3: Estimation of Parameters

• Estimation of Parameters---References
• 3Overview of Estimation of Parameters
• 3.1Maximum Likelihood Principle Illustrated by Measurement Errors---I
• Maximum Likelihood Principle Illustrated by Measurement Errors---II
• Enter Mr. Bayes for Conditional Probablities---I
• Enter Mr. Bayes for Conditional Probablities---II
• Interpretation of Bayes Formulation of Likelihood---I
• Interpretation of Bayes Formulation of Likelihood---II
• The Likelihood Maximizes the Quivering Rod---I
• The Likelihood Maximizes the Quivering Rod---II
• The Likelihood Maximizes the Quivering Rod---III
• General Maximum Likelihood Methods---I
• General Maximum Likelihood Methods---II
• Warning Example of Misuse of Likelihood Method
• Practical Advice on Use of Maximum Likelihood---I
• Practical Advice on Use of Maximum Likelihood---II
• Determination of Lifetime Example of Maximum Likelihood---I
• Determination of Lifetime Example of Maximum Likelihood---II
• Central Limit Estimate of Error
• Maximum Likelihood Estimate of Error in Lifetime---I
• Maximum Likelihood Estimate of Error in Lifetime---II
• Comparison of Two Error Estimates in Maximum Likelihood---I
• Comparison of Two Error Estimates in Maximum Likelihood---II
• Theorem on Asymptotic Validity of Maximum Likelihood Method---Conditions and Statement of Theorem
• Theorem on Asymptotic Validity of Maximum Likelihood Method Conditions---First Assertion
• Theorem on Asymptotic Validity of Maximum Likelihood Method Conditions---Second and Third Assertions
• Proof of Maximum Likelihood Theorem Part (a)---I
• Proof of Maximum Likelihood Theorem Part (a)---II
• Proof of Maximum Likelihood Theorem Part (a)---III
• Proof of Maximum Likelihood Part (b): Formula for Error---I
• Proof of Maximum Likelihood Part (b): Formula for Error---II
• Proof of Maximum Likelihood Part (b): Formula for Error---III
• Multiplication of Experiments
• 3.2Overview of Method
• Derivation of from Maximum Likelihood
• Mean and Standard Deviation of
• Interpretation of Value of
• Correlated Observations in
• Example of Multiple Moments
• Linear fits to Cross Section Data Example of Use of ---Overview
• Formulation of Linear Fit for Cross Section Data---I
• Formulation of Linear Fit for Cross Section Data---II
• Solution and Errors from Linear
• Estimate of Errors to be Used in Fits
• 3.3Counter Physics---Introduction and Poisson Process---I
• Counter Physics---Introduction and Poisson Process---II
• Unnormalized Counter Experiment---I
• Unnormalized Counter Experiment---II
• Unnormalized Counter Experiment---III
• Normalized Counter Experiment
• Gaussian Limit of Counter Physics
• 3.4Bubble Chamber or Spectrometer Physics---I
• Bubble Chamber or Spectrometer Physics---II
• Bubble/Spectrometer---Physics Individual Events with Continuous Distributions---III
• Bubble/Spectrometer---Physics Individual Events with Continuous Distributions---IV
• Bubble/Spectrometer---Physics Individual Events with Continuous Distributions---V
• Individual Events Become Binned Data---I
• Individual Events Become Binned Data---II
• Method of Moments---I
• Method of Moments---II
• Method of Moments---III
• Example of Moment Method
• Comparison of Moment Method with Maximum Likelihood---I
• Comparison of Moment Method with Maximum Likelihood---II
• Several Parameters in Method of Moments---I
• Several Parameters in Method of Moments---II
• Remarks on Counting Errors in Moments---I
• Remarks on Counting Errors in Moments---II
• Remarks on Counting Errors in Moments---III