When is a fit good??? Ulrich Becker 3/4/2009 Repeat from last Mini lecture Fit exercises 1,2,3 2009 and 2008 Likelihood and goodness of fit.

Slides:



Advertisements
Similar presentations
The Maximum Likelihood Method
Advertisements

Lecture 11 (Chapter 9).
Point Estimation Notes of STAT 6205 by Dr. Fan.
NASSP Masters 5003F - Computational Astronomy Lecture 5: source detection. Test the null hypothesis (NH). –The NH says: let’s suppose there is no.
1 Methods of Experimental Particle Physics Alexei Safonov Lecture #21.
8. Statistical tests 8.1 Hypotheses K. Desch – Statistical methods of data analysis SS10 Frequent problem: Decision making based on statistical information.
Lecture #18 EEE 574 Dr. Dan Tylavsky Nonlinear Problem Solvers.
G. Cowan Lectures on Statistical Data Analysis 1 Statistical Data Analysis: Lecture 10 1Probability, Bayes’ theorem, random variables, pdfs 2Functions.
1 6 th September 2007 C.P. Ward Sensitivity of ZZ→llνν to Anomalous Couplings Pat Ward University of Cambridge Neutral Triple Gauge Couplings Fit Procedure.
Chapter 7 Hypothesis Tests and Confidence Intervals in Multiple Regression.
PRIMER ON ERRORS 8.13 U.Becker 9,2007  Random & Systematic Errors  Distribution of random errors  Binomial, Poisson, Gaussian  Poisson Gaussian.
Exercise Exercise3.1 8 Exercise3.1 9 Exercise
Exercise Exercise Exercise Exercise
Exercise Exercise Exercise Exercise
Exercise Exercise6.1 7 Exercise6.1 8 Exercise6.1 9.
Counting And all That WALTA Meeting Toby Burnett, UW.
Statistical analysis and modeling of neural data Lecture 4 Bijan Pesaran 17 Sept, 2007.
Chi Square Distribution (c2) and Least Squares Fitting
Lecture IV Statistical Models in Optical Communications DIRECT DETECTION G aussian approximation for single-shot link performance Receiver thermal noise.
Eta for Au-Au 9 GeV Events (All). Eta for Au-Au 9 GeV Events.
G. Cowan Lectures on Statistical Data Analysis Lecture 10 page 1 Statistical Data Analysis: Lecture 10 1Probability, Bayes’ theorem 2Random variables and.
CONNECTIVITY MATRIX (6 REALIZATIONS) Passive larvae Active larvae Retention increases, heterogeneity decreases.
G. Cowan RHUL Physics Bayesian Higgs combination page 1 Bayesian Higgs combination using shapes ATLAS Statistics Meeting CERN, 19 December, 2007 Glen Cowan.
R. Kass/S07 P416 Lec 3 1 Lecture 3 The Gaussian Probability Distribution Function Plot of Gaussian pdf x p(x)p(x) Introduction l The Gaussian probability.
LINEAR REGRESSION Introduction Section 0 Lecture 1 Slide 1 Lecture 5 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Intermediate 3870 Fall.
G. Cowan Lectures on Statistical Data Analysis Lecture 3 page 1 Lecture 3 1 Probability (90 min.) Definition, Bayes’ theorem, probability densities and.
R. Kass/W03P416/Lecture 7 1 Lecture 7 Some Advanced Topics using Propagation of Errors and Least Squares Fitting Error on the mean (review from Lecture.
Introduction Miha Zgubič, summer student Scintillating fibre tracker software Analysis of performance of momentum reconstruction 1.
1 Methods of Experimental Particle Physics Alexei Safonov Lecture #23.
HYPOTHESIS TESTING Distributions(continued); Maximum Likelihood; Parametric hypothesis tests (chi-squared goodness of fit, t-test, F-test) LECTURE 2 Supplementary.
Radiation Detection and Measurement, JU, First Semester, (Saed Dababneh). 1 Counting Statistics and Error Prediction Poisson Distribution ( p.
ROOT and statistics tutorial Exercise: Discover the Higgs, part 2 Attilio Andreazza Università di Milano and INFN Caterina Doglioni Université de Genève.
The chi-squared statistic  2 N Measures “goodness of fit” Used for model fitting and hypothesis testing e.g. fitting a function C(p 1,p 2,...p M ; x)
