Publications by Jihang Li
ANLY 505 Assignment 11
Chapter 14 - Adventures in Covariance This chapter extended the basic multilevel strategy of partial pooling to slopes as well as intercepts. Accomplishing this meant modeling covariation in the statistical population of parameters. The LKJcorr prior was introduced as a convenient family of priors for correlation matrices. You saw how covariance mo...
3549 sym R (9645 sym/39 pcs) 4 img
ANLY 505 Assignment 1 505 Assignment 10
Chapter 13 - Models with Memory This chapter has been an introduction to the motivation, implementation, and interpretation of basic multilevel models. It focused on varying intercepts, which achieve better estimates of baseline differences among clusters in the data. They achieve better estimates, because they simultaneously model the population o...
3972 sym Python (81549 sym/57 pcs) 4 img
ANLY 505 Assignment 9
Chapter 12 - Monsters & Mixtures This chapter introduced several new types of regression, all of which are generalizations of generalized linear models (GLMs). Ordered logistic models are useful for categorical outcomes with a strict ordering. They are built by attaching a cumulative link function to a categorical outcome distribution. Zero-infla...
3608 sym 2 img
ANLY505 Assignment 8
Chapter 11 - God Spiked the Integers This chapter described some of the most common generalized linear models, those used to model counts. It is important to never convert counts to proportions before analysis, because doing so destroys information about sample size. A fundamental difficulty with these models is that parameters are on a different...
2358 sym Python (18832 sym/17 pcs) 2 img
ANLY505 Assignment 7
Chapter 9 - Markov Chain Monte Carlo This week has been an informal introduction to Markov chain Monte Carlo (MCMC) estimation. The goal has been to introduce the purpose and approach MCMC algorithms. The major algorithms introduced were the Metropolis, Gibbs sampling, and Hamiltonian Monte Carlo algorithms. Each has its advantages and disadvanta...
3242 sym R (15913 sym/22 pcs) 4 img
ANLY 505 Assignment 1
Chapter 2 - Small Worlds and Large Worlds The objectives of this problem set is to work with the conceptual mechanics of Bayesian data analysis. The target of inference in Bayesian inference is a posterior probability distribution. Posterior probabilities state the relative numbers of ways each conjectured cause of the data could have produced th...
3766 sym
ANLY 505 Assignment 2
Chapter 3 - Sampling the Imaginary This chapter introduced the basic procedures for manipulating posterior distributions. Our fundamental tool is samples of parameter values drawn from the posterior distribution. These samples can be used to produce intervals, point estimates, posterior predictive checks, as well as other kinds of simulations. Po...
2583 sym R (5540 sym/20 pcs) 6 img
ANLY 505 Assignment 3
Chapter 4 - Geocentric Models This chapter (Chapter 4) introduced the simple linear regression model, a framework for estimating the association between a predictor variable and an outcome variable. The Gaussian distribution comprises the likelihood in such models, because it counts up the relative numbers of ways different combinations of means ...
2603 sym Python (944 sym/5 pcs) 3 img
ANLY505 Assignment 4
Chapter 5 - The Many Variables & the Spurious Waffles This chapter introduced multiple regression, a way of constructing descriptive models for how the mean of a measurement is associated with more than one predictor variable. The defining question of multiple regression is: What is the value of knowing each predictor, once we already know the ot...
3703 sym
ANLY 505 Assignment 5
Chapter 6 - The Haunted DAG & the Causal Terror Multiple regression is no oracle, but only a golem. It is logical, but the relationships it describes are conditional associations, not causal influences. Therefore additional information, from outside the model, is needed to make sense of it. This chapter presented introductory examples of some com...
4109 sym 3 img 7 tbl