6Ovr972UfiI/Px8AkA4R4kK4eKmVlRUA3L9/v+8F89HhmjVrAOD8+fOcSUwm88GDB1euXHn58iV5eMZkMmtqagoKCqqqqjAMa2pqysrKqqys5FU6Lz8ET548iYqKunv3bktLCyWpuLhYVVUVAFpbW2k0Go1GQ4JE9BEhdPj69WsFBYX9+/eLpWBeOszJyZGSktq4cSOnPG7dujV//vzU1NTa2lpvb+9FixYRkVUrK6vx48cDgKur67Fjxzw8POLj411dXSdOnJiSkiK4HwzDGAyGo6NjbGxsTU3NnTt3Zs6cGRYWRqRev37dzMxsypQpALBp0yYzMzMzM7P09HSxXBPE/yy967Curi4yMvLgwYMLFy68ffu2uArGdbh8+fKSkpKSkpKHDx/Gxsbu2bNHU1Pz8uXLnPmvXbs2ZMgQchNnamq6bNky4vDTp08A8MMPP7x+/Zow3rx5U0pK6vr164L7cXFxcXNzY7FY+GFGRgYAJCYmkitjZ2eH+qUIMdK7Dtvb258/f56Tk3Ps2DFNTU3O5kU0cB0uWLAgLi4uLi4uNjb26NGjEydO9Pb2bm9v56zDuHHjKI1nUlISADx58gQ/ZDKZAGBtbU05d8GCBcrKynjUVxA/hoaGAFBeXo4fstnsoUOHbt26lXwK0iFCvAg3Pjx37pyUlNSlS5f6XjDXfml9ff2oUaM0NTUpj3hiYiIA+Pr6UjIDwF9//YUf4jp0dHSkFBQYGAgAV65cEdBPZWXltWvXyBnU1dVXrlxJtiAdIsSLcDqk0+lycnKKiop9X/LCa3zo5eUFABcuXCAbjx8/DgCWlpYnSfj4+BgYGCQkJOB5eOkQb+6cnZ0F9IOTkpJib2/v5eUVHBw8duxYPT09cirSIUK88NNhYWEhZ8hx0qRJAHDz5s0+FsxLh1FRUZxTIydOnAAA/qNTXjrE5zwdHBwE9FNeXq6hoWFpaVlfX49b1NXV+euQTqfzcYhA9ApPHT569AgAhg8f3tnZSbZPnToVACIiIvpYMC8dxsfHA4CGhgbZiC+CCw0N5eOQlw6Dg4MBICoqShA/zc3NKioqq1evJhsJHb579w7XHkWHnIUiEELBU4eVlZXS0tJ6enrk+YOenh5ZWVkAKC0tJRtFKJiXDjMzMwFg6NChhKW1tbW9vV1FRYVz/UBFRQURycR1uGfPHkoeQ0PD4cOH441br35iYmIAgDw+7OnpkZeXx3Xo4eHR2NiIYZirqysAEPGkffv2iXAFEAgCfv1SY2Pjuro6suWff/4BgI0bNxKW8PBwBQUFrjMN/ElNTQWAdevWUexv3rwBAELqLBbryJEjGIYlJSVJS0vn5OQQOdls9s6dO3FhYP/R4aRJkxgMBpEnLy8PAP7880/Cwt9PXFwcAERGRhKp9+/fnzBhwty5czEMc3Nzw3sHsbGxAPD06VO8hvjgE4EQGX46rKurMzY2jo2NxZ/soqKi8ePH6+vrk5eYuLu7A4C3t7fgRebm5rq6umppaeH9Xhsbm4CAAHKG/fv3A8CJEycwDLtx4wYxS56UlDRr1qzIyMiPHz8WFxc7OjqS14LjOrSwsNi3b19xcXFbW1tMTIyamlp0dDSlAnz8dHR0mJiYjB8/Pjc3l8FgJCQk+Pv7JyYmysrKnj592sXFBc/W1dWlra1tZGRUXV196tQpYs4DgRCNXuKlbDY7NjbW1tbW3Nzc3t6eM8LBZrOJqTYBqaysTEtLe/DgQWFhYV5eXkZGBud6lLt37+7du/f48eMxMTFkO51OT09PDwgISE5OpkwzEuPD7u7u27dv+/v7379/n/yxiIB+MAwrLi4ODg4OCAh4/PgxYUlISCAHSFksVlxcnL+//4sXL4T6+QgEJ1/P/8XgFadBIL58kA4RCMnz9eiwrq4OALZt2ybpiiAQQvOV6NDMzExDQ2Py5MmTJ0+eN2+euBbBIhADw1eiQwTivxqkQwRC8iAdIhCSB+kQgZA8SIcIhORBOkQgJA/SIQIheZAOEQjJg3SIQEie/wOkPRNbtXP0VgAAAABJRU5ErkJggg==” alt=”” width=”270″ height=”125″ />练习:1、实现指数分布的逆转换采样方法,从这个分布中采样,并显示这些数值的分布。同指数分布的累积概率密度分布比较。

K=;
for n=:K
rd=rand();
lamd=;
x(n)=-log(-rd)*lamd;
end;
hist(x,);

**2、Matlab实现了一些函数,例如,当调用exprnd时,Matlab执行了存储在它自己内部路径中的函数。请定位Matlab函数exprnd并查看它的内容。Matlab如何从指数分布中采样?它是使用逆反方法吗?注意这个Matlab函数的路径依赖于你的Matlab安装,路径如下:C:\Program Files\MATLAB\R2009B\toolbox\stats\exprnd.m

function r = exprnd(mu,varargin)
if nargin <
error('stats:exprnd:TooFewInputs','Requires at least one input argument.');
end
[err, sizeOut] = statsizechk(,mu,varargin{:});
if err >
error('stats:exprnd:InputSizeMismatch','Size information is inconsistent.');
end
mu(mu < ) = NaN;
r = -mu .* log(rand(sizeOut));

可以看出exprnd正是采用逆反方法进行采样的。

1.2.3 拒绝采样

很多情况下不能使用逆反方法采样,因为很难计算累积分布和它的逆。在这种情况下,有另外的选择,譬如拒绝采样,以及我们将在下一章讨论的马尔科夫链蒙特卡洛方法。拒绝采样方法的好处是它不需要任何”burn-in” period。所有的采样都能立即用于从目标分布中采样。

展示拒绝采样(也被称为接受拒绝采样)通用思想的一个方法是图1.5。假定我们希望得到圆心为(0,0),半径为1的均匀点。首先,看起来从直接从圆中均匀采样非常复杂,尽管如此,我们可以用拒绝采样,首先从饶圆的正方形中获取(x,y)值,然后拒绝x^2+y^2>1的值得采样。注意在这个过程中,我们使用了一个简单的建议分布,如均匀分布,作为从更复杂分布中采样的基础。

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” 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拒绝采样可以从很难采样但能评估一些特殊采样概率的分布中生成观测点。换句话说,假定有一个分布p(θ),很难直接从这个分布中采样,但是我们能估计概率密度或者针对特殊值θ的概率p(θ)。研究者需要做的第一个选择proposal distribution,proposal distribution是一个简单的分布 q(θ),能直接采样。思想是估计采用的样本在采用分布和目标分布下的概率,拒绝样本相对于建议分布,不可能在目标分布下。

