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# 统计代写|贝叶斯统计代写Bayesian Statistics代考|CASMA578 THE PURPOSE OF STATISTICAL INFERENCE

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## 统计代写|贝叶斯统计代写Bayesian Statistics代考|THE PURPOSE OF STATISTICAL INFERENCE

How much does a particular drug affect a patient’s condition? What can an average student earn after obtaining a college education? Will the Democrats win the next US presidential election? In life, we develop theories and use these to make predictions, but testing those theories is not easy. Life is complicated, and it is often impossible to exactly isolate the parts of a system which we want to examine. The outcome of history is determined by a complex nexus of interacting elements, each of which contributes to the reality that we witness. In the case of a drug trial, we may not be able to control the diets of participants and are certainly unable to control for their idiosyncratic metabolisms, both of which could impact the results we observe. There are a range of factors which affect the wage that an individual ultimately earns, of which education is only one. The outcome of the next US presidential election depends on party politics, the performance of the incumbent government and the media’s portrayal of the candidates.

In life, noise obfuscates the signal. What we see often appears as an incoherent mess that lacks any appearance of logic. This is why it is difficult to make predictions and test theories about the world. It is like trying to listen to a classical orchestra which is playing on the side of a busy motorway, while we fly overhead in a plane. Statistical inference allows us to focus on the music by separating the signal from the noise. We will hear ‘Nessun Dorma’ played!

Statistical inference is the logical framework which we can use to trial our beliefs about the noisy world against data. We formalise our beliefs in models of probability. The models are probabilistic because we are ignorant of many of the interacting parts of a system, meaning we cannot say with certainty whether something will, or will not, occur. Suppose that we are evaluating the efficacy of a drug in a trial. Before we carry out the trial, we might believe that the drug will cure $10 \%$ of people with a particular ailment. We cannot say which $10 \%$ of people will be cured because we do not know enough about the disease or individual patient biology to say exactly whom. Statistical inference allows us to test this belief against the data we obtain in a clinical trial.
There are two predominant schools of thought for carrying out this process of inference: Frequentist and Bayesian. Although this book is devoted to the latter, we will now spend some time comparing the two approaches so that the reader is aware of the different paths taken to their shared goal.

## 统计代写|贝叶斯统计代写Bayesian Statistics代考|THE WORLD ACCORDING TO FREQUENTISTS

In Frequentist (or Classical) statistics, we suppose that our sample of data is the result of one of an infinite number of exactly repeated experiments. The sample we see in this context is assumed to be the outcome of some probabilistic process. Any conclusions we draw from this approach are based on the supposition that events occur with probabilities, which represent the long-run frequencies with which those events occur in an infinite series of experimental repetitions. For example, if we flip a coin, we take the proportion of heads observed in an infinite number of throws as defining the probability of obtaining heads. Frequentists suppose that this probability actually exists, and is fixed for each set of coin throws that we carry out. The sample of coin flips we obtain for a fixed and finite number of throws is generated as if it were part of a longer (that is, infinite) series of repeated coin flips (see the left-hand panel of Figure 2.1).

In Frequentist statistics the data are assumed to be random and results from sampling from a fixed and defined population distribution. For a Frequentist the noise that obscures the true signal of the real population process is attributable to sampling variation – the fact that each sample we pick is slightly different and not exactly representative of the population.

We may flip our coin 10 times, obtaining 7 heads even if the long-run proportion of heads is $\frac{1}{2}$. To a Frequentist, this is because we have picked a slightly odd sample from the population of infinitely many repeated throws. If we flip the coin another 10 times, we will likely get a different result because we then pick a different sample.

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。