Students cultivate learning techniques in school that emphasize procedural problem solving and rote memorization. This leads to efficient problem solving for familiar problems. However, conducting novel research is an exercise in creative problem solving that is at odds with a procedural approach; it requires thinking deeply about the topic and crafting solutions to unique problems. It is not easy to move from a topic-based, carefully curated curriculum to the daunting world of independent research, where solutions are unknown and may not even exist. In developing this book, we considered our experiences as graduate students that faced this transition.
Exercises in Statistical Reasoning is a collection of exercises designed to strengthen creative problem-solving skills. The exercises are designed to encourage readers to understand the key points of a problem while seeking knowledge, rather than separating out these two activities. To complete the exercises, readers may need to reference the literature, which is how research-based knowledge is often acquired.
Features of the Exercises
The exercises are self-contained, though several build upon concepts from previous problems.
Each exercise opens with a brief introduction that emphasizes the relevance of the content. Then, the problem statement is presented as a series of intermediate questions.
For each exercise, we suggest one possible solution, though many may exist.
Following each solution, we discuss the historical background of the content and points of interest.
For many exercises, a brief demonstration is provided that illustrates relevant concepts.
There is an abundance of high-quality textbooks that cover a vast range of statistical topics. However, there is also a lack of texts that focus on the development of problem-solving techniques that are required for conducting novel statistical research. We believe that this book helps fill the gap. Any reader familiar with graduate-level classical and Bayesian statistics may use this book. The goal is to provide a resource that such students can use to ease their transition to conducting novel research.
1 Probability
2 Likelihood Estimation
3 Exponential Family
4 Hypothesis Testing & Decision Theory
5 Linear Models & Regression
6 Asymptotics
7 Time Series
8 Markov Chain Monte Carlo
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