EART60061 Measuring and Predictiong

Measuring and Prediction 1

Introduction

本课程为Measuring and Prediction 的第一部分，旨在定义与衡量污染物流动性和转型有关的技能与技能的一般过程，为了独立项目作准备。

Intended Learning Outcome

• ILO1 Recognise generic processes of research and be able to identify  "good" research   #什么是一个好的研究
• ILO2 Make their measurements meaningful and recognise the quality of those made by others – quantification and propagation of error   #误差与置信度
• ILO3 Design a sampling strategy by applying understanding of variability    #可变性与采样策略
• ILO4 Select appropriate techniques for measurement by applying knowledge of how instruments work    #选择适当的技术
• ILO5 Apply a process of mathematical model development to understanding a simple environmental system    #从数学模型到环境系统
• ILO6 Evaluate whether written arguments are logical and ordered correctly    #论点评估

WEEK1：What is a good research?

For more information about the research, please follow the website: Explorable.com 

Research= Importance x Novelty #新颖性 x Rigour #精确性

Importance- a problem

Novelty- never been done before

What research do you need to do?

For an MSc research thesis：

• Something that can be taught
• Therefore something that can be assessed.
• Appropriate = meets the marking criteria #适当性

***deduction #演绎法 & induction #归纳法  归纳与演绎推理 via.Explorable

**deduction: Deductive reasoning, in contrast to inductive reasoning, proceeds from one or more general axioms and comes to a certain, specific conclusion using logic alone. If the premises are true and the logic of the argument is valid, the conclusion is certainly true.  #演绎法与归纳法相反，从一个或者多个公理出发，仅使用逻辑得出某个结论，如果前提为真，则结论为真。

**induction: Inductive reasoning is the process of using a series of specific observations to support the probability of a more general conclusion. #使用一系列的具体观察结果来证明一般的结论。

    *Writing the theory of evolution, the theory of special relativity and plate tectonics were types of induction.  These ideas which may have been derived from synthesis of a large amount of previous work or "thought experiments"were related to the real world.  Probably a large amount of research based on deduction was carried out before the induction was accepted, this may then have resulted in a paradigm shift.  #写进化论、特殊相对论和板块构造理论都是归纳的类型。这些想法可能是从大量先前工作的综合或“思维实验”中得出的，与现实世界相关。很可能在归纳被接受之前进行了大量基于演绎推理的研究，这可能导致了范式的转变。

**  “范式转变 paradigm shift”指的是科学或思想领域中的重大变革或转变。它不仅仅是小幅的改变或进化，而是指整个框架或观念的彻底改变，从而导致对问题、概念或方法的全新理解。这种转变通常涉及对先前认知或惯例的根本性颠覆，推动新的思维方式、范例或理论取代旧有的框架。范式转变可能由新的发现、理论、科技进步或对问题的新认知所引发。例如，哥白尼的日心说取代了地心说就是一个范式转变的例子。

    *Strictly a hypothesis should be falsifiable, effectively it must be possible to Correct disprove.  However, falsifiability can be too strict because of the descriptive nature of some scientific research.  Falsifiability may also be misleading if it relies on observations/measurements that are highly impractical.  Nevertheless, falsifiability should be a researcher's initial goal in setting a Correct hypothesis. #严格来说，一个假设应该是可证伪的，实际上，它必须有可能被正确地证伪。然而，由于一些科学研究具有描述性质，证伪性可能过于严格。如果依赖于高度不切实际的观察/测量，证伪性也可能会产生误导。尽管如此，在设立正确假设时，证伪性应该是研究者的初始目标。

    *Research requires both inductive and deductive reasoning. Deductive reasoning is often required to identify a research question or set up an aim. In mathematical research, deductive reasoning would then also be used to achieve the aim but in environmental science there will be more reliance on inductive.

In order to gain a high mark the most important characteristic of a MPEC / MESPOM thesis is meeting marking criteria  #研究需要归纳推理和演绎推理两者兼备。演绎推理常用于确定研究问题或设定研究目标。在数学研究中，演绎推理也会用于实现目标，但在环境科学中，更多地依赖于归纳推理。

为了获得高分，MPEC/ MESPOM论文最重要的特点是符合评分标准。

    *Typically, reporting of research proceeds from explanation of a general problem; the requirement to solve this is then the aim of the work.  Having explained this a specific procedure to solve it must be developed, typically this requires that a set of subsidiary problems be solved; these are the objectives.  Defining these requires an argument that makes a clear connection of each to the aim.

