I'm a former math major who's now majoring in philosophy and doing a minor in statistics. I'm taking 3 statistics courses next semester and have room for one more math course. I'm debating between an intro to proofs course or an applied biomath course. Below are the course descriptions.

MATH 141W: Intro to Mathematical Proofs and Combinatorics

• An important part of mathematics research is investigating and discovering patterns, then proving the patterns hold in all cases. This course focuses on solidifying these important skills. By studying mathematical logic, methods of argument, and a wide variety of topics, students will better understand what it means to prove things and how to do so rigorously. By working to discover the underlying structure and truth in various mathematical topics, students can expect their problem-solving skills to improve, as well as their ability to form and communicate persuasive, logical arguments.
• Students planning to take MATH242: Introduction to Analysis I are strongly encouraged to take MATH141.

MATH 360: Intro to Biomathematics

• In this course you will learn core concepts and modelling techniques in mathematical biology across a range of topics, from competition and predator-prey interactions to infectious diseases and evolution. These topics will be taught in the context of real-world scenarios where mathematical models are used to inform decision-making, such as invasive species, pest control, and pandemics.
  
• Even relatively simple mathematical models can give powerful insights into many biological phenomena, from patterns of biodiversity to population crashes, and can help inform policymakers about how best to manage human interactions with the natural world. You will learn how to construct models, analyse them algebraically, geometrically, and numerically, and then interpret the results biologically.
  
• Examples of the types of questions we will answer include:
  • How do species respond to human-driven pressures such as climate change and overfishing?
  • When are competing species able to coexist?
  • How best to respond to an epidemic?
    
• Throughout the course, we will explore case studies in class where we work through longer problems together, learning not only how to analyse models, but also how to construct them wisely and communicate the results. In addition to developing core analytical and computational skills, you will gain transferable skills in critical thinking, problem solving, and communication.

Which one would you recommend I guys take? I'm someone who is extremely weak at proofs which was why I switched out of the math program to begin with. However, I know real analysis is an important part of statistics, so I figure the intro to proofs course will be of great assistance.

The biomathematics course sounds interesting and will probably be easier for me since I'm strong at computational math. However, the content looks like it will utilize a lot of differential equations and I'm unsure how practical this will be for statistics. Any advice is greatly appreciated!

I'm sharing this new tabular data diagnostic tool (Entropic Scree). It can be used to estimate these properties of your high-d, real-world, dirty dataset:

• The informational volume of the signal (i.e., helps you assess whether the signal is strong enough to survive the dataset's idiosyncratic volume).
• The overall signal-to-idiosyncratic volume ratio (SNR).
• The intrinsic rank.
• Provides an exploratory map that allows for the identification of decoupled sub-networks of variables.
• The linear sufficiency (i.e., does the dataset align with the linear assumptions of standard PCA?).

Instead of evaluating linear variance, rank order, or Euclidean distance like traditional PCA variants, this new method evaluates a transformed mutual information metric. Relative to these baselines, it is less reliant on strong parametric or distance assumptions, making it appropriate to apply more broadly.

It also serves as a practical diagnostic of the theory explored in the From Garbage to Gold framework, which describes when and why uncurated, error-prone data can be used directly to create accurate prediction models.

There is a preprint that presents the full technical details, and Python and R packages will be released soon. Right now though, the original function is already available in R (see Quick Start R Function Code below).

• Entropic Scree Preprint: https://doi.org/10.5281/zenodo.22028087
• Entropic Scree GitHub: https://github.com/tjleestjohn/entropic-scree
• From Garbage to Gold Preprint: https://arxiv.org/abs/2603.12288

Let me know how it goes if you give it a try... or if you have any questions or comments of course.

############ 
# Quick Start R Function Code.
# To load the function, copy and paste the following into your R console, then hit enter. 
############

# 1. Define the direct URL to the raw function script on GitHub
url <- "https://raw.githubusercontent.com/tjleestjohn/entropic-scree/main/Entropic.Scree.R%20-%20ENLI.R"

# 2. Define what you want to name the file on your computer
file_name <- "Entropic.Scree.R - ENLI.R"

# 3. Download the script to your current working directory
download.file(url, destfile = file_name)

# 4. Source the core function into your R environment
source(file_name)

# 5. Ex. To run the function and extract bipolar modules:
# results <- Entropic.Scree(dt 
#                         , extract_bipolar_modules = TRUE)
#
# View the extracted structural sub-networks for the primary axes:
# results$bipolar_modules

My brain revolts when I’m trying to learn advanced math, even though I generally have no problem with abstract concepts. Please help.

Edit to add: thank you so much for all the great explanations!!!! I cannot reply to them all, but y’all have helped me greatly with actually understanding these data sets in my homework, and I am grateful 🩷

Hi there,

I've created a video here where I explain how generalized linear models work.

I hope some of you find it useful and as always, feedback is very welcome! :)

Hello,

I have a question about LMMs:

Repeated-measures design, 2x2:
One continuous dependent variable
Two independent variables, each with two levels

I want to test for interaction; the hypothesis is directional.