图 1.6 展示了整个过程。首先找到常量c,使对于所有的采样 θ,cq(θ) ≥p(θ)。常量c乘以建议分布 q(θ)作为比较分布,全部在目标分布上方。找到常量c并不困难,嘉定我们使用一些计算就能找到。现在从均匀分布[0,cq(θ)]中找出一个数字u,换句话说,这是0到我们提议的θ的比较分布的高度之间的一些点。如果u > p(θ),我们将拒绝采样,其它就接受。如果我们接受采样,采样值 θ就是从目标分布 p(θ)中获得的值。这是这个计算过程的总结:

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” alt=”” />

这个算法的一个有高效操作的关键是包含尽可能多的采样。这严重依赖于建议分布的选择。一个建议分布与目标分布差别太大,将导致大量的采样被拒绝,减慢过程。

练习:

1、假定我们要从Beta(a,b)分布中采样,其中a=2,b=1。给定概率密度p(x)=2x,0<x<1。不适用matlab自带的Beta随机数生成器。目标是实现Matlab中的拒绝采样。作为练习,使用一个简单的均匀建议分布(即使不是一个好的建议分布)。常量c应为2,用直方图可视化采样值,检查分布是否契合Matlab自带的betarnd采样函数。接受的概率是多少?我们怎么改进拒绝采样器?

K=;
i=;
x=[];
for n=:K
randValue=rand();
rd=unifrnd(,*);
if rd<*randValue
x=[x,randValue];
end;
end;
hist(x,);
length(x)

**2、图1.5的过程组成了Box-Muller方法的基础,生成高斯分布随机变量。首先生成均匀坐标(x,y),从单位圆中,使用拒绝采样过程拒绝(x,y)对x^2+y^2>1。然后对于每一个(x,y)对,我们估计数量,z1和z2是每一个均为为0,方差为1的高斯分布。写一个Matlab程序,实现Box-Muller方法,验证采样值是高斯分布。

K=;
x=[];
for n=:K
rv1=* rand(,)-;
rv2=* rand(,)-;
if (rv1^+rv2^)<=
xxyy=rv1^+rv2^;
z1=rv1*(-*log(xxyy)/xxyy)^(/);
z2=rv1*(-*log(xxyy)/xxyy)^(/);
x=[x,z1];
x=[x,z2];
end;
end;
hist(x,);

第2章 马尔科夫链蒙特卡洛

数据概率模型的应用常需要用到复杂高维分布的积分,马尔科夫链蒙特卡洛是一种通用的计算方法,可以替代分析积分,通过累积从迭代算法生成的采样。用分析方法不能解决的问题,经常使用MCMC可以解决,即使是高维问题。MCMC的发展是统计中计算方法的最大进步。当MCMC成为一个非常活跃的研究领域,已经有了一些广泛使用的标准技术。本章我们将讨论两种MCMC, Metropolis-Hastings 和 Gibbs sampling ,在我们使用这两种技术之前,先了解MCMC的两个主要概念:蒙特卡洛积分和马尔科夫链。

2.1 蒙特卡洛积分

概率推断的许多问题需要在大亮结果空间的复杂积分或求和计算。例如,一个频繁问题是计算函数g(x)的期望,x是一元随机变量。如果x是连续纸,期望定义如下:

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” alt=”” />

如果是离散变量,积分可用求和代替:

aaarticlea/png;base64,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” 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这些期望在许多情况下是上升的,当我们想计算一个分布的一些统计,如均值和方差。例如,g(x)=x,我们要计算分布的均值,使用分析技术积分或求和对于特定的分布就变得极具挑战性。例如,概率密度p(x)可能的函数形式不能使用分析积分。对于离散分布,结果空间太大,以至于对所有可能输出求和是不现实的。

蒙特卡洛积分是使用采样来估计一个复杂分布的期望。特别的,我们包含采样集合x(t),t=1,..,N,从分布p(x)中独立采样,在这种情况下,我们能使用有限和才估计2.1和2.2的期望:

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” alt=”” />

在这个过程中,我们能使用合适的采样集来代替分析积分。一般情况下,估计的精度能够通过增加n来增加。估计的精度依赖于采样的独立性。当采样是相关的,采样大小增加的就有效。上一章讨论的拒绝采样不是个问题,但是一个与MCMC方法潜在的问题。

练习:

1、写Matlab代码来估计Beta(α,β) 的均值,使用蒙特卡洛积分,其中 α = 3, β = 4,你可以使用Matlab函数betarnd来从Beta分布中采样,你可以将你的答案跟分析答案 α/(α + β)比较。【提示:这只需一行Matlab代码】。

x=betarnd(,,,);
mean(x(:))
/

2、类似的,估计Gamma(a,b)分布的方差,其中a=1.5,b=4,使用蒙特卡洛积分。Matlab命令gamrnd允许你从分布中采样。你的估计应该接近理论答案ab^2。

x=gamrnd(1.5,,,);
var(x(:))
1.5*

2.2 马尔科夫链

一个马尔科夫链是一个随机过程,从一个状态使用一个简单的序列过程转换到另一个状态。我们启动一个马尔科夫链,从一些状态x(1),通过转换函数p(x(t)|x(t-1)),转到另一个状态,x(2)条件决定于上一个状态。我们通过迭代创建一个状态序列:
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每一个这样的状态序列称为马尔科夫链。从马尔科夫链生成T个状态序列的过程如下:
1. Set t = 1

