4 Single Parameter Inference
4.1 Introduction
In this chapter, we introduce Bayesian thinking for several one-parameter problems. We first consider normally distributed data and discuss learning about the normal mean given a known value of the variance an
Science 19 November 1999: Vol. 286. no. 5444, pp. 1460 - 1464 DOI: 10.1126/science.286.5444.1460
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NEWS FOCUS
STATISTICS:
Bayes Offers a 'New' Way to Make Sense of Numbers
David Malakoff A 236-year-old approach to statistics
1 Probability
1.1 Introduction
Bayesian thinking is based on the subjective viewpoint of probability. In this chapter, we will talk about the different ways of thinking about probability.
1.2 Measuring Uncertainty
We live in a world of uncertain events an
5 Markov Chain Monte Carlo
5.1 Comparing Two Poisson Means
Lets revisit the problem of comparing the means from two independent Poisson samples. Counts cfw_yAi from the weekend days are assumed Poisson with mean A and counts cfw_yBj from the weekday day
5 Many Parameter Inference
5.1 Introduction
In this chapter, we illustrate Bayesian learning from several two parameter problems. Building on the one-parameter posteriors of Chapter 4, we first illustrate learning about both parameters of the normal densi
3 Learning About a Proportion
3.1 Introduction
Suppose data y is observed from a sampling distribution f (y|) that depends on an unknown parameter . We assume that one has beliefs about before sampling that are expressed through a prior density g(|y). Onc
Introduction
A Brief History of Statistics
Statistics, the science of learning from data, is a relatively new discipline. One can divide the history of Statistics into three periods using the years 1900 and 1960. In the early days of Statistics (before 19
6 Hierarchical Modeling
6.1 Introduction: Learning About OGT Success Rates
The Ohio Graduation Test (OGT) is a test administered to all high school students in the state of Ohio. To graduate from high school, a student must develop a prociency in reading,
Introduction
Goods 1967 paper
Example
Good smoothing
Good Smoothing
Jim Albert
Bowling Green State University
December 8, 2009
Introduction
Goods 1967 paper
Example
Good smoothing
Outline
Introduction Goods 1967 paper Example Good smoothing
Introduction
G
2 Bayes Rule
2.1 Introduction
Here is a basic exposition of Bayes rule. Suppose you have events E1 , ., Ek that form a partition of the sample space. One is given 1. P (Ei ), i = 1, ., k 2. P (A|Ei ), i = 1, ., k One is interested in computing the probabi
1 Bayesian Testing and Model Selection
1.1 Review of Frequentist Testing
We begin by reviewing some basic notations of frequentist testing. As a simple example, suppose we observe a random sample y1 , ., yn from a normal population with mean and known var