uoft | Siqi Zheng

Learning Stats at UofT #8: Problems in Statistics Application

Sat, 27 Mar 2021 09:00:00 +0000

This is the eighth post of the series Learning Stats at UofT. In case you did not read my last post, here is the introudction.

The fundamental statistics courses at UofT are normally unchanged, at least from my experience in the past three years. Still, I think it is worth devoting some blogs to this topic. Before starting the introduction to courses, I would like to spend some time on discussing statistics.

Now it’s approaching the end of semester for me. To reflect back on the past 2020, a lot of things were going on and everyone had a tough time. It was also the time to develop skills to collaborate virtually and be compassionate about other people in workplaces around the world.

In a data driven world, we are connected by data and the study of data, statistics, is very essential to our day to day life. However, the abuse of statistics also created problems for us.

Misspecified Models

At the early stage of the pandemic, people proposed many models to predict the number of cases around the world. Some even argued that the cases would grow exponentially. This was based on their past experience with virus spread. However, this was a very unreasonable guess because there was no up-to-date evidence to support this. this created some rumors and pessimistic expectations on our world. In fact, this could be avoided if the posters were more cautious about what they were going to say and the implications. But they were not. Statistics became a tool to spread rumors, and readers should be more critical towards such models. We statisticians have the responsibility to stand out and correct this mistake.

Data Exploration

New data were released every day from the government. The data analysis should be the job of data analyst. However, many people who had no such backgrounds also spread their ideas on the internet. It was not that harmful if they were accidentally correct. However, some people enjoyed playing around with data and sharing some false conclusion based on them. Hence I see the necessity for a general education about statistics for the public.

Learning Stats at UofT #7: Detail-oriented and Communication Skills

Sat, 20 Mar 2021 09:00:00 +0000

This is the seventh post of the series Learning Stats at UofT. In case you did not read my last post, here is the introudction.

I am a student in Applied Statistics Specialist, or Method and Application, at UofT. Though there were some changes in the requirements, the main focus of the two programs is the same. In particular, you will go through some fundamentals in R and (Frequentist) statistics in your first two years, and take upper year courses in some advanced topics. Compared to the Theory one, you do not need to take so many courses in theory, but you need to choose a focus depending on your interest. The focus seemed less important, but I gave a lot of thoughts about it in my past years. So I would like to share some of them with you. Note that all of these can be found on the official website of Arts & Science, and I hope this paragraph serves well as an introduction.

By meeting with a Vic alumnus, I summarize a set of core skills that are important for our future career. This is the last part of the core skills.

Detail-oriented

In workplace, noticing the details means you are careful every pieces of your writing and avoid making errors due to carelessness. In real life, the skill refer to the followings. Be curious about the surroundings and the environment. Catch sight of the beautiful and show your appreciation. Remark on the unusual and take a note of it. Notice the changing seasons and take a photo of them. Savour the moment, whether you are walking to work, eating lunch or talking to friends. Be aware of the world around you and what you are feeling. You are not a robot, so you should not only work or study. Lastly, reflecting on your experiences will help you appreciate what matters to you (credit to Chad Jankowski).

Communication Skills

Communication is every where. You need to communicate verbally or in writing with family, friends, colleagues and neighbours. You apply communication skills at home, work, school or in your local community. Therefore, you need to think of your past communications as the cornerstones of your life and invest time in enhancing these skills. Building these connections skillfully will support and enrich you every day (credit to Chad Jankowski).

In workplace, communication should be clear and precise. Sometimes you need to be a bit diplomatic when you talk to people, sometimes you need to be bold to speak up your needs. People should develop the ability to communicate differently with various people in many contexts.

Learning Stats at UofT #6: Critical Analysis and Problem Solving

Sat, 13 Mar 2021 09:00:00 +0000

This is the sixth post of the series Learning Stats at UofT. In case you did not read my last post, here is the introudction.

By meeting with a Vic alumnus, I summarize a set of core skills that are important for our future career. This is the first part of the core skills.

Critical Analysis

Critical analysis involves the ability to analyze the situation, to retrieve information from different sources, and the ability to communicate the idea quantitatively and qualitatively.

Statistics courses at U of T provide great training of quantitative analysis. In recent years, instructors also think about different assignments that requires student to apply their skills in analyzing real-life cases. Nonetheless, this is not enough from my perspective. First, such tasks have to align with the specific course objective. In particular, the data provided for the assignment are so good that you don’t need to consider any absurd situations. Second, the professors may not necessarily know what nowadays employers are looking for. Hence it is important to explore the real world by yourself.

