Here, the concepts behind the most important data analysis techniques will be explained using a minimum of mathematics, but in such a way that the book still can be used as a student’s text. Its structure more or less follows the steps made in 1 Introduction 3 a “classical” data analysis, starting with the data pretreatment in Part I. This step is hugely important cck-8 mw, yet is often treated only cursorily. An unfortunate choice here can destroy any hope of achieving good results: background knowledge of the system under study as well as the nature of the measurements should be used in making decisions. This is where science meets art: there are no clear-cut rules, and only by experience we will learn what the best solution is. The next phase, subject of Part II, consists of exploratory analysis. What structure is visible? Are there any outliers? Which samples are very similar, which are differ ent? Which variables are correlated? Questions like these are most easily assessed by eye—the human capacity for pattern recognition in two dimensions is far superior to any statistical method. The methods at this stage all feature strong visualization capabilities.
Usually, they are model-free; no model is fitted, and the assumptions about the data are kept to a minimum. Once we are at the modelling phase, described in Part III, we very often do make assumptions: some models work optimally with normally distributed data, for example. The purpose of modelling can be twofold. The first is prediction. Given a set of analytical data, we want to be able to predict properties of the samples that cannot be measured easily. An example is the assessment of whether a specific treatment will be useful for a patient with particular characteristics. Such an application is known as classification—one is interested in modelling class membership (will or will not respond). The other major field is regression, where the aim is to model continuous real variables (blood pressure, protein content, …). Such predictive models can mean a big improvement in quality of life, and save large amounts of money. The prediction error is usually taken as a quality measure: a model that is able to predict with high accuracy must have captured some real information about the system under study. Unfortunately, in most cases no analytical expressions can be derived for prediction accuracy, and other ways of estimating prediction accuracy are required in a process called validation cck8 chemicals. A popular example is crossvalidation. The second aim of statistical modelling is interpretation, one of the topics in Part IV. Who cares if the model is able to tell me that this is a Golden Delicious apple rather than a Granny Smith? The label in the supermarket already told me so; but the question of course is why they taste different, feel different and look different. Fitting a predictive model in such a case may still be informative: when we are able to find out why the model makes a particular prediction, we may be able to learn something about the underlying physical, chemical or biological processes. If we know that a particular gene is associated with the process that we are studying, and both this gene and another one show up as important variables in our statistical model, then we may deduce that the second gene is also involved. This may lead to several new hypotheses that should be tested in the lab. Obviously, when a model has little or no predictive ability it does not make too much sense to try and extract this type of information. The variables identified to be worth further study in many cases are indicated by the term biomarkers, according to Wikipedia “measurable indicators of some biological state or condition”. Of course, with high-dimensional data sets it is very well possible that no biomarkers can be identified, even though predictive models can be fitted—much as we would like the world to be a simple place, it usually 4 1 Introduction is not. In areas like Machine Learning one often uses models that do not allow much interpretation and consequently focus has shifted almost completely to prediction. Our knowledge of the system can also serve as a tool to assess the quality of our model. A model that fits the data and seems to be able to predict well is not going to be very popular when its parameters contradict what we know about the underlying process.
Often, prior knowledge is available (we expect a peak at a certain position; we know that model coefficients should not be negative; this coefficient should be larger than the other), and we can use that knowledge to assess the relevance of the fitted model. Alternatively, we can constrain the model in the training phase to take prior knowledge into account, which is often done with constraints. In other cases, the model is hard to interpret because of the sheer number of coefficients that have been fitted, and graphical summaries may fail to show what variables contribute in what way. In such cases, variable selection can come to the rescue: by discarding the majority of the variables, hopefully without compromising the model quality, one can often improve predictions and make the model much more easy to interpret. Unfortunately, variable selection is an NP-complete problem (which in practice means that even for moderate-sized systems it may be impossible to assess all possible solutions) and one never can be sure that the optimal solution has been found. But then again, any improvement over the original, full, model is a bonus. For each of the stages in this “classical” data analysis pipeline, a plethora of methods is available. It can be hard to assess which techniques should be considered in a particular problem, and perhaps even more importantly, which should not. The view taken here is that the simplest possibilities should be considered first; only when the results are unsatisfactory, one should turn to more complex solutions. Of course, this is only a very crude first approach, and experienced scientists will have devised many shortcuts and alternatives that work better for their types of data. In this book, I have been forced to make choices. It is impossible to treat all methods, or even a large subset, in detail.
Therefore the focus is on an ensemble of methods that will give the reader a broad range of possibilities, with enough background information to acquaint oneself with other methods, not mentioned in this book, if needed. In some cases, methods deserve a mention because of the popularity within the bioinformatics or chemometrics communities. Such methods, together with some typical applications, are treated in the final part of the book. Given the huge number of packages available on CRAN and the speed with which new ones appear, it is impossible to mention all that are relevant to the material in this book. Where possible, I have limited myself to the recommended packages, and those coming with a default R installation RNA dye. Of course, alternative, perhaps even much simpler, solutions may be available in the packages that this book does not consider. It pays to periodically scan the CRAN and Bioconductor repositories, or, e.g., check the Task Views that provide an overview of all packages available in certain areas—there is one on Physics and Chemistry, too.
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