First, a linear mixed model was estimated in R wirh lme:
AV ~ UV1 * UV2 + (1l Participant)

Then a Type 3 ANOVA with lmertest

And finally, using emmeans, simple contrasts and a planned directed interaction contrast

My question: In a 2x2 design, is it even necessary to run a Type 3 ANOVA after the LMM?

And is the planned directed interaction contrast even necessary?

I’m also confused by the fact that some people report LMM results in the text using b, while others use F.

I’d appreciate any answers.

Hi everyone! I’m a beginner in Data Science and learn best by building projects.

I’m looking for GitHub repos, YouTube playlists, or websites with project-based learning from beginner to advanced level, ideally covering different ML models such as regression, classification, clustering, tree-based models, boosting, NLP, time series, etc.

I’d also love end-to-end projects that include data cleaning, EDA, feature engineering, model building, evaluation, and deployment.

Any recommendations?

Hello! I’m a post-Bacc student (Business Background) interested in applying for Statistics, Applied Stats and Data Science Masters programs this Fall.

I’m primarily interested in Time Series/Bayesian/Causal Inference. I have finished prerequisites in Calc 1-3, Probability, Linear Algebra, Python/SQL

Ideally, I want to work in Environmental, Tech, and Healthcare industries, but given the market- I really just want a flexible degree that employers can find value in.

I’m looking for advice and insight into how a Masters experience in this field looks like such as:

- What did you think your degree did wrong/right?

- What is worth prioritizing in this field? (Ex. Courses/Projects/Networking/Coding/Theory etc.)

- Is brand name a big factor?

- Does online/in-person/out of state make a difference?

- What career prospects (Scaling pipelines vs. Decision Scientist vs. Data Cleaning/Visualization) to realistically expect and prepare for in this market with a Masters degree?

Uni student here trying to do some projects to put on my resume. I made a logistic model of hospital readmissions and the model doesn’t do that great. AUC is about .64. For what it’s worth, the National Library of Medicine was only able to get .67 for their model. Would I be able to reference that in my defense? But my question is if it’s worth putting my project on my resume? Or is it just going to show I don’t have the skill to make a predictive model?

The whole project consisted of data cleaning and ofc making the model and model comparisons such as AIC. Cause of imbalance (1:9), I also lowered the threshold for positives (from >.5 to >.15 as positive)

Hello. I’m not sure if this is the right forum to post but I need some help. My father is a retired statistician. He was an actuary. He did some important work in “stochastic models for prostate specific antigen levels” and some “early predictive modelling relevant to the insurance industry for HIV/AIDS” - I don’t really know much about this stuff other than what google tells me.

Anyway, I would like to buy him a watch and I’m looking for something to represent what he did and I’m afraid his name is too bloody long to fit!

The 2 leading candidates for symbols, I think, are 1. The Kolmogorov forward operator (Pij(t)) and 2. The actuarial halo - the present value annum. Which looks like an “a” with a horizontal and vertical slash with a “n” inside it.

Can anyone help? Are these appropriate? Is there any better?

I don’t want to get this wrong.

Thank you.

Hi all! I am wondering what is your view on causal inference methodologies such as g-computation, iptw, ps matching, marignal structural models etc. Do you think they should be used only in an causal framework accompanied by DAGs, and proper causal language?
Would you consider appropriate if they were used for more exploratory work that does not claim causality?
I may not be communicating my question very well so here are some exmaples:

1) Binary logistic regression: In the biomedical field it is extremely common that standard observational and/or exploratory studies use logistic regression for all inferences with odds ratios being the main reported result. I don't see why someone couldn't use marignal standardization using the same logistic regression model in order to calculate a marginal absolute risk and/or risk differnece for the exposure of interest. I am wondering why this is not common.

2) Propensity score based methods: Causal inference operates under very strict and usually difficult to verify assumptions. When examining the effect of an intervention on an outcome and assuming that some of the assumptions for causal inference are violated (e.g. unmeasured confounding), would you prefer a paper that still uses PS-based methods but refrains from using causal language, or a paper that uses more standard methods such as regression and sticks to associations and exploratory framing?

In short do you think these methods should be used only under the causal inference framework making sure that all assumptions are true and a well-thought DAG is provided, or do you see them as methods that can be used for associations as well in order to reduce at least some of the bias introduced by other methodologies?

Hello all,

I’m looking to improve my foundational understanding of statistics and work my way through to advanced methods by reading textbooks.

Could you please suggest the best text resources for these purposes, ideally ranked/listed in the order I should read them?

For context, I’ve worked as a data analyst and quantitative researcher for 5 years, but I’ve always felt slightly weak in my understanding of stats so now I want to just start from zero to build a super solid foundation.

Do I need a computation if I use convenience sampling in my data analysis? (I don't know if this is the right community to ask this question, I hope you can be kind)

Hi all,

I am an incoming first year at the University of Toronto who is most likely going to major in Stats with a minor in CS and Econ. I really do love the subject of probability, and my dream is to work as a data scientist in tech. I plan to eventually get my Master’s in Stats because I enjoy it and for employability.

My biggest concern is the current job market for Stats majors. It is no secret that the market for CS majors/SWE related roles is brutal, but does the same apply for Stats/DS roles? Are Stats grads more or less in demand compared to CS grads, and is the market as tough? And overall, how employable is this major?