Problem Solving

The following materials were adapted from the learning strategies at UofT, Rahul Bhat.

Background

What background information do I need to solve the problem? This should be combined with critical analysis. Specifically, you may want to know what information is missing all ignored.

Rules

What theories, solutions, rules, proofs, or approaches might I use to solve the problem? In quantitative analysis, you will need to use mathematical knowledge, for example, theorems, to solve questions.

Steps

Can I break the problem into steps - those I understand and those I can gather more information for? This way, you can explore the steps that can be done fairly easily, and save more time for the difficult tasks.

Connection

Is there something I have seen in the past that resembles this problem? You practice active retrieve of knowledge in this aspect, and look for solutions that are applicable in some sense to this question.

Learning Stats at UofT #5: A Dialogic Way to Introduce MLE

Sat, 06 Mar 2021 09:00:00 +0000

This is the fifth post of the series Learning Stats at UofT. In case you did not read my last post, here is the introudction.

A Dialogic Way to Introduce MLE

Imagine you walk into Starbucks at Robarts Library, and you meet one of your TAs from STA257. Now you may want to say hi to this TA, but you also want this TA to clarify the concept of MLE. If I were the TA, I would explain the concept of MLE in the following way.

Sure, I can explain the concept of likelihood while we wait in line. In statistics, we often need to estimate the parameter of a model. But how? Well, Maximum Likelihood estimation (MLE) can help. First of all, we need to know likelihood means the probability of a value being the true value of a parameter θ in a model given a set of data. MLE provides a way to find a value θ ̂ with the maximum probability to be θ.

Let’s use an example to illustrate this. Suppose you are interested in a model that describes the waiting time for a customer in this restaurant. Now you can first collect the data of individual waiting time randomly. Then you may assume that the true population of waiting time follows some classical distributions so that we only need to estimate the parameter θ of a known distribution. Then we may be able to use MLE here. Does that make sense so far?

Alright, now, here comes the tricky part. In order to use MLE, we need the joint distribution of all data X, which gives the probability that each of X falls within a specific range for a variable. But wait, we do not actually know it since we only know the marginal distribution, i.e. the density function of individual X with an unknown θ. Hence we can consider making an assumption that all data are independent, meaning knowing one waiting time does not tell us about the next waiting time. It may not be true in reality, but it is sufficient for our purpose. Under this assumption, we can multiply all marginal density to get our joint density. To find the maximum likelihood estimate, we can set the first derivative with respect to θ equal 0 and find a value. We can calculate the second derivative as well to ensure that θ ̂ is a maxima. This θ ̂ is our Maximum Likelihood estimate for the parameter. Did that explanation help?

To sum up, Maximum Likelihood estimation gives an estimate for a parameter in a model given a set of data. In particular, with a known joint probability density function of all data and the parameter, we can use derivatives to find an estimate of the parameter with the maximum probability to be the true value for the model. Let’s pause for a moment! It is my turn to get the drink!

Learning Stats at UofT #4: Model Selection

Sat, 27 Feb 2021 09:00:00 +0000

This is the fourth post of the series Learning Stats at UofT. In case you did not read my last post, here is the introudction.

Model Selection

In the third year course STA302, you will learn about simple linear regression and multiple linear regression models. In fact, you will learn more about assumptions behind models and possible remedies for improvements. Nonetheless, what you will not learn is whether it is appropriate to apply this model in a particular field.

In reality, you will find that many models fit the data pretty well, but those models are incorrect. So here comes the question: to what extent you can apply a complex model on your data? The disciplinary knowledge is crucial in this context. It not only provides a justification for model, but also a way to interpret the model.

Does Disciplinary Knowledge Play a Role in Model Selection?

In NFS284, you learn about some thresholds to determine whether the consumption of nutrients is adequate. These thresholds, however, depend on the normality assumption. In fact, if you look at the hypothesis testing in the academic papers, you will notice that almost always P=0.05 is selected as significant level and a normal assumption is approximated. But this requires some reasons. You cannot select a P value that just serves your convenience.

I believe that the researchers have more knowledge in nutrition science than me, and they may have very good reasons for their application of statistics. However, it is not very common to see the justifications in the well-written papers. In fact, you cannot tell whether disciplinary knowledge plays a role in Model Selection.

