Physics
8 minute read
Physics with Big Data Applications {#sec:534-week5}
E534 2019 Big Data Applications and Analytics Discovery of Higgs Boson Part I (Unit 8) Section Units 9-11 Summary: This section starts by describing the LHC accelerator at CERN and evidence found by the experiments suggesting existence of a Higgs Boson. The huge number of authors on a paper, remarks on histograms and Feynman diagrams is followed by an accelerator picture gallery. The next unit is devoted to Python experiments looking at histograms of Higgs Boson production with various forms of shape of signal and various background and with various event totals. Then random variables and some simple principles of statistics are introduced with explanation as to why they are relevant to Physics counting experiments. The unit introduces Gaussian (normal) distributions and explains why they seen so often in natural phenomena. Several Python illustrations are given. Random Numbers with their Generators and Seeds lead to a discussion of Binomial and Poisson Distribution. Monte-Carlo and accept-reject methods. The Central Limit Theorem concludes discussion.
Unit 8:
8.1 - Looking for Higgs: 1. Particle and Counting Introduction 1
We return to particle case with slides used in introduction and stress that particles often manifested as bumps in histograms and those bumps need to be large enough to stand out from background in a statistically significant fashion.
8.2 - Looking for Higgs: 2. Particle and Counting Introduction 2
We give a few details on one LHC experiment ATLAS. Experimental physics papers have a staggering number of authors and quite big budgets. Feynman diagrams describe processes in a fundamental fashion.
8.3 - Looking for Higgs: 3. Particle Experiments
We give a few details on one LHC experiment ATLAS. Experimental physics papers have a staggering number of authors and quite big budgets. Feynman diagrams describe processes in a fundamental fashion
8.4 - Looking for Higgs: 4. Accelerator Picture Gallery of Big Science
This lesson gives a small picture gallery of accelerators. Accelerators, detection chambers and magnets in tunnels and a large underground laboratory used fpr experiments where you need to be shielded from background like cosmic rays.
Unit 9
This unit is devoted to Python experiments with Geoffrey looking at histograms of Higgs Boson production with various forms of shape of signal and various background and with various event totals
9.1 - Looking for Higgs II: 1: Class Software
We discuss how this unit uses Java (deprecated) and Python on both a backend server (FutureGrid - closed!) or a local client. We point out useful book on Python for data analysis. This lesson is deprecated. Follow current technology for class
9.2 - Looking for Higgs II: 2: Event Counting
We define ‘‘event counting’’ data collection environments. We discuss the python and Java code to generate events according to a particular scenario (the important idea of Monte Carlo data). Here a sloping background plus either a Higgs particle generated similarly to LHC observation or one observed with better resolution (smaller measurement error).
9.3 - Looking for Higgs II: 3: With Python examples of Signal plus Background
This uses Monte Carlo data both to generate data like the experimental observations and explore effect of changing amount of data and changing measurement resolution for Higgs.
9.4 - Looking for Higgs II: 4: Change shape of background & number of Higgs Particles
This lesson continues the examination of Monte Carlo data looking at effect of change in number of Higgs particles produced and in change in shape of background
Unit 10
In this unit we discuss;
E534 2019 Big Data Applications and Analytics Discovery of Higgs Boson: Big Data Higgs Unit 10: Looking for Higgs Particles Part III: Random Variables, Physics and Normal Distributions Section Units 9-11 Summary: This section starts by describing the LHC accelerator at CERN and evidence found by the experiments suggesting existence of a Higgs Boson. The huge number of authors on a paper, remarks on histograms and Feynman diagrams is followed by an accelerator picture gallery. The next unit is devoted to Python experiments looking at histograms of Higgs Boson production with various forms of shape of signal and various background and with various event totals. Then random variables and some simple principles of statistics are introduced with explanation as to why they are relevant to Physics counting experiments. The unit introduces Gaussian (normal) distributions and explains why they seen so often in natural phenomena. Several Python illustrations are given. Random Numbers with their Generators and Seeds lead to a discussion of Binomial and Poisson Distribution. Monte-Carlo and accept-reject methods. The Central Limit Theorem concludes discussion. Big Data Higgs Unit 10: Looking for Higgs Particles Part III: Random Variables, Physics and Normal Distributions Overview: Geoffrey introduces random variables and some simple principles of statistics and explains why they are relevant to Physics counting experiments. The unit introduces Gaussian (normal) distributions and explains why they seen so often in natural phenomena. Several Python illustrations are given. Java is currently not available in this unit.