2. Generate a initial value u, and set x (t) = u
3. Repeat
t = t + 1
Sample a new value u from the transition function p(x (t) |x (t−1) )
Set x (t) = u
4. Until t = T
很重要的是,在这个迭代过程中,下一个状态只取决于上一个状态。所以,每一个马尔科夫链遍历状态空间,对下一个状态的转换只依赖于上一个状态。正是这种本地依赖造就了马尔科夫或无内存过程。我们将看到,这是马尔科夫链对于MCMC的一个重要特性。
当初始化每一个马尔科夫链时,状态空间将在起始状态周围。所以,如果我们启动许多链,每一个有不同的起始条件,这些链讲会接近于初始状态。这个时期称为收敛。马尔科夫链的一个重要特性是链的初始状态一旦经过充分长的转换序列后不再影响链的状态(假设马尔科夫链满足特定的给条件),在这点上,链达到了它的稳定状态,状态通过从稳定分布中采样反映出来。马尔科夫这种不管从什么地方开始都能收敛到稳定分布的特性是非常重要的。当应用MCMC时,它允许我们使用序列过程从分布中采样,起始状态也不会影响到估计过程。
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dn6kfbMWPGiOtCfv31V3V1dR8fH4TQ2bNnyZVbmZmZ/fr1CwwMJM/866+/evfuXVNTQ4YUFhZiiSPyzp06daK2/KqqqiFDhhw9epR6zoMHDzp37kx1dqapqTly5Eg8Ioi5ePEiQRDMLmUSExPl5eVpQ2VOTk4TJ06kFlb37t1pxkgkbJ6dAdIMLVy4sHXr1uTULITQy5cvL168iH+LVNu0r4THjx+nrdRG4osMCantc+fOLVq0iNp82GTUypUr27RpQ/twr66uzmyz+Hy+kpKSpqYmGZKTk6OkpLRt2zb8L9Zbf/zxB7W4FRUV586dW9cc0NLSEu475eXl1dTUsLjEbNu2rVu3bsylNmzYsPj4eGrInDlzyA9oFy5cwBJZ+MK1a9cuXLiQfPFOTU0lCILWzRsYGPTv3x9P009ISJg9ezbpT1dfX1/cTBJhY4s+m81du3aRHyKwIy0XFxfyHDY2WSQfP35s06bNpk2byJCjR48SBEEtKTyGSr2K1sARY3axLH2RCFtFlsZEouVEjL2PSO7fv//dd99FR0dTA//66y/haQDCtRTPJNm9ezc1UF9fv23bttSQW7duEV/7Crt27VqbNm3IAQKGNP/xxx+0LJ00adKGDRtoOaCjo8NcEAxdhjD4Ox6t22JpyYVzqU7dCmJnMdiobewVhPpS6uzs3K1bt4KCAiTT/kuaKtQofW5gYOCiRYuoN3ny5EmjqG1FRcVr166RIcIWXmL9Z4Zzte3v7//48eM7d+74+Pj88MMPItW2sDR0dHQkCOLNmzdkyLhx46hOAzGdOnWiqW3s5I6qZbENmjx5Mu3at2/fysnJ/f3339TA+/fvEwQh8Ys2SXFx8YABAzQ0NFjORkBNb962lpYWrc/AXRfZZ8yfP19dXZ36xeTZs2dXrlwh/2UwnRMmTGjXrh316xImKSkJf/QkQ7y8vIjPnqowzC2fJm2tra3btWsn/Fln+PDhS5cuJf+dN28eQRDU6TpPnjzB35FFxoKZNm3a1KlTaYHv37/Hw4fikiQONs/OAGmGQkJCaHrIycmJFFgi1Xbfvn1//vln8t+EhASCIGjmUlyRoa/V9qVLl2xsbGgnsMmoe/fuEQSBJ5dj3r17Z2FhwfDI6LM+o05rwbN4TUxM8L+40tKa85w5c4YNG0YNYZMDIvvOzp070+yPs7MzQRDMU4a6dOmya9cuasjBgwdx/4oY5ePy5cu/++47qqOMXr16LVu2jHoOLg5ywJIKg9oWaRmw2Tx16hQ1sEOHDlSJzNImi2TevHk9e/Yk0xMZGUkQBLUDNjc3p82nEm5NEtW2xNIXibBVZGlMJFpOJL73EUltbe2wYcOEWxD2mkKTSsK1lKXaHjNmDK3UeDxe+/btyYoqLs04/2mVxNHRsXXr1mResSyIOqltkd0WS0sunEt16laQFBaDSk1NzYABA6h7jCCE1q1b16FDh7y8PCS7/kvKKtQofa6bm9sPP/xAPQE7sRWZhvrBUm0zW3g29Z+ZBp1J4uXlxVJt29vbEwRB9fujrKw8evRo2oWdO3dmqbaFX5Vw/aN5/SwoKBAOZGDp0qXKysp1mvvR1NT2vHnzmPsMPOXrxx9/3Lx589mzZ4XlBbPaFrdWLycnh/wyzuPxsOK8f/8+eUKdWv7YsWNFRqSlpdWxY0dyxG7evHmdO3cWflhfX1+RsaDPg3wiX7U7deo0Z84ccUliQOKzM0CmpLa29scffxwxYgT+t6amZs+ePeRpItV2UVERKaMFAgGuJLQxRYYiI9X2kSNHZs6cKXxzlhk1atQoalt2cnKS2By0tLQIgqAO5COE8AwNDC5H2hKxefPmDRw4kJZIiTkgTm3TWhk2NRkZGQzJNjU1JQhi1KhR5ubm169fp20zxCAfeTwetaEVFhYOGjRoxowZ1HNwcYhcalI/tU2bON65c+c1a9aQ/7K0ySI5ffo0QRDkK7qBgcG8efN+++03/C+fz9fT06NdUg+1LbH0RSJsFdkbE5Zqm+VA3YsXLwiC2LFjBy387NmzslLb7969Iwhi8eLFtChGjx5NBopLM566iQe8SfBkcTKQZUHIRG2zseTSq+16Wwwq+IOS8H5npAWTVf8lZRVqlD43Jyena9euHTp00NHROX78+OvXr0XGLg0s1TazhWdT/5lpULV97do1lmr79evXbdu2PX78OP63srKyffv2tCqO6qK2aSNMCCFLS0v8Fr7va5ydnWnficTh4uKioaFRVw+UzU5tI4QCAgJ++ukngiAIgmjVqpWBgQF1IQKz2v79999FHhIIBFeuXFm8ePG2bdsOHz6Md06hfv9i3/J5PF7btm3JzpvK8uXLqbkt7mGPHTsmMhaE0O3btwmCoHmxxfTp04d6N/ZqW+KzM0DtBbGYw18nz58/HxcXRx4St0oyNjZ23bp1GzZs2L9//7FjxwiCoE1NYygyXHUdHBwWLlwobLvZZxSeHYgXSAgEAjZf4gYMGNChQweGE4QrLUJo3rx5ffv2pZ0pMQfEqW2RpgbPPBZHdXW1lZVVly5dcNvp3r37iRMnyKMM8hEhlJubu2vXrmXLltnb2wcGBvbt21dNTY16Ai4OkRPP6qe2aUapc+fOK1asIP9laZNFUlFR0bFjR5yBNTU1enp6+MsM/p4TFRV19uxZ2iX1UNtsSl8YmlWU3pgIq23h3kck2JMMdcgfI0O1jb8qTJs2bZ8QISEhzGlWUVHBQpN2oYuLC7mglmVByERts7Hk0qttVF+LQeXEiRMEQTg7O4s8KsP+S8oq1Fh97uPHj3///XfiM9TpdjKBpdpmtvBs6j8zjeZvm4rIDmDDhg0jRowICgp68eLFggULNmzYILzUlL3aptkg9LkNBwUF1e2pPhMQELBw4ULqFwSW862bndomJ8mkpaX5+fnNmTOHIAjqJkw000ld4T5hwgRVVVXhZFdUVEydOvX3338nB/ACAgKY1faHDx+oLZDa8gUCQefOnUeOHCkckY6ODkGZIcqmg6SBhyW2bNkifKhHjx7U/RpZqm02z84AVW3jSSn4cz9tXodItb1jx44+ffqQa+Fzc3NFqm2RRYYQMjExadOmzb1792praydNmtS/f3/qpG32GYUXBOOdgG7cuMHGcduYMWNatWrF4NJOXDdPK242OVAntc3ckHHb4fP5MTExnp6eo0aNovZ5NPkYHx9PmrgLFy506NCBOlA3dOhQkWpbZLw0tU1tknVS27RHZmOTxbFy5cr27duXl5dfuXLl8uXLPB6vR48e2CwbGRlRP1NgJKptanaxLH2R0KyibI2JuN5HJEFBQcTXc8MwMlTbuPSFvyRIvA+OkSAIcc5nMCwLgqHLEKbeg0SIhaBk6FYw9bYYVHDVFVcNZFjlpKxCjdLnkgIjPz8/ODh48+bNrVu3Fp4MIw3SqG3SKrKp/8w0UbVdXl6ur69fXl5+9uxZf39/cVNau3fvTsug3bt3s1TbeP6o8FsgQkjizluRkZErV66k9v2vXr2i7TEpjqamtrW1tWmNISoqitoYVq1aRcuQLVu2UMUTzXQaGhqSv8VJtw0bNsjJyVEXxp06dYpUnNjxEK3lR0VFUT+M0Mzi1KlTu3fvLvzCM3HixN69e5P/1kNt19TUtGnTRnjns7KyslatWi1ZskRcksTB5tkZoH3hnTJlSufOnVNTU2mDOsJq+7///iO+dhqYnZ1N9hxkvMxqm/Tdm5KS0qFDh1WrVpFH2WcUQmjVqlXt27cvKSnZsmULmzUPq1evFtlq6qS3WOaADNX2X3/9Rf23urr6119/JcfyafJx9+7deE5aWlpa27ZtDQwMqNcOHjwYq+27d+9WVFSguqhtapOst9pmaZPFce3aNYIg/vvvP319fbzwaNOmTT///HN1dbXIJeYS1TaZXUimahuxNiYSLSeqo9p+8+YNQRDUwsLIUG3X1tbKy8traWkJx04aeXFpdnBwIL6eSkS7ENVXbQs/MhVO1TZztyKNxaCSnp5OUPynUcEWTFb9l5RVqFH6XAcHB9rC+nPnzhFfr6KWEpmobTb1n5kmqrYTEhKoE+3FoaCgQDtt/vz5LNU2n89XVlYW3tEqIiKCdHwjktjYWD09Pdqgjre3N3U1a0xMjMh1ZohRbWdkZDBPAxVGerW9atWqH374gRri5uZGbQxqamp3796lnnDr1q1Ro0aR/2poaJD/FhcXU9/7xUm3vn37/vrrr9QQc3NzUnFiRxO1tbVycnLkMExwcDB19JfW8nFPTBsezs/P/+6776jrLeqhthFCW7du7dChA234DS+sZkiSONg8OwO0FUg+Pj4EQaioqNC8aAmrbezGjlotceXB5UXGy1JtI4QOHz5MEATVAyvLjEII3b17F0e9c+dO5ufFPHr06H//+5/wuzHNJwlzN88yB2Sotrt27UrLDWtra7JK40wgP6+ZmJjgrgt/rab28ZWVla1atcJq29bWFn+4ZFDbeI41OQxDnd5Tb7XN0iaLo7a2tlevXn/88QcpBfDUIwsLC6rlJBFuTeKyC8labbM0JhItJ6qj2kYIzZo1S1FRkRaIbyurVZKmpqadOnWiDdHl5+eTk33FpTk3N7dr167C0wx2795N5h7LgmDoMoSRrdquU7cijcWgMXfu3B9++IE27/TevXt4wxAZ9l/SVKFG6XNtbW1payJra2tbt25NVtGSkhLhDWvqhEzUNpv6zwyHaltRUZEgCDaOhLHbIOrgXFVVVa9evRYsWGBgYGBubm5ra+vp6SmcWWvWrKG+IsfHx+PZP1Q3/njho/C6AYTQ69evu3XrRq2pRUVFq1atYvDqlZGR0b9//1mzZs3+jKam5tSpU7t06UJ6UMLLCsV9Ctm8ebPIN6SCgoJ27dp16NChTmsusZQR9riJs5S2dBr7+aINSvn6+rZp04Zcv1VWVrZy5UqCsjWmmpratGnTqK+wHh4e1Fl9lpaW8vLy+A4RERHUvnP06NFKSkrCyVZTU+vRowdpeoqLi//55x+CIM6cOfPx40dyfpuKioqKigr+bW9vT7qNEwgEHTp0oE4qRQitXbt2xowZ1LcgQ0PDyZMnUz9BTJ8+vVu3btSr8CcOmotDGuXl5aNGjcKu1jBVVVWTJ0+mViqcJDZyhOWzi+T+/fs///wz1XtDWVmZcFbweLw2bdr069ePGmhra0trGhYWFgMGDMBrd8zMzHCguCJDCG3durV9+/bkq3xtbW3fvn179OhB2iM2GUUycuTIVq1asV8Ts3Pnzu7du1PddFy9evX06dP4Ny5Hmo+86dOn9+zZs645oKmpSZtmyufz27Vrt3DhQmogHuqgOfij8d1339FUy8KFC8khsdLSUnl5eUtLS/wvqYmjo6OJr/emPXLkyB9//PHLL78ghMzNzXERbN26lSAIketG8PRcvDtDcXExdZaRsLEln4X6QR8/MtUzF0ubzADe1oTcqUcgEPTr1+/HH38Uno4isoGLyy7ErvTFga0irR6yMSYSLSdi7H1Ekp6e3rNnT+r8xuzs7AkTJtBea5GoWorjMjY2pgZu2LDhu+++o/ZoVVVV48aNo+atQCDQ09Mjvc0wpDkgIKB9+/bU9SEvXrwg/QIh1gXB0GUIgwuItkCCpSUXziVUl26FvcX48ccfGR4BIZSVlfX9999TS6eqqkpXV5esY7Lqv6SpQnXKHFml2dbWtlevXtSPvS9evKCuHcKJp+3wVSeGDBlCEARt0JAKSwsvsf4zI3u1XVlZOWvWrGHDhrVt21ZeXr579+7jxo3T0tISJ2GnT58+YMAAeXn5Xr16qaiokKpu586dCgoK48aNGz9+vKKiYvfu3QmCUFRUTEtLI6/NysqaOnWqoaHhlStXDh065O7u7u3tTRBE165dp0+fjhBavXr10KFD5eTkOnXqNHbsWOF8efv27YIFCzZt2nTmzBkvLy9jY2PmeTl4wF4YeXl5UoUkJSUpKCiQTRFz8eLFGTNmDB06tH379vLy8j169Pjtt9+0tLTIoS88F1ZVVZXl/G9nZ+eJEyd2795dXl5eTk5u+PDhmpqa+C2czNLvv/9eVVU1IyMjISFBRUWlZ8+e8vLyP/30k7a2NnkfHo/3999/a2lpXbhwwdfX18rKKiYmhiCIdu3a4R0QZs+e7eXltXHjxsDAwJCQkN27dxsZGVG//ldUVGhoaMyePdvPz8/IyAjng5ubm5KSUrt27eTk5IYNG6apqUl9rszMTDU1talTp164cOHUqVNWVlZlZWV6enoDBgxYtWoV2fASExMHDx5sYGBw6NAh0lGMqanpqFGj8E5A48ePp771Hj16dOHChe7u7seOHfvrr7927txJ1jo/P79JkybhvBozZgzus9XU1BQUFOTl5Xv37q2mpsYwTllRUaGvr//333+fOHHC2dlZS0uL+gEEJwm/LI0aNYo6v0IYls9O49WrV0pKSh06dJCXl+/Zsyf1W7Curi75Tvv69WsNDQ0FBQU5Obl27doNHjx4xowZ+J5VVVUbN24cNmyYj49PcHDwrl27Xr9+HRAQ0K1btxUrVty8eZOhyKKioqZMmdKlSxc5OblRo0ZhL8uurq6tW7eWk5Pr1q0b6QmbOaOoeHp61nVynr+//9ixY/fs2XP27Flra2sstfl8PlmOvXr1UlVVTU5OPnXqFFncv/32G15mIDEHAgICJk2a1L59+3bt2o0ePRqvaDQwMBg5cqScnFyHDh0mTZoUFBT08uVLFRWVHj16yMvLDx48WHiPIZKBAwcePnx4x44dly5dOnv2rJ6e3qFDh6gnnD17VkFBwc3NzcrKiurf0NPTU0FBwcHBITQ01MnJ6erVq/Hx8b17954/f/7hw4ejoqKUlZU7d+4sLy/fv39/NTU14YXdJiYmo0eP9vHx2bZtGzn5UtjYxsTE/P777/hZBg4ciL3J7tixAzexDh06qKqqkp00G5vMwIMHD/r160f98GpiYiI8h5ihgQtnF/vSF4ZqFX/44QdVVVXqEkwGY4KRaDkl9j4iycnJ0dHR2blz5/Xr148cOWJlZYVnmnXs2HHixIl4s0/hWkrG1bVr1ylTpty/fz8iIoKsJAoKCurq6qTnhKqqKiMjIy0tLT8/Pz8/PwMDA7L+SEzzgwcPVFRUrKysgoKCnJyc9u7di8VWnQpCZJfBUEBycnIDBw7U19dHrC25yFzCsO9W6mQxFBUVqQMNwrx//37hwoV//vnnqVOnjh49amJigt3/kciq/6pfFapr5sgqzfb29tgOHDlyJCwszMPDY+3atdSP/IaGhgMHDqT6HmXJvHnzJk+e3LdvXzk5OXl5+S5duowePXr27Nk0F891svDi6j8bOBnbFl7MxLC8iZpW/JvH402fPl3YDV9sbOz48eOFXY+9e/fuyZMneM1ZTk7Os2fPMjMz8dRGWkaIy5eqqqoXL17gSziCz+cLy2iGbJFIbW0tzUiRd6M+Jp/PFwgEAoGAGrtwPhQXF8fExODmWlFR8fDhw9TUVDw5AbsH5vP5r169YsiltLQ0css64ShE5vyHDx+ePHlCnZ5VUFAgfGFcXNzbt29F3go/Gu22WVlZeOtg2n2oIWRNI0NwRol8NOo5iYmJwj4QaWlmU6xsnp2KxBIkT2PO+bKyspiYmKSkJPJhy8rK8Csfw4W0zMGHhFsu9XyRGUWlurqa/S5cVLKzs2NjY6kzNISTKrK4MQw5QHtMnOG0+obPYVMW6HPbqaioiI2NTUpKElkxysrKnj9/LjzxjMfjJSYmxsbGkkuxeTwe/qwhnE6RVffDhw8xMTHUSIWLjNaChEsWP2xdbbI4aJ9cS0pKaG62hWOnPZpwdtWp9KnQypH2L5lgYWNChcFysux9RFJRURETE4PrD7YV6enpeDCYZS2VWElwI6UJPpZpLiwsjIuLk2gxmAuC1mUII7KhsbTkInOJehX7boW9xWBTxNXV1TExMQxzD2TVf9W1ClFv3pB9Lrn/QFZW1tOnT8l/paempkY4qbW1tcLPS/5maeFF1n+JcDiTpN6EhoaK89x0584dOTm5Ou22CAAAAEgD2GQAAABpaIpqOz4+vl27drRVXxhfX1/q+jwAAACAa8AmAwAASENTVNsIoT179qioqKSmplIDr169OmTIEJZb7gEAAACyAmwyAABAvWmiahshlJCQYGxsbGpqamlpaWlpqa+v7+npKY1rcQAAAKDegE0GAACoH01XbQMAAAAAAABAcwfUNgAAAAAAAABwBahtAAAAAAAAAOAKUNsAAAAAAAAAwBWgtgEAAAAAAACAK0BtAwAAAAAAAABXgNpuIVA3sgYAoGGoqKho7CQACCFUXl5O3aW5qqqKYbt1AACABqZx1HZZWVmdzndxcVm8ePHUqVNtbW05SpLM+e+//5YtW6amprZu3TqJJ//zzz8LFiyYPHny5cuX6xpRWFiYlpbWvn37xo4dC9tM0GheNad5pfZbRiAQ7N+/f+nSpbt27Zo0adLHjx8bO0UtgaKiovXr12tpaU2cOPHRo0fUQ6WlpSIvefrXK1qUAAAfMUlEQVT06erVq3fs2OHh4WFjY7N58+Zr167NmTNnz549kyZNOn/+fIMkHJANYWFhK1asmD59upaWVuOmRJoeGQBE0ghqe/78+XJycrGxsewvSUtLO336NEEQGzdu5C5hsiU3N/fatWtdu3ZVVVWVeHJsbOyuXbsIgjh58mSdYrl3756cnNybN2/S0tIIgti0aVM9k9tCaV41p3ml9ltm7969w4cPr6mp+ffffwmCCAwMbOwUtQRqa2ufPHmyadMmgiCioqLI8P379//vf/87cuQI7fzz58/36NHj5cuX+N9Xr161b9+eIIi7d+9WVVW1adNGXV29wRIPSE9BQUFkZOSgQYN++umnxk1JvXtkABBHI6jtuXPntm3bljZ0wYaOHTuyUSF6enr1ShcnKCkpsVHbCKHY2Nh6tO158+bNmDED/z59+nRmZib+3aQyodFhWXMakry8PBsbG5GHmmBqASoCgaBLly6Ojo4IoeLi4lOnTpWXl9fvVufPn6fKyrqyffv22trael8uc6R8HMyVK1doatvFxYUgCHd3d+pphYWF8vLyuBQw+fn5ffr0GTFiBP43JCQkLi5OysTIBIbGLo5v2YAvWLCg0dU2qm+PDADiaAS1LRAICgsL63Fh586dJaoQgUAwa9aseqWLEyZMmMBSbb98+bIebbt///6bN2+mBTa1TGh02NScBubx48fm5uYiDzXB1AJU3rx5QxDE6dOnpb/Vvn37wsPD63357NmzeTye9MmQFVI+DiY0NJSmthFCwvvD37x5kyCImzdvUgOVlJTmzp0rZQJkDkNjF8k3bsC1tbWbgtquX48MAOJoTqsk2aiQyMhIZWXlhkkPG7hW2927d9fX16cFNrVMaHSaoH61tLQEtd1MwU31woUL0t9KRUWl3vK0tLRUXl6+SaltaR6HRKTaFnfa8+fPqYFjxozR1taWMgEyh6Gxi+QbN+CgtoEWSZNW23w+n7quXKIKqaqqUlZWblJ2quHVdhPMhEanqenXN2/e9OzZE9R2M0VWavvSpUsEQdRbnhoaGhIE0XTUtpSPQ9LC1DZzYxcGDDiobaBFInu1HRMTo6urq62tvXjxYoTQiRMnjI2N161bV1VVhRCysbFZuXLljBkzrl27Rr2qoqLCwcHBzMzsn3/+8fDwSE9Pd3BwcHd3HzduHJ/Px+dgFVJTU3PkyBFHR8cNGzZYWlqSMyZ9fHx+++03giD69Olj+Bk2vgIyMzMtLS1tbGwsLCw2bNiQlZVFHuLz+YaGhitWrNDQ0Hj06NHHjx+dnZ3t7OzWrFlz/Phx4VtVVVUdPHjQ1tbW1tZ2z549Hz9+lF5tBwYGmpmZ7d2718zM7NChQ2S4h4eHoaGhnJzcr7/+ih82Li6urpmAC2vRokUqKip8Pv/UqVNGRkYbN240MTFJTEyknVxeXu7q6mppaWlra7ty5Uqa/5NDhw6tXbtWU1PzyJEjPB7v6NGje/fupZURSW5u7o4dO/bu3evk5KSnp/fmzRvyUEVFxb59+7y8vNzd3S0tLQMDA//55x+Juefv7+/i4nLgwAErK6ujR4/q6uoWFBSQR5lrDkllZaWTk5OdnZ29vb2FhQXp0KCkpMTY2Njc3HzXrl2mpqZBQUF37941NTXdtWuXubm5sbFxSUkJQsjR0RGfs2vXLnHprKqqsrS07Nu3L0EQEydOxAVE80DCMrUMeSiO7OxsGxubQ4cOOTs7W1lZBQQE7N27lzxaU1OzZ88eGxsbJyen7du3R0RECN8hKChIV1fXwMDA2NgYtxQzMzN8KDU1devWrX/++ee0adPIRnTkyJF169bNmTPH2tqaeh+GuOpUkaqrq52cnIyMjMzMzLZt23bu3DnaCeKaDzMnT560srJydHS0trZ2dXUlFS2PxzM0NFy9ejVBEPPmzcPFx+B8U1xlTktL27x5s5ycHEEQixYtwvf577//qNcGBATs3LnTzs5u3bp1fn5+1EO3bt1asGABQRAEQRgYGODLHz58yPLBHz58aGtr6+Xl5eDgsGfPHg8Pj9DQUIl5wmAn2TwOA0+ePNm9e7eDg4ONjU1ISAhNbf/3339///333LlzySnaHz58MDQ01NbWJghi5cqVhhR69uw5ZMgQ/JucZCKushUXF2/btm3p0qXTpk3Lycm5ffv2rl27lixZkpKSQqZNXCtLTU3V09NbvHixqqpqbW1tbGzsvn37LCwsVq9efevWLXwOm8ZOg40BF1eyIhvOmjVrbGxscBWNjY3Flo2aSFTHXgCJt5NIUu+PYajYGPZqm9ns5+bmGhkZmZubm5iYGBgYPH36lHotQ33G1LVHRvVtWcA3guzVdmFhYWhoqJKSkoKCwrFjx+7evYuX7eM2+fjx4x07dtAqcUlJyfDhwx0cHPC/enp6vXr1qqysLC8v19XVJbs6rELs7Oxww6iqqho9evSyZcvw0YyMjOTk5OHDh48bNy75MzU1Ncypfffunb6+PmkLzp4926FDh3v37pEn3LlzZ9u2bQRBnDlzxsLCAputtLS0tm3bHj16lHqrhISE0aNHHzx4EP9bWlpqaGg4aNCgeqttgUCAlQp+CoFAMH369LVr1+KjWVlZycnJXbt2XbRoEX7YsrKyumZCYWFhWFjY5MmTCYIwNDR8/PgxDr9w4UKXLl2oplAgEGzZsiUnJwf/m5KS0qVLF+q6pYSEhOPHjxMEYW5uvnv3bpFlhHnw4EHfvn1v376N/719+3aPHj3IMaqZM2fGxMSQJ/v6+g4dOpQ56+zs7Dw9Pak52bFjx9zcXDKEueaQTzR+/Hiyh+bz+f/f3pWHRVW18ZddUkcyTRQXAlOxxFLcUGAYEHEBfdLUFFAzlzAEZQRkgEcFBxAENTJFIlwQTUk01KK0UKonFywDFyYeMZcMMBgWxRHmfH+c5zvP6c7MvWcQ27y/v+aeuctZ3uV333POe4ODgxcuXNja2tra2nru3Dlvb28ASExMvHv3bl1d3ddff929e/eBAweeP38e71Q7d+7cwIEDx40bR3syDlpbW1UqVWlpKQC8++67eIBu3LhBn8NSW/4+1Iva2tqxY8eq1WpSsmjRIhJEr66uHj16NNHB2tra3r17Z2dnk5PVarW/v//o0aOrq6sRQg8fPgwNDa2qqrK2tsYnNDc3l5aWSqVSAFCpVLjw6tWrWCrmzZtHbsX/LHZBunPnzsiRI2NiYsgM2JEjR4hM8quPITx48GDmzJnJycmkZM+ePRMmTMCSr9VqVSrViRMnACA1NRUPHwkH6MKQMDc2NqpUqg8//BAAdu/eje9z7949cubmzZvPnj1LOnbUqFEzZ84kzayurlapVJj0X7t2DV9ORpa/4cXFxbNnzya3UqvVzs7OeXl5/N3CbycFm8ODuLi4119/nWjr559/Pn36dJptV1ZW7t69GwBIKlWNRqNSqbKzswFg3759KgpDhgyZMGEC/o13B/EI2+PHj7/55pugoCAAOHz4cEZGBs7sFBISgk/m0bKmpqaioiJsE4qLi7OysvA5eXl5ZmZm5eXliE3ZOeA34Pwjy6M48+fPP3XqFHFYdCWRMV4A8dpJJOT9kZBgYzCybX6zf+bMGTs7uxMnTpB6xsTEEIkV9PvIeI/cPs0S8ezgaa0kkcvlL774Io6c3b9/PyUlheyM1N3qGxkZ2alTJxIiunLlCgDs2LGDc0+JRNKnTx9iIxBCCoXCwsKCjng5OzsbNQe3bdu25557rrCwkJSMGDGCc4eLFy8CgI+PDx3EGj9+/Pjx48nhw4cPBw0aFBwcTF/Y2NjYqVOndrPtXbt2mZub006rrKwM57ciJd27d9fN521sJ6xZs0Z3v9GGDRvMzc3Jpv7Lly+bmZmtXbuWnLB69WorKysc1iXo0qXLkCFDeMaopaXFwcGBs+N+5syZ3t7eCKHr168///zzHOM7adIk/vrb2trSnAYhtGDBAg7b5pectra2MWPGcGZ7tVqtk5PT5s2b8eGFCxcAgLbv4eHhPXv2pJNChISEkLQwPKirq8NOUe+/grXl70ND2Llz5/Tp0+mSqqoqwrbnzZvn7OxM93xGRkb37t3J+AYGBkokEjp01NjYOGzYMIA/2ZBNmzbRbBujS5cuNNsWfBZiECSE0JQpU5ydnQnZ1Wq1dnZ29vb2+JBFfXQhl8t1dWf58uX03jvGKWZBYT5y5IihpRcvvPCCm5sbOfzss890z1y5cqXelST8DZ87d+6WLVvo83NycgQ5AYud5GmOIWRnZ1tYWNy+fZsuVCgUuitJbGxsOIZO74ITZ2dnkqMJQ1DYcAoUwpm2bduGpY5Fy3CylLi4OFKi0WhMTEwUCgUp4Vd2vTBkwFlEWq/imJubR0RE8FQSsXkBFjuJeL0/i2Azsm0es69Wq3v37k2PXVlZmYWFxcKFC/Ehizwb65Hbp1