Publications by Ken Wood
Bayesian Models
\(y_i=\mu+\epsilon_i,\space \space \epsilon \stackrel{iid}{\sim}N(0,\sigma^2),\space i=1,..,n\) \(\therefore \space y_i \stackrel{iid}{\sim}N(0,\sigma^2)\) Likelihood: \(P(y|\theta) = \frac{P(y,\theta)}{P(\theta)}\), where \(P(\theta)\) is the prior probability distribution of \(\theta\). Posterior: \(P(\theta|y) = \frac{P(y,\theta)}{P(y)} = \frac{...
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Bayesian Models
\(y_i=\mu+\epsilon_i,\space \space \epsilon \stackrel{iid}{\sim}N(0,\sigma^2),\space i=1,..,n\) \(\therefore \space y_i \stackrel{iid}{\sim}N(0,\sigma^2)\) Likelihood: \(P(y|\theta) = \frac{P(y,\theta)}{P(\theta)}\), where \(P(\theta)\) is the prior probability distribution of \(\theta\). Posterior: \(P(\theta|y) = \frac{P(y,\theta)}{P(y)} = \frac{...
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Bayesian Statistics - Linear Regression
Read in the data golf=read.table('http://www.stat.ufl.edu/~winner/data/pgalpga2008.dat') colnames(golf) <- c('drive_distance', 'accuracy', 'gender') golf_female <- subset(golf,gender==1) golf_male <- subset(golf,gender==2) Plots We fit a linear regression model to the female golfer data. golf_female_lm = lm(accuracy~drive_distance,data=golf_femal...
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Normal Distribution Assessment
A normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. \(X_i \stackrel{iid}{\sim} N(\mu,\sigma_0^2)\) prior: \(\mu \sim N(m_{\space0},s_0^2)\) temps = c(94.6,95.4,96.2,94.9,95.9) mean(temps) ## [1] 95.4 qnorm(.975,95.41,.042) ## [1] 95.49232 pnorm(100,95.41,.042) ## [1] ...
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Exponential Distribution Analysis
The exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. \(Y \sim Exp(\lambda)\) with conjugate \(Gamma\) function. prior: \(\lambda \sim Gamma...
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Poisson Distribution Assessment
The Poisson likelihood is often used to model count data since Poisson random variables are integer-valued, starting at 0. Example scenario where could we appropriately model with a Poisson likelihood? Predicting the number of goals scored in a hockey match. Each of the following gamma distributions is being considered as a prior for a Poisson mean...
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Bernoulli-Binomial Distribution Analysis
Suppose we are giving two students a multiple-choice exam with 40 questions, where each question has four choices. We don’t know how much the students have studied for this exam, but we think that they will do better than just guessing randomly. 1. What are the parameters of interest? Parameters of interest are \(\theta_1\)=true probability the ...
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Bayesian Statistics Lesson 7 Assessment
Flipping a coin with unknown probability of heads (\(\theta\)) Suppose we use a Bernoulli likelihood for each coin flip, i.e., \(f(y_i|\theta) = \theta^{y_i}(1-\theta)^{1-y_i}I_{(0\le\theta\le1)}\) for \(y_i=0\) or \(y_i=1\), and a uniform prior for \(\theta\). What is the posterior distribution for \(\theta\) if we observe the following sequence ...
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Binomial Distribution Analysis
Suppose we are giving two students a multiple-choice exam with 40 questions, where each question has four choices. We don’t know how much the students have studied for this exam, but we think that they will do better than just guessing randomly. 1. What are the parameters of interest? Parameters of interest are \(\theta_1\)=true probability the ...
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Data Science Capstone in R - Week 2 Milestone Report Using Quanteda
Instructions The goal of this project is to display that we’ve become familiar with the data and that we are on track to create our prediction algorithm. This report (to be submitted on R Pubs (http://rpubs.com/)) explains our exploratory analysis and our goals for the eventual app and algorithm. This document should be concise and explain only...
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