Here are a few chapters of statistical analysis that I frequently use in applications
- The linear model and generalised linear model
- Non-linear regression analysis
- Time-series models (including continuous time), state-space models and Kalman filtering, Hidden Markov models
- Maximum likelihood theory and profile-likelihood
- Bayesian inference
- Extreme-Value modelling
- Gaussian Processes (GP) including Latent GPs hierarchical modelling
Although I am occasionally involved in some research, I feel free of any promotion task when working with data. Given a real-world statistical problem I never take for granted that such or such method should be used until a careful analysis of data is completed. It is not uncommon that a well-chosen "classical" model outperforms some more fashionable models.
I enjoy using/building statistical models that relate to physics or other sciences or domains of expertise in some way. I favour interpretable models, as opposed to black-box models - which are useful to give hints about large amounts of data.
I do not like much the fashionable expression data science, maybe because all sciences are data sciences - except perhaps pure mathematics, which could be named "the no-data science".