kinh08LbYdEREBAHrT/OkKsZubW//+/cnho0ePACAgIIBzoUQiGT58OF2SlpYGADSvMpZofvXVVw4ODiR6gRAKCgrq0aMHfc6lS5cAIDQ0lC708/OjY65KpRIAaBuHMXTo0Paxba1W27NnT057EUI9evQICwsjhx3CtvFgcb4fUVtba25uPmXKFHxYU1MzePDgtLQ0cgIOWnCaLDhGH3zwAQAUFBTQ5+BCtVqtUqkAgEx9Yhw6dIi//nZ2dn5+fjjminHy5En6C0qCtdq7d6/uGlCEUERExHPPPVdfX48PBw0aNHbsWPIvnvQga6Jw+J+/qhiCbPtJ+tDQQ7OysqytrQsKCuhYLO5b7DM4El5eXg4AR48eRQh9++23AEA7bIzAwEAO205PT9dl2xKJhLBtwWcxdsLp06cBID09nT5nwYIF+M6M6sPBjRs3zMzMOPdE/yd2ZAUCI9sWFGYeejpt2rSZM2fSFQMAMm+GoZdtCzZ8/vz5AwcOJDmq8c1JONMQWOyksWz7wYMH3bp1mzVrFqf80KFDujRa19CxsG0WYcP3oZdUYbBoGZZ2zjldu3al9110FNtmFGlDisNfScTmBRjtJI/3ZxFsRrbNY/ZjY2M59aytrfXw8CA6yyLPxnrk9mmWiGcHT5dt66ZtQvp81RtvvGFpaUlIQGNjIwBw3rwRQhKJBK8GI8DGjp6bM5ZoEjQ3N1+5cuXkyZNSqdTc3Jz+C7Pt7du304X+/v70G8LEiRMBQHfNRrvZdmVlJQB4e3t//Wc4OjrSEcqnx7YRQi+//HK3bt04hRqNprKy8vTp0ytWrNCNFAqOUUBAAADk5ubSjUpISAAAHKhYvHgxAFhbW0+bNi05OZl/4hVj3759AGBqaurq6rp27VrdD2oK1uqdd94BANpwY2zdupX26OvWrQMAvHbz8ePHK1aseO2118hr4ZkzZxgjGYJs+wn7UC9aWlqGDh0KAC+++GJAQMDOnTtJeA9PQMvlcvqGhYWFAICjNYmJiaBvXyCWHN2q8rBtwWcxdkJ8fDwAGPrSG6P6cJCbmwsAn3zyCaccT8eRECb79il+YRakp1qt9s6dO999993OnTsBYOPGjfS/etm2YMMrKiqsra0BYMiQIcHBwfn5+TwrYXTBYyeNZdvfffedXi3oQLbNImz4Pvn5+ZxqsGgZlskrV67QF0okkqCgIHLYUWybUaQNKQ5/JRGbF2C0kzzeH4NfsBnZNo/Zl8lketuiCx55NtYjP6FmifjP4+mybb1/6fqqkpISU1NTsto1Ly9PIpHcvHmTcyHtszF0XXs72PaFCxfeeuutN998Mzc398aNG4sWLTI1NaVPwGx7165ddKG/v3+fPn3IoZ2dnY2Nje7N2822v/zySwAIDAw8rwO6Z54q2/b09AQAMnF2+/ZtuVzu7e39/vvvl5WVYU9GFuFhCI6Rq6srAJSUlHAadfHixUePHiGE2traPvroIzc3NysrKwCwsrLSXVOki2+++cbPz8/GxgYAAGDRokWcbDb8tRo/fjwA0OFwjKysLDr0UlFRAQAJCQkIoZMnTxYUFKSkpHTp0uXBgwcIIblczviVE0G2/YR9aAgNDQ0xMTHDhg0zMTEBAFtbW+yioqOjAWDr1q2cG164cAEvHZk/fz4AlJaWcm7YDrYt+CzGTsBVMrRUnVF9OMBrGOj5ZYxffvkFAEgUlp1t8wszDz1tbm7eunWru7v7+vXrv//+e7y4jrPBTi/bZml4ZWXl22+/3b9/f6wsLi4uNTU1gm0RtJPGsm2sXJxv1qAOZdsswmYoBQqLlglKO+o4ts0o0ixeUu9pLF6A0U7yeH8WwWbfJWnI7NvZ2UkkEv5rBeW5HR65fZol4hnBP4JtNzQ0zJo1y8fHZ/369QkJCe7u7hcuXNC9sB1sWzBL17Fjx8zNzenp3aVLl7aDbY8dO9bKykr3/u1m21VVVcDwJXYWti3YCYbsrJOTU+fOnfELemVlpa2t7XvvvUdYbF5eXjvYNt7aZWgHVX19PfmrpaWluLjYzc3N1NS0oqKCp/7Xrl3DP7Ra7c8//7xkyRIAoHf4Cdbqrbfe0lsrHLM5duwYKRk5cqSTkxNCaOXKlY8ePbp16xYAHDhwQKPR6CY+NwSOA66oqKA/eveEfWgIKpWKLDGvq6s7ePBg//79BwwY0NbWlpOTA7yfH4+KigKAoqIiTnk72Lbgs3Qv0XtnTKTILigOGNWHg8zMTL11w7HtVatW4UNGti0ozBx6evz4cUzjHj586O7uPm7cODL58Ntvvwmybazmgg0nyoIQ+vXXX1NTUzt16hQYGMjfFhY7aag5hvDFF18AQFJSEqe8A9k2i7AZYtssWtYOts1Rdr3Qa8AZRbrD2TbtBRjtpCHvzyjYjGybx+zjNyWe2AeLPBvrkdunWSKeHfwj2PahQ4eOHz+OEKqqquL5zCSLHXnttdeIndJqteHh4TyVbG1tlUgkU6dOpQsDAgKw1pWVlWEqycK2Q0JCAICk7CBoN9tGCPXq1UvvtVVVVeS3XrZtVCcgA3a2ubnZ0tJSKpXiwylTpnTv3p12n3Rsm0TsBMdox44den1bTU1NU1NTSUkJjhzT1bC1tc3JyeGpv+42Sn9//wULFpBDwVphb8HZIYQQWrZsmYmJCT2seBHk999/T9ZKurm5+fn5FRYWYhlmgVqtph3w6dOn6XjqE/ahoYcmJCSUlJTQJViwq6qqrl69Cn/e7IXR2tqKd7B9+umnAECv2sfAK9fpku3bt3NUsrm5GaicJILPYuyEgoICvZHR6upqLMks6sMBZtXr1q3jlB84cIAmbYxsW1CYjx49StPT2NhYPHwpKSkAQEcc8Cw2JiVE18LCwmi2vXr1avyDv+HTp0/npCxMT08fMGAAT0MY7aSh5hhCdXW1qanpkiVLOOUdyLZZhM0Q22bRMhYiy6/semHIgLOIdMeybY4XYLSThrw/o2Azsm0es4/t0k8//cQ5obKyEjHLs7EeuR2aJeKZwj+CbWdmZsrlcsF7stiRGTNmODo64t/V1dW6e19oXL9+HQA4ZBTPs2u12uLiYhxUYGHbt2/f7tKlC2fNwxPmJNm7dy+9Hxzj6tWrdDpnvWzbqE5A/x8sensHQmjLli0mJiZkMZytre3IkSPpE/ALRnFxsVarJWE/wTFqaWlxcnKaO3cupw5Lliypq6s7e/bssGHDOGkcZDIZJzs7B1ZWVpxwS3x8fGRkJDkUrFVzc7OjoyMn/4BWq+3Xrx8nYn337l0TExMnJ6dTp07hkh07dlhYWAQEBBj1nREbG5vFixfj35988gm9o+gJ+9DQE+Pj43UbaGlpiZfBvP322y+99BL+TZCZmYnJU1tbm4uLy5AhQ+ih0