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Large-scale Markov chains behave like differential equations, and this makes it easy to get a back-of-the-envelope sense of how they're likely to behave. Second year Data Science and Machine Learning course, Cambridge University / Computer Science. Taught by Dr Wischik. www.cl.cam.ac.uk/teaching/2122/DataSci/materials.html

What is the long-run behaviour of a Markov chain? Second year Data Science and Machine Learning course, Cambridge University / Computer Science. Taught by Dr Wischik. www.cl.cam.ac.uk/teaching/2122/DataSci/materials.html

Hitting probability, multi-step transition probability, and so on: there are many calculations we can do with Markov chains, and they all involve the same two ideas. Second year Data Science and Machine Learning course, Cambridge University / Computer Science. Taught by Dr Wischik. www.cl.cam.ac.uk/teaching/2122/DataSci/materials.html

Markov chains have all sorts of different behaviours, which is why they're so useful for modelling. A Markov chain model for an epidemic, for example, might die out, or it might enter exponential growth, or it might settle down and become endemic. Second year Data Science and Machine Learning course, Cambridge University / Computer Science. Taught by Dr Wischik. www.cl.cam.ac.uk/teaching/2122/D...

A Markov chain is memoryless (what happens next depends only on the current state, not on the past). What if we want to model something with longer-range dependence, such as text? Second year Data Science and Machine Learning course, Cambridge University / Computer Science. Taught by Dr Wischik. www.cl.cam.ac.uk/teaching/2122/DataSci/materials.html

We can fit a Markov model to time series data using maximum likelihood, the same way we'd fit any other probability model. This is given the name "autoregression" or "teacher forcing". Second year Data Science and Machine Learning course, Cambridge University / Computer Science. Taught by Dr Wischik. www.cl.cam.ac.uk/teaching/2122/DataSci/materials.html

Markov chains are models for systems that evolve randomly in time the probabilist's answer to differential equations. Second year Data Science and Machine Learning course, Cambridge University / Computer Science. Taught by Dr Wischik. www.cl.cam.ac.uk/teaching/2122/DataSci/materials.html

Hypothesis testing and confidence intervals, without the hassle of even having to fit a model. Second year Data Science and Machine Learning course, Cambridge University / Computer Science. Taught by Dr Wischik. www.cl.cam.ac.uk/teaching/2122/DataSci/materials.html

How much evidence is enough to persuade you to reject your default beliefs? Fisher's hypothesis testing procedure gives an answer. Second year Data Science and Machine Learning course, Cambridge University / Computer Science. Taught by Dr Wischik. www.cl.cam.ac.uk/teaching/2122/DataSci/materials.html

How to compute a 95% confidence interval for an unknown parameter, by simulating alternative-reality versions of the dataset. Second year Data Science and Machine Learning course, Cambridge University / Computer Science. Taught by Dr Wischik. www.cl.cam.ac.uk/teaching/2122/DataSci/materials.html

The mystical multiverse of frequentist philosophy Second year Data Science and Machine Learning course, Cambridge University / Computer Science. Taught by Dr Wischik. www.cl.cam.ac.uk/teaching/2122/DataSci/materials.html

The medium is the message; the dataset is the distribution. Second year Data Science and Machine Learning course, Cambridge University / Computer Science. Taught by Dr Wischik. www.cl.cam.ac.uk/teaching/2122/DataSci/materials.html

What's the best possible random variable to fit to a dataset? Second year Data Science and Machine Learning course, Cambridge University / Computer Science. Taught by Dr Wischik. www.cl.cam.ac.uk/teaching/2122/DataSci/materials.html

The two big pieces of Bayesian analysis are (1) deciding what to represent as a random variable, (2) finding the posterior. This video goes through the process. Second year Data Science and Machine Learning course, Cambridge University / Computer Science. Taught by Dr Wischik. www.cl.cam.ac.uk/teaching/2122/DataSci/materials.html

7.4 Bayesian readouts

7. Bayesianism

5.2 Computational Bayes

5.1 Monte Carlo integration

4.3 Deriving the likelihood

4.2 Calculations with Bayes's rule

4.1 Bayes's rule for random variables

Exam walkthrough 1: fitting probability models

1.7 Supervised learning

1.6 Generative modelling

1.5 Likelihood notation

1.4 Numerical optimization

1.3 Maximum likelihood estimation

1.2 Standard random variables

1.1 Specifying probability models