10.1 - Statistics Overview and Fundamental Idea: Random Variables
We go through the many different areas of statistics covered in the Physics unit. We define the statistics concept of a random variable.
10.2 - Physics and Random Variables I
We describe the DIKW pipeline for the analysis of this type of physics experiment and go through details of analysis pipeline for the LHC ATLAS experiment. We give examples of event displays showing the final state particles seen in a few events. We illustrate how physicists decide whats going on with a plot of expected Higgs production experimental cross sections (probabilities) for signal and background.
10.3 - Physics and Random Variables II
We describe the DIKW pipeline for the analysis of this type of physics experiment and go through details of analysis pipeline for the LHC ATLAS experiment. We give examples of event displays showing the final state particles seen in a few events. We illustrate how physicists decide whats going on with a plot of expected Higgs production experimental cross sections (probabilities) for signal and background.
10.4 - Statistics of Events with Normal Distributions
We introduce Poisson and Binomial distributions and define independent identically distributed (IID) random variables. We give the law of large numbers defining the errors in counting and leading to Gaussian distributions for many things. We demonstrate this in Python experiments.
10.5 - Gaussian Distributions
We introduce the Gaussian distribution and give Python examples of the fluctuations in counting Gaussian distributions.
10.6 - Using Statistics
We discuss the significance of a standard deviation and role of biases and insufficient statistics with a Python example in getting incorrect answers.
Unit 11
In this section we discuss;
E534 2019 Big Data Applications and Analytics Discovery of Higgs Boson: Big Data Higgs Unit 11: Looking for Higgs Particles Part IV: Random Numbers, Distributions and Central Limit Theorem Section Units 9-11 Summary: This section starts by describing the LHC accelerator at CERN and evidence found by the experiments suggesting existence of a Higgs Boson. The huge number of authors on a paper, remarks on histograms and Feynman diagrams is followed by an accelerator picture gallery. The next unit is devoted to Python experiments looking at histograms of Higgs Boson production with various forms of shape of signal and various background and with various event totals. Then random variables and some simple principles of statistics are introduced with explanation as to why they are relevant to Physics counting experiments. The unit introduces Gaussian (normal) distributions and explains why they seen so often in natural phenomena. Several Python illustrations are given. Random Numbers with their Generators and Seeds lead to a discussion of Binomial and Poisson Distribution. Monte-Carlo and accept-reject methods. The Central Limit Theorem concludes discussion. Big Data Higgs Unit 11: Looking for Higgs Particles Part IV: Random Numbers, Distributions and Central Limit Theorem Unit Overview: Geoffrey discusses Random Numbers with their Generators and Seeds. It introduces Binomial and Poisson Distribution. Monte-Carlo and accept-reject methods are discussed. The Central Limit Theorem and Bayes law concludes discussion. Python and Java (for student - not reviewed in class) examples and Physics applications are given.
11.1 - Generators and Seeds I
We define random numbers and describe how to generate them on the computer giving Python examples. We define the seed used to define to specify how to start generation.
11.2 - Generators and Seeds II
We define random numbers and describe how to generate them on the computer giving Python examples. We define the seed used to define to specify how to start generation.
11.3 - Binomial Distribution
We define binomial distribution and give LHC data as an eaxmple of where this distribution valid.
11.4 - Accept-Reject
We introduce an advanced method – accept/reject – for generating random variables with arbitrary distrubitions.
11.5 - Monte Carlo Method
We define Monte Carlo method which usually uses accept/reject method in typical case for distribution.
11.6 - Poisson Distribution
We extend the Binomial to the Poisson distribution and give a set of amusing examples from Wikipedia.
11.7 - Central Limit Theorem
We introduce Central Limit Theorem and give examples from Wikipedia.
11.8 - Interpretation of Probability: Bayes v. Frequency
This lesson describes difference between Bayes and frequency views of probability. Bayes’s law of conditional probability is derived and applied to Higgs example to enable information about Higgs from multiple channels and multiple experiments to be accumulated.