MAS2317 Presentation Jake McGlen. Assuming vague prior knowledge, obtain the posterior distribution for µ and hence construct a 95% Bayesian conﬁdence.

Slides:

Advertisements

Similar presentations

“Students” t-test.

Advertisements

Chapter 16 Inferential Statistics

Bayesian inference of normal distribution

Week 11 Review: Statistical Model A statistical model for some data is a set of distributions, one of which corresponds to the true unknown distribution.

Inference and Confidence Intervals. Outline Inferring a population mean: Constructing confidence intervals Examining the difference between two means.

Psychology 290 Special Topics Study Course: Advanced Meta-analysis April 7, 2014.

Uncertainty and confidence intervals Statistical estimation methods, Finse Friday , 12.45–14.05 Andreas Lindén.

Sampling: Final and Initial Sample Size Determination

Confidence Intervals This chapter presents the beginning of inferential statistics. We introduce methods for estimating values of these important population.

ELEC 303 – Random Signals Lecture 18 – Statistics, Confidence Intervals Dr. Farinaz Koushanfar ECE Dept., Rice University Nov 10, 2009.

Confidence Intervals Underlying model: Unknown parameter We know how to calculate point estimates E.g. regression analysis But different data would change.

BCOR 1020 Business Statistics Lecture 17 – March 18, 2008.

Continuous Random Variables and Probability Distributions

ESTIMATION AND CONFIDENCE INTERVALS Up to now we assumed that we knew the parameters of the population. Example. Binomial experiment knew probability of.

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Confidence intervals.

1 Equivalence and Bioequivalence: Frequentist and Bayesian views on sample size Mike Campbell ScHARR CHEBS FOCUS fortnight 1/04/03.

Statistical inference form observational data Parameter estimation: Method of moments Use the data you have to calculate first and second moment To fit.

Statistical Background

8-1 Introduction In the previous chapter we illustrated how a parameter can be estimated from sample data. However, it is important to understand how.

1 Confidence Intervals for Means. 2 When the sample size n< 30 case1-1. the underlying distribution is normal with known variance case1-2. the underlying.

Standard error of estimate & Confidence interval.

Standard Error of the Mean

10-Opening Picture of Probability and statistics 9.

1 Bayesian methods for parameter estimation and data assimilation with crop models Part 2: Likelihood function and prior distribution David Makowski and.

Additional Slides on Bayesian Statistics for STA 101 Prof. Jerry Reiter Fall 2008.

The paired sample experiment The paired t test. Frequently one is interested in comparing the effects of two treatments (drugs, etc…) on a response variable.

McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. A PowerPoint Presentation Package to Accompany Applied Statistics.

Bayesian Inference, Basics Professor Wei Zhu 1. Bayes Theorem Bayesian statistics named after Thomas Bayes ( ) -- an English statistician, philosopher.

Prof. Dr. S. K. Bhattacharjee Department of Statistics University of Rajshahi.

Normal Distributions Z Transformations Central Limit Theorem Standard Normal Distribution Z Distribution Table Confidence Intervals Levels of Significance.

Normal distribution and intro to continuous probability density functions...

ME 322: Instrumentation Lecture 3 January 27, 2012 Professor Miles Greiner.

1 A Bayesian statistical method for particle identification in shower counters IX International Workshop on Advanced Computing and Analysis Techniques.

1 Estimation of Standard Deviation & Percentiles Dr. Jerrell T. Stracener, SAE Fellow Leadership in Engineering EMIS 7370/5370 STAT 5340 : PROBABILITY.

OPENING QUESTIONS 1.What key concepts and symbols are pertinent to sampling? 2.How are the sampling distribution, statistical inference, and standard.

Lecture 7 Dustin Lueker. 2  Point Estimate ◦ A single number that is the best guess for the parameter  Sample mean is usually at good guess for the.

- 1 - Bayesian inference of binomial problem Estimating a probability from binomial data –Objective is to estimate unknown proportion (or probability of.

Normal Distribution.

Week 41 Estimation – Posterior mean An alternative estimate to the posterior mode is the posterior mean. It is given by E(θ | s), whenever it exists. This.

Example: Bioassay experiment Problem statement –Observations: At each level of dose, 5 animals are tested, and number of death are observed.

12.2 (13.2) Comparing Two Proportions. The Sampling Distribution of.

Chapter 2 Statistical Background. 2.3 Random Variables and Probability Distributions A variable X is said to be a random variable (rv) if for every real.

Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 1 Estimates and Sample Sizes Chapter 6 M A R I O F. T R I O L A Copyright © 1998,

Confidence Interval & Unbiased Estimator Review and Foreword.

Inen 460 Lecture 2. Estimation (ch. 6,7) and Hypothesis Testing (ch.8) Two Important Aspects of Statistical Inference Point Estimation – Estimate an unknown.

Bayes Theorem. Prior Probabilities On way to party, you ask “Has Karl already had too many beers?” Your prior probabilities are 20% yes, 80% no.

One Sample Mean Inference (Chapter 5)

ES 07 These slides can be found at optimized for Windows)

Class 5 Estimating  Confidence Intervals. Estimation of  Imagine that we do not know what  is, so we would like to estimate it. In order to get a point.

§2.The hypothesis testing of one normal population.

Parameter Estimation. Statistics Probability specified inferred Steam engine pump “prediction” “estimation”

Sample Size Needed to Achieve High Confidence (Means)

Ivo van Vulpen Why does RooFit put asymmetric errors on data points ? 10 slides on a ‘too easy’ topic that I hope confuse, but do not irritate you

Bayesian Estimation and Confidence Intervals Lecture XXII.

Lecture Slides Elementary Statistics Twelfth Edition

Inference: Conclusion with Confidence

Bayesian Estimation and Confidence Intervals

Inference: Conclusion with Confidence

Statistics in Applied Science and Technology

Estimation Interval Estimates (s unknown) Industrial Engineering

Bayesian Inference, Basics

Tutorial 9 Suppose that a random sample of size 10 is drawn from a normal distribution with mean 10 and variance 4. Find the following probabilities:

Summary of Tests Confidence Limits

More Parameter Learning, Multinomial and Continuous Variables

6-3 and 6-4 Quiz Review Pages , #24, 30, 32, 38, 39, 42, 45–46

CS639: Data Management for Data Science

Homework We wish to classify two species of fish (salmon and bass) based on their luminosity as measured by a camera. We have the following likelihoods:

Estimating a Population Variance

How Confident Are You?.

Classical regression review

Presentation transcript:

MAS2317 Presentation Jake McGlen

Assuming vague prior knowledge, obtain the posterior distribution for µ and hence construct a 95% Bayesian conﬁdence interval for µ and comment on your results.

If we now proceed to use vague prior knowledge about µ, we let the prior variance tend to ∞ (d → 0).

The mean does not change for a normal distribution. The posterior distributions shape is much more compact than the original prior distribution as the variance is ten times smaller This makes the distribution more precise.

We now need to find the 95% Bayesian conﬁdence interval for µ and comment on the results. This confidence interval shows the probability of capturing the true value of µ to be A range of is a precise region for µ. This is a smaller range than would have been given if we used the frequentist prior distribution.