Metropolis-in-Gibbs Sampling and Runtime Analysis with Profviz

First off, here are the previous posts in my Bayesian sampling series: Bayesian Simple Linear Regression with Gibbs Sampling in R Blocked Gibbs Sampling in R for Bayesian Multiple Linear Regression In the first post, I illustrated Gibbs Sampling - an algorithm for getting draws from a posterior when conditional posteriors are known. In the … Continue reading Metropolis-in-Gibbs Sampling and Runtime Analysis with Profviz

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Blocked Gibbs Sampling in R for Bayesian Multiple Linear Regression

In a previous post, I derived and coded a Gibbs sampler in R for estimating a simple linear regression. In this post, I will do the same for multivariate linear regression. I will derive the conditional posterior distributions necessary for the blocked Gibbs sampler. I will then code the sampler and test it using simulated … Continue reading Blocked Gibbs Sampling in R for Bayesian Multiple Linear Regression

NYC Motor Vehicle Collisions – Street-Level Heat Map

In this post I will extend a previous analysis creating a borough-level heat map of NYC motor vehicle collisions. The data is from NYC Open Data. In particular, I will go from borough-level to street-level collisions. The processing of the code is very similar to the previous analysis, with a few more functions that map streets to colors. … Continue reading NYC Motor Vehicle Collisions – Street-Level Heat Map

Visualizing Hubway Trips in Boston

Most Popular Hubway Stations (in order): Post Office Sq. - located in the heart of the financial district. Charles St. & Cambridge - the first Hubway stop after crossing from Cambridge over Longfellow Bridge. Tremont St & West - East side of the Boston Common South Station Cross St. & Hannover - entrance to North End combing from financial … Continue reading Visualizing Hubway Trips in Boston

Finding and Plotting Lorenz Solution using MATLAB

I use MATLAB to solve the following Lorenz initial value problem: $latex \begin{cases} x'=-10(x+y) \\ y'=-x(z+28)-y \\ z'=xy-\frac{8}{3}z \\ x(0)=y(0)=z(0)=5 \end{cases} $ I wrote a function, LorenzRK4IVP(), that takes the system of three differential equations as input and solves the system using the Runge-Kutta method with step size $latex h=.01$. I plot the strange attractor as … Continue reading Finding and Plotting Lorenz Solution using MATLAB