Publications by Hemant Yadav
Small world and Large world Assignment_Hemant
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...
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Anly_505_90_O_Assignent_Hemant
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...
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ANLY_505_90_Assignment_3_Hemant
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 ...
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Anly_505_90_Assignment_4_Hemant
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...
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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...
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ANLY 505 Assignment # 6
Chapter 7 - Ulysses’ Compass This week began with the problem of overfitting, a universal phenomenon by which models with more parameters fit a sample better, even when the additional parameters are meaningless. Two common tools were introduced to address overfitting: regularizing priors and estimates of out-of-sample accuracy (WAIC and PSIS). ...
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ANLY 505 Assignment # 7 - Hemant
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...
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ANLY 505 Assignment # 8 - Hemant
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...
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ANLY 505 Assignment # 9 - Hemant
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...
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ANLY 505 Assignment # 10 - Hemant
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...
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