One possible reason is that this requires researchers to devote some paragraphs on it. The page limit of an academic journal, nevertheless, may not allow them to do so. To take a step back, even if there is some restrictions on the length of the article, this justification should not be given up just because of it.

Learning Stats at UofT #3: Some Controversies

Sat, 20 Feb 2021 09:00:00 +0000

This is the third post of the series Learning Stats at UofT. In case you did not read my last post, here is the introudction.

Data Science Program

The first controversy is about the data science program. It is controversial because of its high enrollment requirements and different views towards data science. The enrollment requirements are the highest among all stats programs offered at UofT. Moreover, it requires you to learn both knowledge in computer science and knowledge in statistics, but it doesn’t require you to learn a lot of theories about statistics. Rather, it asks more for probability theories and the application of statistics. On the other hand, it involves a lot of things about data structure, but less computer science knowledge. Therefore some people think that this course it’s kind of awkward between pure CS program and stats program. There is another view. Many also think so it’s better for the workplace because this program offer an internship opportunity.

The Changes in Course Content

Statistics departments at U of T went through many changes. In particular, many courses changed their instructors every year. Furthermore, the course content evolved with the changing focus in nowadays workplace. The pro was that you could always learn the most up-to-date knowledge in statistics and instructors also had more flexibility in designing a course. Note that the scope of a course remained the same throughout the time, but the way to convey knowledge might change. For students, however, it was hard to prepare for the upcoming courses. Sometimes the course organization would have many small issues when the new content was added.

Learning Stats at UofT #2: A Guide to Second-year Courses

Sat, 13 Feb 2021 09:00:00 +0000

This is the second post of the series Learning Stats at UofT. In case you did not read my last post, here is the introudction.

STA237/238

There are three combinations of courses offered by DoSS. The first combination is STA237 and STA238. This combination primarily focuses on R. It also goes through the fundamentals of statistics. However, it may not be the best introductory courses for statistical theories because every year the focus is adjusted. The organization of the courses was not very satisfactory last year because students from RC without strong stats background found it too programming-based and students from CS found it less interesting because of lack of in-depth theories.

STA247/248

There is another combination called STA247 and STA248. This combination is designed solely for computer science students and it is great to learn if you want more knowledge in probability, especially because it involves many creative questions about probability and some knowledge that computer science students may need for programming,

STA257/261

The last combination, which is the combination I took in my second year, is STA257 and STA261. This combination is so-called the hardest one for second-year stats students. Typically, the instructor will introduce a bunch of distributions, some new concepts about CDF and PDF, and some calculations using double integration. Now this was the tricky part for me at that time. Many students didn’t learn convolution and double integration when they took this course. As a result, many of us needed to spend more time getting familiar with these things.

Another interesting aspect of this course is that it doesn’t involved too much about Bayesian. I would say this is not really a limitation, but it somehow affects how students think about statistics in the future. This course introduces many concepts that was thought to be important in the future, particularly the part about ordered statistics and quantile thing. They will play an important role in the third-year courses

Learning Stats at UofT: A Guide to Focuses in Applied Statistics

Sat, 06 Feb 2021 09:00:00 +0000

Focus can be changed, but you have to plan ahead

The selection of focus really depends on the courses you take in your first year. Most students in MP take ECO101/102 and CSC148/165 in their first year. This courses combination of CS and ECO has certain benefits. Specifically, this combination gives students much flexibility in their second and third year since it allows them to choose Data Science Specialist in Statistics program, CS programs and Economics programs

However, a common solution is not necessarily good. As a student who would like to take new challenges and learn more about education, I chose to take Education courses in Victoria College. This to some extent limited my choices of programs. In particular, if I would like to enroll in other programs, I might need to start from the beginning. Nonetheless, I met great friends there and discovered that being a teacher in a primary/middle school was not what I really wanted.

Then I decided to select Astrophysics as my focus in my second year, hoping to explore the broader universe that I have never learnt before. It was fun to learn, but it was too theoretical and I started to get interested in Finance and Economics soon. Hence I reached a crossroads again. If I continued on Astrophysics, I believed I could still do well in academia, but I could not imagine what I was going to do after that. On the other hand, if I chose Economics, I needed to take first-year courses in Economics in my second year and caught up with others in my third year. This was exactly the disadvantage of my first-year course selection.

The key point is that there is going to be a trade-off when you want to select a focus - it is more common to stick to your first-year courses when you think about choosing a focus, but then you do not have the opportunity to choose some other interesting courses in the university.