Wq1zs7OHDXfv38/ANBpeouKiuDPGQD5n8XYCTg9wrBhwziLIyMiInDkjEV9dDF37txXX32VUxgQEDBixAgyM8DItgWFGZP7ffv24UNiA+fOnQt/nq/Pz88HAJyznLzmYepDWCO5nL/hMpmMs0b57NmzY8aM4WkIo5001BwehIWF9e3bl7PdJSYmpqPYNmIQNkNsm0XLGIksj7LrhSEDziLST8i2+b0Ao5005P0ZBZuRbfOY/bt370okEs6eda1Wi5OGMcqzsR5ZULMOHDgguONfxH8YT4VtazQarFeXLl2i86MhhLRaLf7k2MaNGwk7uXXrVteuXR0dHV1cXCZMmODt7R0YGJibm0u/Z9+7d8/MzMzd3Z3kyGxtbcXRHfpVOysry8zMDL9rfvzxx7pvt5zKODo6Ojs7k5Dt/v374+LiAODatWuZmZkqlUqr1WKLEB0dTdrS0tLi4uLStWtXOgXEwYMHHRwcyEaolpaWkJCQXr169e/f/86dO/w9RrolPj6eZg/BwcEuLi7k6wZ//PHHwoULSbdUV1dbWlp6eXlxtq0Y1Qno/8Zx+fLlxCf98MMPPXv2pJM6LVq0yNramrSuvLw8KSnJ0tJyx44d169fx+lmGcfo0qVLffv23b17NynJzc39+OOPEUJnz54FAPq5VVVVo0ePpj+OoAtTU9M33niD+OyWlhY3NzcyX89Yq3Pnztnb29O71CMjI6VSqW58TiaT9e7dmwzT/fv3zc3NjV20MH/+/MGDB2OJWrNmDZHAJ+9DQ4iPj7eysqJ3tebn5xMGU19f7+rqumTJEtKNP/74IwmXIoTKy8v79etH/Hpra2tycrK7uzvHrdbX10skEuKiGhoa4uLi+vTp4+Li8vvvvzM+i7ETrl69am9vr1AoCKMtKiqip0H41UcvamtrR40aRb+gFhYWOjo6ktw7RFWjo6P5Y7eCwqzRaOzt7TEP02g0hJ7u2bMHAA4ePIgPGxsbo6OjR40aNWfOnMePH5MsnOXl5RYWFpjd/vLLL3RuSp6Gy2QyBwcH2mK89957/G8OLHaSpzk8aGpqcnNzo/OKnjp1Cm9xS01NJZFCbOgmT55Mp+zEsyjZ2dlk9BsbG3v37v3qq6/Sk1H8wkbuk5GRofuVIn4te/z4MY6hfvHFF+QELLoymYx2fIaU3RB4DDi/SPMojmAlWbwAYrCTPN6fRbBbWlrGjh1rY2ND7+LQC36zn5+f361bN3q+MS0tDX/ghtHvG+uR+TWruroaAExMTHjSRon4b6Pj2fZXX33l7u7u7e09efJkLy8vLy8veieTl5eXTCbDf3l4eGA5LisrmzFjxrvvviuXy+VyeXBwsK+vr7W1tYODA+apISEhUqnU19fXx8fHw8Pj0KFDP/30k4eHB36KTCajZ4U2btyILTjL7rp79+4tXbp06tSp8fHxSqUSJ/mKiIgYN27cBx980NbWJpVKcYW9vb09PDwqKip2797t4eHh4+Pj6+vr6elJ504pLy9fvHixUqlMS0uLj4+/devW8OHDe/bs6eTklJGRwVMN0i34KfTM4GeffRYUFLR27dq0tLQNGzYQwxoeHi6VSidNmjRp0iRPT09OoMKoTsB29ubNm+vXr1cqleHh4UFBQZwAjEajiY+Pl0qlCoVi06ZNmF7v379/xIgRoaGhGo3GqDGqq6sLCwsLDQ3dsGGDUqkk0b7z588rFIrjx4+vWbNm48aNSqVSLpfTGR71ws/P7+effw4LC0tISFAqlaGhoeSzYUbV6v79+6tXr161alVkZGRwcHBGRgYnMImRm5tL8wOE0Jw5c3QTofBDrVYvXLhwypQpCoWChMk7pA8NYdu2bYWFhVu2bFEoFEqlct26dUlJSfRrTFtbW3p6+tKlS2NiYjZv3rx9+3ZO8+vq6lauXBkcHJyWlpaYmHjt2rXg4GDdINa5c+f8/f2jo6NjY2NTUlLUarW9vX2vXr1eeeUVku6D51lGdYJarQ4PD1+8eHFUVJRCoeCkOUOG1YcHra2tKSkpISEhkZGRoaGhkZGRdCJwoqo+Pj5SqTQlJcXQfViEuayszMfHJygoKCIigs7UnpeX5+npGRISkpqampiY2NTU9OOPP7q6us6ePZs+raCgYMKECStXrly3bh2Hwxlq+LJlyy5fvhwVFbV+/frExES5XK6bg0UX/HZSsDk8aGtrS01NXb169aZNm5KSkvLy8g4fPty5c+cBAwaMHj26qakJGzpfX9+JEye6u7uXlpbW1NR4eHh4eXlhP4KpXnJyMm2WfX196UfoFTb6PhMnTvT09NT9tKEhLSstLaVlcvLkyQihsLAwIrpSqZQEMvUqOz94DLihkRVUHP5KsngBDB47ye/9kZBg79u3Dw/ipEmTpFIp5wO0HPCYfYyKiorAwMAVK1YoFIqoqCg6bC8oz+3wyIKaFRUVpbuoScSzg6e1koQdJSUl9vb2ui+yd+/exUzub6nVMwVD+2NEiOCHXrYtQoSIfx1ELyBCxFPF3+8pw8LC6A1tNJKTk728vP7a6jyLEO2siPZBZNsiRPw3IHoBESKeKv5+T3nkyBEHBwfdFZBtbW0ymUypVP4ttXqmIJfLAYDzDXYRIgSxfPlyANC73kaECBH/IoheQISIp4q/n20jhLZu3SqVSouKish2hNLS0hkzZoSEhHC2WYjoWNy8eXPXrl04s0RkZCSdWFqECB5UVlZmZmYOHjwYZ1g7efLk310jESJEtAeiFxAh4i/AP4JtI4QaGhpycnJiY2Pj4uJiY2O3b98uuDdOxJNDpVJ99NFHe/fu3b9/f05ODtktLkIEP65cuUJLju6Hr0WIEPGvgOgFRIj4C/A/c26LkZ9IxZQAAAAASUVORK5CYII=” alt=”” />
例。图2.1是一个马尔科夫链的例子,涉及到一个连续变量。对于转换函数,从Beta分布采样。这个函数和它的常量使任意选择的,但是能够体现马尔科夫链的基本概念。这个过程从四个不同的初始值开始,每一个链持续迭代到100代。图显示了两个不同时间范围的序列。不同颜色的线代表四种不同的链。注意前10代显示了对初始状态的依赖,这是收敛过程,后面就稳定多了,如果我们不停止链将继续稳定。怎么能确定链收敛达到稳定状态了呢?尝尝不容易受,特别是高维状态空间。我们稍后将区分讨论收敛。

练习
1、开发matlab代码去执行例子中描述的马尔科夫链。创建一个类似于图2.1的面板。从0-1均匀分布中生成四个不同的初始值,启动马尔科夫链。[tip:……]

ix=unifrnd(,,,);
x=zeros(,);
for m=:
v=ix(m);
for n=:
x(n,m)=v;
v=betarnd(*(0.9*v+0.05),*(-0.9*v-0.05));
end;
end;
plot(x)
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