@statistical-rethinking
10/02/23 14:56:25
Lecture 3
workflow, from a scientific question, to the development of a causal model and from there to a Bayesian estimator
Trying to make that distinction between a statistical model, like linear regression and a causal model. So we project some causal model on to the ‘geocentric’ model that is linear regression (really accurate but it’s causality doesn’t exist).
- There are many more ways for a sequence of coin tosses to put you on the half way line than away from it
- The coin toss reduces likelihood that you’ll get a sequence of right or left movements.
Gaussian is a model with very little assumptions (mean and variance).
(1) State a clear question Describe the association between adult height and weight (2) Sketch your causal assumptions. Causal model: weight is some function of height. (3) Use the sketch to define a generative model Assume that they effect each other with no mechanism. (4) Use the generative model to build an estimator Want to estimate how the average weight changes with height.
Conceptually useful to defined unobserved things that might affect height (eg causality).
Generative model starts out as
Estimator:
hmm, the lectures are different than the book here. The benefit here I suppose is that we’re learning about scientific modelling in general as well.
So, in chapter 3, we’re trying to fit the data to a Gaussian distribution. To define a Gaussian distribution you need a mean and variance. These are the parameters for our model and based on the data we’ll try to infer them.
The priors is some sensible guess at a normal distribution for heights.
10/02/23 17:52:17 IM CONFUSEDDDDD!
Ok, so one of the pain points is that there seems to be distributions within distributions, it’s hard to keep track. What I really need is some conceptual model of a distribution (and how that links, say, to a density plot).
Lecture 2
The goal is to make a generative model of globe tossing (???) I interpret this as meaning, we’re creating a small world of the big world, we’re going to toss our statistical model and try and match it to the real world toss.
We have a couple variables for this p,W,N,L. We want to think causally (scientifically) about the connections between the variables.
Spends time on drawing out these causal influences (using arrows) that W and L dpeend on N etc. W, L = f(p, N). DAG shows functional relationships but does not say what the functions are.
Apparently we will see what this function ‘has to be’
For each possible proportion of water on the globe. Count all the ways the observed tosses could happen. Proportions with more ways to produce the sample are more plausible.
The garden of forking paths iterate based on tosses. So you’ve a stated globe and then you just march through it’s permutations (sample space). You selectively go through and see where the data could pop up.
Exponential way of writing number of ways to see the given data.