Publications by Varun Prakash
VarunPrakash_ANLY505-2022-Latefall.html
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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Varun Prakash_ANLY505-2022-Late fall Semester_ Assignment2.html
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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Varun Prakash_ANLY505-2022-Late fall Semester_ Assignment3.html
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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Varun Prakash_ANLY505-2022-Late fall.html
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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Varun Prakash_ANLY505-2022-Late fall Semester_ Assignment5.html
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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Varun Prakash_ANLY505-2022-Late Fall.html
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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