NON-LINEAR REGRESSION Introduction Section 0 Lecture 1 Slide 1 Lecture 6 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Intermediate 3870 Fall.
1 Introduction to Statistics − Day 4 Glen Cowan Lecture 1 Probability Random variables, probability densities, etc. Lecture 2 Brief catalogue of probability.
How Good is a Model? How much information does AIC give us? –Model 1: 3124 –Model 2: 2932 –Model 3: 2968 –Model 4: 3204 –Model 5: 5436.
17/09/19991 Status of the  Dalitz analysis Paolo Dini Luigi Moroni Dario Menasce Sandra Malvezzi Paolo Dini Luigi Moroni Dario Menasce Sandra Malvezzi.
Remembering way back: Generalized Linear Models Ordinary linear regression What if we want to model a response that is not Gaussian?? We may have experiments.
AP Statistics Section 11.4 B. A significance test makes a Type I error when ___________________________________ P(Type 1 error ) = ___ A significance.
2005 Unbinned Point Source Analysis Update Jim Braun IceCube Fall 2006 Collaboration Meeting.
G. Cowan Lectures on Statistical Data Analysis Lecture 10 page 1 Statistical Data Analysis: Lecture 10 1Probability, Bayes’ theorem 2Random variables and.
R. Kass/W03 P416 Lecture 5 l Suppose we are trying to measure the true value of some quantity (x T ). u We make repeated measurements of this quantity.
The Language of Statistical Decision Making Lecture 2 Section 1.3 Mon, Sep 5, 2005.
Richard Kass/F02P416 Lecture 6 1 Lecture 6 Chi Square Distribution (  2 ) and Least Squares Fitting Chi Square Distribution (  2 ) (See Taylor Ch 8,
Introduction to Exponents Brought to you by powerpointpros.com.
S. Ferrag, G. Steele University of Glasgow. RooStats and MClimit comparison Exercise to use RooStats by an MClimit-formatted person: – Use two programs.
Lecture 8. Comparison of modulaters sizeCapacitanceInsertion loss Chirping Electro- absorption smalllowerhighersome Electro-optic type (LiNbO3) largehigherlowernone.
NASSP Masters 5003F - Computational Astronomy Lecture 4: mostly about model fitting. The model is our estimate of the parent function. Let’s express.
The Maximum Likelihood Method
Parameter Estimation and Fitting to Data
The Maximum Likelihood Method
EBL Absorption Signatures in DC2 Data
Generalized Linear Models (GLM) in R
The Maximum Likelihood Method
School on Data Science in (Astro)particle Physics
Counting Statistics and Error Prediction
تحليل الحساسية Sensitive Analysis.
Chi Square Distribution (c2) and Least Squares Fitting
Sampling Distribution
Sampling Distribution
Computing and Statistical Data Analysis / Stat 8
10:00.
Lecture 3 1 Probability Definition, Bayes’ theorem, probability densities and their properties, catalogue of pdfs, Monte Carlo 2 Statistical tests general.
The Language of Statistical Decision Making
Psych 231: Research Methods in Psychology
Computing and Statistical Data Analysis / Stat 7
Psych 231: Research Methods in Psychology
Types of Errors And Error Analysis.
Anneline S.J.M. te Riele et al. JACEP 2015;1:
EBL Absorption Signatures in DC2 Data
Presentation transcript:

When is a fit good??? Ulrich Becker 3/4/2009 Repeat from last Mini lecture Fit exercises 1,2,3 2009 and 2008 Likelihood and goodness of fit

8

More in Bevington, ch 11 and Taylor. Let’s go to :

Your data analysis

Problem 1 good: error bars comparison not so: Size of letters/#’s Result: Can’t tell ! But for higher statistics Poisson-> Gauss

Problem 2.1 not good worse

learned: very sensitive to background 2.1 was a Lorentzian with little background. 2008 results: learned: very sensitive to background

Problem 2.2 Result: Gaussian

2.2 was a Gaussian with background. 2008 results: Note: for set a) hypotheses are indistinguishable!

Problem 3 I0 = 98±3 102 ±3 = 0.78 ±.03 0.80 ±.03 = -1.72 ±..015 +1.73 ±.016 Bkgrd = 18.0 ±.2 2/394 = 1.05  = 3.46 ±.02

PDG: for future use….