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.
This unit is devoted to Python and Java experiments looking at histograms of Higgs Boson production with various forms of shape of signal and various background and with various event totals. The lectures use Python but use of Java is described.
Files: :download:`HiggsClassI-Sloping.py </files/python/physics/mr_higgs/higgs_classI_sloping.py>`_
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.
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.
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.
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.
This 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.
Files:
We discuss how this unit uses Java and Python on both a backend server (FutureGrid) or a local client. WE point out useful book on Python for data analysis. This builds on technology training in Section 3.
This video contains Java information, but we are no longer using Java in this class.
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).
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.
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.
We introduce 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.
We go through the many different areas of statistics covered in the Physics unit. We define the statistics concept of a random variable.
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.
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.
We introduce the Gaussian distribution and give Python examples of the fluctuations in counting Gaussian distributions.
We discuss the significance of a standard deviation and role of biases and insufficient statistics with a Python example in getting incorrect answers.
We discuss 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.
Files:
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.
We define binomial distribution and give LHC data as an example of where this distribution valid.
We introduce an advanced method accept/reject for generating random variables with arbitrary distributions.
We define Monte Carlo method which usually uses accept/reject method in typical case for distribution.
We extend the Binomial to the Poisson distribution and give a set of amusing examples from Wikipedia.
We introduce Central Limit Theorem and give examples from Wikipedia.
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.
..bibliography:: physics-references.bib