统计代写|Why study probability？ stat 代写
Mathematics is the logic of certainty; probability is the logic of uncertainty. Probability is extremely useful in a wide variety of fields, since it provides tools for understanding and explaining variation, separating signal from noise, and modeling complex phenomena. To give just a small sample from a continually growing list of applications:
- Statistics: Probability is the foundation and language for statistics, enabling many powerful methods for using data to learn about the world.
- Physics: Einstein famously said “God does not play dice with the universe”, but current understanding of quantum physics heavily involves probability at the most fundamental level of nature. Statistical mechanics is another major branch of physics that is built on probability.
- Biology: Genetics is deeply intertwined with probability, both in the inheritance of genes and in modeling random mutations.
- Computer science: Randomized algorithms make random choices while they are run, and in many important applications they are simpler and more efficient than any currently known deterministic alternatives. Probability also plays an essential role in studying the performance of algorithms, and in machine learning and artificial intelligence.
- Meteorology: Weather forecasts are (or should be) computed and expressed in terms of probability.
- Gambling: Many of the earliest investigations of probability were aimed at answering questions about gambling and games of chance.
- Finance: At the risk of redundancy with the previous example, it should be pointed out that probability is central in quantitative finance. Modeling stock prices over time and determining “fair” prices for financial instruments are based heavily on probability.
- Political science: In recent years, political science has become more and more quantitative and statistical, with applications such as analyzing surveys of public opinion, assessing gerrymandering, and predicting elections.
- Medicine: The development of randomized clinical trials, in which patients are randomly assigned to receive treatment or placebo, has transformed medical research in recent years. As the biostatistician David Harrington remarked, “Some have conjectured that it could be the most significant advance in scientific medicine in the twentieth century…. In one of the delightful ironies of modern science, the randomized trial ‘adjusts’ for both observed and unobserved heterogeneity in a controlled experiment by introducing chance variation into the study design.” $$
- Life: Life is uncertain, and probability is the logic of uncertainty. While it isn’t practical to carry out a formal probability calculation for every decision made in life, thinking hard about probability can help us avert some common fallacies, shed light on coincidences, and make better predictions.
Probability provides procedures for principled problem-solving, but it can also produce pitfalls and paradoxes. For example, we’ll see in this chapter that even Gottfried Wilhelm von Leibniz and Sir Isaac Newton, the two people who independently discovered calculus in the 17 th century, were not immune to basic errors in probability. Throughout this book, we will use the following strategies to help avoid potential pitfalls.
- Simulation: A beautiful aspect of probability is that it is often possible to study problems via simulation. Rather than endlessly debating an answer with someone who disagrees with you, you can run a simulation and see empirically who is right. Each chapter in this book ends with a section that gives examples of how to do calculations and simulations in $R$, a free statistical computing environment.
- Biohazards: Studying common mistakes is important for gaining a stronger understanding of what is and is not valid reasoning in probability. In this book, common mistakes are called biohazards and are denoted by (since making such mistakes can be hazardous to one’s health!).
Probability and counting
- Sanity checks: After solving a problem one way, we will often try to solve the same problem in a different way or to examine whether our answer makes sense in simple and extreme cases.
- 医学：随机临床试验的发展，其中患者被随机分配接受治疗或安慰剂，近年来已经改变了医学研究。正如生物统计学家大卫哈灵顿所说：“有人猜测这可能是 20 世纪科学医学最重大的进步……现代科学令人愉快的讽刺之一是，随机试验对观察到的和通过在研究设计中引入机会变异，在对照实验中未观察到异质性。” $$
概率为有原则的问题解决提供了程序，但它也可能产生陷阱和悖论。例如，我们将在本章中看到，即使是戈特弗里德·威廉·冯·莱布尼茨和艾萨克·牛顿爵士这两位在 17 世纪独立发现微积分的人，也不能幸免于概率的基本错误。在本书中，我们将使用以下策略来帮助避免潜在的陷阱。
- 模拟：概率的一个美丽方面是，通常可以通过模拟来研究问题。与其与不同意你的人无休止地争论答案，你可以运行一个模拟并凭经验看看谁是对的。本书的每一章最后都有一节给出了如何在免费的统计计算环境 $R$ 中进行计算和模拟的示例。
统计代写|Why study probability？ stat 代写 请认准UprivateTA™. UprivateTA™为您的留学生涯保驾护航。