Efficient MCMC with Caching

This post is part of a running series on Bayesian MCMC tutorials. For updates, follow @StableMarkets. Metropolis Review Metropolis-Hastings is an MCMC algorithm for drawing samples from a distribution known up to a constant of proportionality, $latex p(\theta | y) \propto p(y|\theta)p(\theta)$. Very briefly, the algorithm works by starting with some initial draw $latex \theta^{(0)}$ then running … Continue reading Efficient MCMC with Caching

Speeding up Metropolis-Hastings with Rcpp

Previous posts in this series on MCMC samplers for Bayesian inference (in order of publication): Bayesian Simple Linear Regression with Gibbs Sampling in R Blocked Gibbs Sampling in R for Bayesian Multiple Linear Regression Metropolis-in-Gibbs Sampling and Runtime Analysis with Profviz The code for all of these posts can be found in my BayesianTutorials GitHub … Continue reading Speeding up Metropolis-Hastings with Rcpp

Exploring P-values with Simulations in R

The recent flare-up in discussions on p-values inspired me to conduct a brief simulation study. In particularly, I wanted to illustrate just how p-values vary with different effect and sample sizes. Here are the details of the simulation. I simulated $latex n $ draws of my independent variable $latex X $: $latex X_n \sim N(100, 400)$ where $latex … Continue reading Exploring P-values with Simulations in R

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

Iterative OLS Regression Using Gauss-Seidel

I just finished covering a few numerical techniques for solving systems of equations, which can be applied to find best-fit lines through a give set of data points. The four points $latex \{(0,0), (1,3), (2,3), (5,6)\}$ are arranged into an inconsistent system of four equations and two unknowns: $latex b+a(0) = 0 \\ b+a(1) = 3 \\ b+a(2) … Continue reading Iterative OLS Regression Using Gauss-Seidel