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URLhttps://cloud.tencent.com/developer/article/1639197
Last Crawled2025-09-16 00:47:39 (6 months ago)
First Indexed2022-10-27 17:35:24 (3 years ago)
HTTP Status Code200
Meta Title最大似然估计(MLE)原理及计算方法-腾讯云开发者社区-腾讯云
Meta Description1)有两堆球,其中A堆有99个白球和1个黑球,B堆有99个黑球和1个白球。假如随便摸一个球,发现是黑球,那么这个球更有可能来自于哪一堆?
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1. 实际例子 1)有两堆球,其中A堆有99个白球和1个黑球,B堆有99个黑球和1个白球。假如随便摸一个球,发现是黑球,那么这个球更有可能来自于哪一堆? 2)猎人和徒弟去打猎,打倒了一只兔子,更可能是谁打中的? 3)一堆球,里边有黑白两色的球,其中一种颜色的有90个,另一种颜色的有10个。如果摸出一个球是黑色的,那么里边哪种颜色有90个? 第一个肯定觉得是来自B堆,第二个中更可能是师傅,第三个里边黑球有90个。我们的估计基于,概率最高的事情,更可能发生。一次实验就出现的事件,这件事有较大的概率发生。 2. 数学表述 最大似然估计这个名字是由高斯先提出,Fisher后来重新提出并证明了一些特征。这是统计学中的常用方法,机器学习中的逻辑回归中也是基于它计算的损失函数。 当样本分布是离散型: 当样本分布为连续型时: 一般情况下求估计值的步骤: 1)构造似然函数?(?) 2)取对数:???(?) 似然函数是连乘,不好求导;取对数后可化为加法,求导方便。 3)求导,计算极值 4)解方程,得到? 如果似然方程无解,或者似然函数不可导,则需要考虑其他方法。 3. 计算实例 (此题来自于 https://wenku.baidu.com/view/0d9af6aa172ded630b1cb69a.html ) 参考: 1) https://wenku.baidu.com/view/0d9af6aa172ded630b1cb69a.html 2) https://medium.com/@rrfd/what-is-maximum-likelihood-estimation-examples-in-python-791153818030 、
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[生信编程日常](https://cloud.tencent.com/developer/user/7144248) ## 最大似然估计(MLE)原理及计算方法 关注作者 [*腾讯云*](https://cloud.tencent.com/?from=20060&from_column=20060) [*开发者社区*](https://cloud.tencent.com/developer) [文档](https://cloud.tencent.com/document/product?from=20702&from_column=20702)[建议反馈](https://cloud.tencent.com/voc/?from=20703&from_column=20703)[控制台](https://console.cloud.tencent.com/?from=20063&from_column=20063) 登录/注册 [首页](https://cloud.tencent.com/developer) 学习 活动 专区 圈层 工具 [MCP广场![](https://qccommunity.qcloudimg.com/image/new.png)](https://cloud.tencent.com/developer/mcp) 文章/答案/技术大牛 搜索 搜索 关闭 发布 [首页](https://cloud.tencent.com/developer) 学习 活动 专区 圈层 工具 [MCP广场![](https://qccommunity.qcloudimg.com/image/new.png)](https://cloud.tencent.com/developer/mcp) [返回腾讯云官网](https://cloud.tencent.com/?from=20060&from_column=20060) 生信编程日常 [首页](https://cloud.tencent.com/developer) 学习 活动 专区 圈层 工具 [MCP广场![](https://qccommunity.qcloudimg.com/image/new.png)](https://cloud.tencent.com/developer/mcp) [返回腾讯云官网](https://cloud.tencent.com/?from=20060&from_column=20060) [社区首页](https://cloud.tencent.com/developer) \>[专栏](https://cloud.tencent.com/developer/column) \>最大似然估计(MLE)原理及计算方法 # 最大似然估计(MLE)原理及计算方法 ![作者头像](https://ask.qcloudimg.com/http-save/yehe-7144248/64cmtrzzq0.jpeg) 生信编程日常 关注 发布于 2020-06-05 11:04:30 发布于 2020-06-05 11:04:30 8\.7K 0 举报 文章被收录于专栏:[生物信息学、python、R、linux](https://cloud.tencent.com/developer/column/85939)[生物信息学、python、R、linux]() ###### 1\. 