Collection of various pedagogical notes, tutorials (homeworks), and resources that are helpful to get started on a research project (or pick up a niche technique/skill).
Ph.D. thesis - link
Below are some solved homework problems from Neil Cornish's problem set. See here for Justin Ripley's version.
Intro to Metropolis-Hastings Markov Chain Monte Carlo: Sample from a t-distribution, Poisson distribution, Gaussian distribution (with comparison of different proposals/jumps).
Parameter estimation of t-distribution tutorial : link (additionally you will need to download this mathematica notebook)
Intro to statistics and data analysis (in general):
As a beginner, I have found it very useful to go through chapters 3,9-12 of the book Bayesian Logical Data Analysis for the Physical Sciences by Phil Gregory (https://doi.org/10.1017/CBO9780511791277). Another useful book to pick up Bayesian stuff is Data Analysis: A Bayesian Tutorial by Sivia & Skilling (https://doi.org/10.1093/oso/9780198568315.001.0001), particularly chapters 1-4. David Mackay's book (http://www.inference.org.uk/itila/) is particularly useful to obtain more insight into information theory (chapter 4 is a good follow up to both Gregory and Sivia & Skilling).
Advanced topics: For parallel tempering MCMC, Gregory's chapter 12.5 is a good start. To get a better understanding, I found it more useful to actually try and code up a simple PTMCMC routine (it didn't work great, but I learned a lot). For nested sampling, chapter 9 of Sivia & Skilling is a good start. The examples given in dynesty and bilby are also very useful. Justin Ripley's notes on Bayesian statistics also provide a lot of mathematical detail and are excellent for a "first-principles" approach to the topic. David Hogg's Data Analysis Recipes papers are also quite useful once you are familiar with the basics.