研究设计与统计

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经典参数估计方法：普通最小二乘（OLS）、很大似然（ML）和矩估计（MM）、很大后验估计、贝叶斯估计

2016-06-11 MedSci MedSci原创

最小二乘矩估计
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普通最小二乘估计（Ordinary least squares，OLS） 1801年，意大利天文学家朱赛普?皮亚齐发现了第一颗小行星谷神星。经过40天的跟踪观测后，由于谷神星运行至太阳背后，使得皮亚齐失去了谷神星的位置。随后全世界的科学家利用皮亚齐的观测数据开始寻找谷神星，但是根据大多数人计算的结果来寻找谷神星都没有结果。时年24岁的高斯也计算了谷神星的轨道。奥地利天文学家海因里希?奥尔伯斯根据

参数估计(Parameter Estimation)在统计学领域有两个学派：频率学派（最大似然估计MLE、最大后验估计MAP）与贝叶斯学派（贝叶斯估计BPE） 。频率派认为参数是客观存在，不会改变，虽然未知，但却是固定值；贝叶斯派则认为参数是随机值，因为没有观察到，那么和是一个随机数也没有什么区别，因此参数也可以有分布，个人认为这个和量子力学某些观点不谋而合。 频率派最常关心的是似然函数，而贝叶斯派最常关心的是后验分布。我们会发现，后验分布其实就是似然函数乘以先验分布再normalize一下使其积分到1。因此两者的很多方法都是相通的。贝叶斯派因为所有的参数都是随机变量，都有分布，因此可以使用一些基于采样的方法（如MCMC）使得我们更容易构建复杂模型。频率派的优点则是没有假设一个先验分布，因此更加客观，也更加无偏，在一些保守的领域（比如制药业、法律）比贝叶斯方法更受到信任。因此，参数估计也分为经典参数估计方法（普通最小二乘（OLS）、最大似然（ML）和矩估计（MM））和贝叶斯估计。普通最小二乘估计（Ordinary least squares，OLS） 1801年，意大利天文学

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  1. [GetPortalCommentsPageByObjectIdResponse(id=89739, encodeId=14f989e39fb, content=厉害！不过还是看不懂，怎么办, beContent=null, objectType=article, channel=null, level=null, likeNumber=90, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=a8c41734875, createdName=WEIXINb3b3c07d, createdTime=Mon Jun 13 12:43:00 CST 2016, time=2016-06-13, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=89496, encodeId=8b378949642, content=有点难啊, beContent=null, objectType=article, channel=null, level=null, likeNumber=79, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=7cde98330, createdName=milkshark, createdTime=Sun Jun 12 00:54:00 CST 2016, time=2016-06-12, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=89497, encodeId=1e088949e27, content=这个不错, beContent=null, objectType=article, channel=null, level=null, likeNumber=119, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=7cde98330, createdName=milkshark, createdTime=Sun Jun 12 00:54:00 CST 2016, time=2016-06-12, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=89416, encodeId=d7538941670, content=了解, beContent=null, objectType=article, channel=null, level=null, likeNumber=97, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=/v1.0.0/img/user_icon.png, createdBy=d0921674448, createdName=gyczyxy, createdTime=Sat Jun 11 16:52:00 CST 2016, time=2016-06-11, status=1, ipAttribution=)]
    2016-06-13 WEIXINb3b3c07d

    厉害！不过还是看不懂，怎么办

    0

  2. [GetPortalCommentsPageByObjectIdResponse(id=89739, encodeId=14f989e39fb, content=厉害！不过还是看不懂，怎么办, beContent=null, objectType=article, channel=null, level=null, likeNumber=90, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=a8c41734875, createdName=WEIXINb3b3c07d, createdTime=Mon Jun 13 12:43:00 CST 2016, time=2016-06-13, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=89496, encodeId=8b378949642, content=有点难啊, beContent=null, objectType=article, channel=null, level=null, likeNumber=79, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=7cde98330, createdName=milkshark, createdTime=Sun Jun 12 00:54:00 CST 2016, time=2016-06-12, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=89497, encodeId=1e088949e27, content=这个不错, beContent=null, objectType=article, channel=null, level=null, likeNumber=119, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=7cde98330, createdName=milkshark, createdTime=Sun Jun 12 00:54:00 CST 2016, time=2016-06-12, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=89416, encodeId=d7538941670, content=了解, beContent=null, objectType=article, channel=null, level=null, likeNumber=97, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=/v1.0.0/img/user_icon.png, createdBy=d0921674448, createdName=gyczyxy, createdTime=Sat Jun 11 16:52:00 CST 2016, time=2016-06-11, status=1, ipAttribution=)]
    2016-06-12 milkshark

    有点难啊

    0

  3. [GetPortalCommentsPageByObjectIdResponse(id=89739, encodeId=14f989e39fb, content=厉害！不过还是看不懂，怎么办, beContent=null, objectType=article, channel=null, level=null, likeNumber=90, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=a8c41734875, createdName=WEIXINb3b3c07d, createdTime=Mon Jun 13 12:43:00 CST 2016, time=2016-06-13, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=89496, encodeId=8b378949642, content=有点难啊, beContent=null, objectType=article, channel=null, level=null, likeNumber=79, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=7cde98330, createdName=milkshark, createdTime=Sun Jun 12 00:54:00 CST 2016, time=2016-06-12, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=89497, encodeId=1e088949e27, content=这个不错, beContent=null, objectType=article, channel=null, level=null, likeNumber=119, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=7cde98330, createdName=milkshark, createdTime=Sun Jun 12 00:54:00 CST 2016, time=2016-06-12, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=89416, encodeId=d7538941670, content=了解, beContent=null, objectType=article, channel=null, level=null, likeNumber=97, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=/v1.0.0/img/user_icon.png, createdBy=d0921674448, createdName=gyczyxy, createdTime=Sat Jun 11 16:52:00 CST 2016, time=2016-06-11, status=1, ipAttribution=)]
    2016-06-12 milkshark

    这个不错

    0

  4. [GetPortalCommentsPageByObjectIdResponse(id=89739, encodeId=14f989e39fb, content=厉害！不过还是看不懂，怎么办, beContent=null, objectType=article, channel=null, level=null, likeNumber=90, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=a8c41734875, createdName=WEIXINb3b3c07d, createdTime=Mon Jun 13 12:43:00 CST 2016, time=2016-06-13, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=89496, encodeId=8b378949642, content=有点难啊, beContent=null, objectType=article, channel=null, level=null, likeNumber=79, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=7cde98330, createdName=milkshark, createdTime=Sun Jun 12 00:54:00 CST 2016, time=2016-06-12, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=89497, encodeId=1e088949e27, content=这个不错, beContent=null, objectType=article, channel=null, level=null, likeNumber=119, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=7cde98330, createdName=milkshark, createdTime=Sun Jun 12 00:54:00 CST 2016, time=2016-06-12, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=89416, encodeId=d7538941670, content=了解, beContent=null, objectType=article, channel=null, level=null, likeNumber=97, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=/v1.0.0/img/user_icon.png, createdBy=d0921674448, createdName=gyczyxy, createdTime=Sat Jun 11 16:52:00 CST 2016, time=2016-06-11, status=1, ipAttribution=)]
    2016-06-11 gyczyxy

    了解

    0