A Research Proposal should justify the requirement for resources required to fund the activities detailed in the methods, the proposal must therefore make a clear argument that connects these activities to the aim of the work via the objectives. #通常，研究报告从阐述一个普遍问题开始；解决这个问题的需求随后成为工作的目标。在阐明问题后，必须制定解决方案的具体步骤，通常需要解决一系列附属问题；这些便是目标。明确定义这些目标需要一个论证，清晰地将每个目标与工作目标联系起来。

一个研究提案应当证明所需资源的必要性，以资助方法中详细列出的活动。因此，提案必须进行清晰的论证，将这些活动与工作目标通过目标连接起来。

WEEK2: Making measurement meaningful

Excel 的指导书： Excel 2016 for environmental sciences statistics : a guide to solving practical problems

本周目标：ILO2、3、6

M1 - Recognising the need to quantify variability

Measurement is a requirement of investigations and research.  Because of unavoidable variation, measurements should be considered as being samples of a population that may be infinite.

Examples

A single measurement with a ruler is only a sample of all the possible repetitions of such a measurement, repetitions may vary because of the position of the measurer’s head, slight temperature changes etc..  The true length of the object measured would be the mean length of an infinite number of repeated measurements.

A single measurement of the concentration of Pb in a water sample using ICP-OES is only a sample of all the possible repetitions of such a measurement, repetitions may vary because of variations in temperature of the instrument, in power supply, vibration etc.. 

A single quadrat measurement of the population density of limpets on a rocky shore is only a sample of all the possible repetitions of such a measurement. 

Q: In which of the examples is it possible to measure the true value and why?

A: A true measurement of limpets on the shore could be made as limpets are discrete variables, however, quadrats would have to cover the entire survey area.

Given that measurement of the true value is only possible when variables are discrete and even then rarely possible, there is a requirement to somehow make measurement meaningful, this can be achieved by: Increasing the number of repetitions (multiple measurements).

Q:  How can this make measurement meaningful?

A: multiple measurement will increase the probability of better approximating the population (true) mean  #多次测量能够接近平均（真实）值

Q: Why may this be insufficient to make measurement useful?

A: constraints of time and finance will always prevent the true mean being found, and no indication of the likelihood that the result is the true mean is given.

Q: How else may multiple measurements be more useful in making measurements meaningful?

A: The advantage of multiple measurements may not be predominantly to increase the probability of better approximating the population (true) mean

Consideration of the variability of the sample can give an indication of whether the sample mean is likely to be close to the true mean.  Such an indication is often the most appropriate way of making measurements useful, however, this presupposes that the scientist also knows the degree of difference from the true value that is acceptable for the study.

(It is important to note that the sample variability cannot be considered if the sample consists of a single measurement.)

M2 - Deriving measures of variability appropriate to data

使用Excel工具创建并且导出变异性

M3 - Modelling random variability (the Normal distribution)

随机变量是可以被预测和建模的 (Random variability can be modelled/predicted) ，这种分布就叫做正态分布。

标准差(Standard deviation)是正态分布函数的一个参数，决定了它的形状。

当计算标准差的时候，注意样本空间与总体数量。Excel标准差计算函数的区别

The value of standard deviation is identical to the width of the curve at the point that the gradient stops increasing if the curve is followed up from the x-axis.  Similarly, the area that lies within one standard deviation of the central mean value defines a constant proportion of the central area under the curve. #对于正态分布来说，标准卡是x轴，而置信度就是x轴与上方曲线的面积

e.g. 68% of the sample will lie within one standard deviation of the mean and 95% of the sample within 1.96 standard deviations.

These proportions are always the same for all normal distributions. 

The curve is asymptotic to the x-axis, in other words the range of measurements is not fixed – truly random effects could produce infinite deviations from the mean, these will, however, be infinitely rare. 

置信区间和置信度怎么来的，就是

• 可以引用总体平均值所在的样本平均值（d value乘以标准差）两侧的范围以及该陈述正确的置信度 
• 或者引用该陈述的可接受的置信度，并给出总体平均值所在的样本均值两侧的适当范围。

M4 - Using the Normal distribution in measuring and predicting