What statistical methods should statisticians master to advance their careers?

In my experience, the supervised machine learning is the basic where to start. Build your model and train it by using part of your dataset. Training means to provide the machine learning model both the features and label of each event.The remains part is used to test the model on a never-seen set of events. It should be able to correctly predict the event label.

Bayesian statistics is particularly useful when there is a need for quantifying the uncertainty of a model outcome/prediction. The essential idea is to treat the moving parts of our model as random variables and assign them some appropriate probability distributions. The uncertainty in these variables accumulate and gets fed into the final model prediction. Then, a suite of methods can be used to ascertain the level of uncertainty in the model outcome. Personally, I believe Bayesian statistics is the best way we have to marry assumptions and data. I am biased, of course.

It’s more about having the toolkit of all methods and being clever about which one to use, when and why. Having said that, I find Bayesian inference the dog’s danglies! So much that I am trying to subtly teach the core principles to my kids as foundations to thinking critically. “Listen baby, if at first you don’t succeed, figure out why, change something, copy success from elsewhere and go again”

I totally agree with Tom Bzik's comments. But there should be another category added to the list. I did not see Time Series Analysis as required. It is quite important.

Time series analysis, variational inference and causal inference are important topics worth learning. In addition, Monte Carlo methods have many practical applications.

Communication. It is one thing to know the fancy math and models, but without good communication skills nobody listen. I would typically try to avoid any complex terms or math when communicating with non experts. You might feel that you "hide" things but you can always present them if needed. In my opinion, it is a lot of practice and looking for resources like data story telling by Brent Dykes or following LinkedIn account like Christopher Chin.

All of the six statistical themes named are useful in your skills portfolio. Some or all of these are necessary but not sufficient to advance your career in statistics. Career advancement primarily rests upon many non-statistical skill sets. A short list includes: social skills, ability to judge and pick which projects are likely to be career enhancing, ability to explain results in English instead of Statistical-ese, ability to see well beyond the often very narrow reason you were invited to join the team, not cramming the problem into a methodology one is familiar with but does not quite fit, playing well with others, and having the ability and will to understand the problem's context.

Attending conferences that are statistics focused and conferences that are industry specific allow Statisticians to stay current on statistical methods and see opportunities to apply statistics in novel ways to their industry. Conferences can be an excellent source of motivation and learning, these benefits are multiplied when you speak at the conference.

Mastering spatial statistics is also essential. In terms of tools: ● R: Utilize packages such as 'sp', 'spdep', 'rgeos', and 'sf' for spatial data manipulation, visualization, and modeling. ● Python: Leverage libraries like 'geopandas', 'pySAL', 'shapely', and 'rasterio' for spatial data analysis, geoprocessing, and modeling. ● QGIS: An open-source GIS platform for spatial data editing, visualization, and analysis, enhanced with plugins and scripting.