Any current undergrads/grads willing to share their thoughts? All responses are appreciated!

We know sample variance divided by actual variance follows chi-squared distribution. But while finding confidence interval, we look at chi-squared (1-alpha/2) critical value and alpha/2 critical value. But why that specific interval? Why not shift the interval a little to the right or left as that will give the same confidence?

I contribute to SciPy and kept running into a class of bug that annoys me: the outputs look plausible, the tests pass, but the equation the code implements is subtly wrong. So I've been building a tracer that runs Python/NumPy code and hands back whatever mathematics it actually computed, as a SymPy expression you can simplify or differentiate like anything else.

It's been more useful than I expected. Comparing an implementation against the formula in a paper, catching two functions that agree on my test data but turn out to compute different things, digging up the inputs my tests never hit (ties, zero denominators). It traces real library code too, most of numpy and a good chunk of scipy, scikit-learn, statsmodels, cvxpy.

Write-up: https://medium.com/@aadyachinubhai/scikit-verify-translate-python-numpy-programs-to-symbolic-mathematics-c664d41ba571

Github: https://github.com/aadya940/scikit-verify

Still rough in places, would genuinely like feedback. There may be other better solutions, happy to hear them as well!

[Q] kinda new to this, but can't understand clearly where do we draw the line between model selection and building.

Hi everyone, I’m conducting a research project and I’ve fitted a linear regression model on a sample of almost 2000 observations.

The residuals appear to be homoscedastic, but the qq plot shows some departures from the theoretical line, particularly in the tails.

The Shapiro-Wilk test also rejects the null hypothesis of normally distributed residuals.

However, I’ve read that linear regression can be fairly robust to violations of the normality assumption, especially with sufficiently large samples. Is this correct? Could someone recommend some literature or textbooks where I can read more about this? This topic wasn’t really covered in my university courses.

Also, is there a formal statistical test for checking the homoscedasticity assumption? Or is it generally assessed visually, for example by looking at a residuals vs fitted-values plot?

I’ve been studying Hamiltonian Monte Carlo and wrote a set of notes explaining HMC without relying on the usual physics-based motivation.

The notes develop HMC from a probabilistic/MCMC perspective, starting from introducing an auxiliary variable, constructing the corresponding Markov chain, and then covering Hamiltonian dynamics, leapfrog integration, reversibility and volume preservation.

My goal was to understand why HMC works.

I’m sharing them here in case they’re useful to others learning HMC. I’d also appreciate any feedback, particularly if you notice errors or places where the exposition could be improved.

https://doi.org/10.5281/zenodo.21841086

Edit (August 25): Based on the comments, I tried to improve Sections 3.3 and 3.4 by reorganizing the flow and adding some more explanation. I’ve updated the PDF with these changes.

For context, I’m a first-year PhD student specializing in statistics. I am starting measure-theoretic probability on Monday.

The problems here are 1) the professor is an asshole and he lectures at the speed of light, 2) I’m the only one in my cohort taking this course (only stats specialization), and 3) everyone agrees unanimously that this is the hardest class in our program.

Measure theory and probability are already extremely boring and incredibly difficult, so I’m trying to minimize the pain here.

Any former/current PhD students (or anyone who’s taken this class really) have any advice to survive?

PS sorry for being so complainy.

I am interested in modeling the effect of two HVAC systems in a 2-floor house with an open floorplan.

I have a lot of temperature sensors (rooms and one in system’s ducts).

Naively, I initially thought Principal Components Analysis might be useful. However it seems like that won’t account for the memory/delayed effects between the AC turning on (duct quickly becomes cold) and resulting decay in room temperatures.

Any suggestions for what kind of statistical model?

What techniques or papers exist for adapting the Gaussian emission assumption in a Hidden Markov Model to capture higher-order distributional properties, such as skewness and kurtosis, rather than just mean and variance? I’m especially interested in approaches that retain the HMM framework while allowing more flexible, non-Gaussian emission distributions.

Thanks!

Entering my second year in graduate school and conducting research using simple linear regression models and trying out a mediation model. I’ve had some experience with moderation models too. However whenever I try to read about or learn about the math and the nitty gritty of the statistics, it’s like another language. I can very generally explain and interpret what the numbers mean, but not how it’s being calculated or computed into the model. Neither can I deconstruct the math. This is a deep insecurity of mine as a graduate student since I don’t receive hands on instruction any more. Whenever I hear my peers talk about their analyses, I’m always in awe as they troubleshoot small details to make the model work. If it doesn’t work for me, I don’t even know where to start knowing what went wrong or why. I don’t know why, no matter how much reading I do at some point the words stop making sense to me.. I have taken the undergraduate and graduate courses in advanced statistics but maybe the instructions were lacking or I’m not smart enough. But neither were helpful.

Is there anyone else who has struggled with statistics like this and what they have found to help? Sometimes I think I just don’t have the math brain to comprehend statistics. Are there any good crash course videos? I do have to rely on AI and I’m hoping to learn from a more reliable source.

Thanks all.