实际例子 1)有两堆球,其中A堆有99个白球和1个黑球,B堆有99个黑球和1个白球。假如随便摸一个球,发现是黑球,那么这个球更有可能来自于哪一堆? 2)猎人和徒弟去打猎,打倒了一只兔子,更可能是谁打中的? 3)一堆球,里边有黑白两色的球,其中一种颜色的有90个,另一种颜色的有10个。如果摸出一个球是黑色的,那么里边哪种颜色有90个? 第一个肯定觉得是来自B堆,第二个中更可能是师傅,第三个里边黑球有90个。我们的估计基于,概率最高的事情,更可能发生。一次实验就出现的事件,这件事有较大的概率发生。 ###### 2\. 数学表述 最大似然估计这个名字是由高斯先提出,Fisher后来重新提出并证明了一些特征。这是统计学中的常用方法,机器学习中的逻辑回归中也是基于它计算的损失函数。 当样本分布是离散型: ![](https://ask.qcloudimg.com/http-save/6869393/bk9772is9f.png) 当样本分布为连续型时: ![](https://ask.qcloudimg.com/http-save/6869393/jyd5jolo4p.png) 一般情况下求估计值的步骤: 1)构造似然函数?(?) 2)取对数:???(?) 似然函数是连乘,不好求导;取对数后可化为加法,求导方便。 3)求导,计算极值 4)解方程,得到? 如果似然方程无解,或者似然函数不可导,则需要考虑其他方法。 ###### 3\. 计算实例 (此题来自于[https://wenku.baidu.com/view/0d9af6aa172ded630b1cb69a.html](https://cloud.tencent.com/developer/tools/blog-entry?target=https%3A%2F%2Flinks.jianshu.com%2Fgo%3Fto%3Dhttps%253A%252F%252Fwenku.baidu.com%252Fview%252F0d9af6aa172ded630b1cb69a.html&objectId=1639197&objectType=1&contentType=undefined)) ![](https://ask.qcloudimg.com/http-save/6869393/8enqplfloo.png) ![](https://ask.qcloudimg.com/http-save/6869393/8a2vdfxq86.png) ![](https://ask.qcloudimg.com/http-save/6869393/90xzq9miud.png) 参考: 1)[https://wenku.baidu.com/view/0d9af6aa172ded630b1cb69a.html](https://cloud.tencent.com/developer/tools/blog-entry?target=https%3A%2F%2Flinks.jianshu.com%2Fgo%3Fto%3Dhttps%253A%252F%252Fwenku.baidu.com%252Fview%252F0d9af6aa172ded630b1cb69a.html&objectId=1639197&objectType=1&contentType=undefined) 2)[https://medium.com/@rrfd/what-is-maximum-likelihood-estimation-examples-in-python-791153818030](https://cloud.tencent.com/developer/tools/blog-entry?target=https%3A%2F%2Flinks.jianshu.com%2Fgo%3Fto%3Dhttps%253A%252F%252Fmedium.com%252F%2540rrfd%252Fwhat-is-maximum-likelihood-estimation-examples-in-python-791153818030&objectId=1639197&objectType=1&contentType=undefined) 、 本文参与 [腾讯云自媒体同步曝光计划](https://cloud.tencent.com/developer/support-plan),分享自作者个人站点/博客。 如有侵权请联系 [cloudcommunity@tencent.com](mailto:cloudcommunity@tencent.com) 删除 前往查看 [https](https://cloud.tencent.com/developer/tag/10813) [网络安全](https://cloud.tencent.com/developer/tag/10681) [html](https://cloud.tencent.com/developer/tag/10205) 本文分享自 作者个人站点/博客 前往查看 如有侵权,请联系 [cloudcommunity@tencent.com](mailto:cloudcommunity@tencent.com) 删除。 本文参与 [腾讯云自媒体同步曝光计划](https://cloud.tencent.com/developer/support-plan) ,欢迎热爱写作的你一起参与! 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