Glen Cowan, those engaged in research or laboratory courses which involve data analysis. A probability and random variables, Monte Carlo techniques, statistical tests, . Use of the characteristic function to find the p.d.f. of an. G. Cowan, Statistical Data Analysis, Clarendon, Oxford, R.J. Barlow . Sometimes we want to consider some components of joint pdf as constant. Glen Cowan, Royal Holloway, University of London, phone: () 44 , The main lectures on Statistical Data Analysis will be from to the entire assignment should be contained in a single pdf attachment with all of the.
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G. Cowan, Statistical Data Analysis, Clarendon, Oxford, R.J. Barlow . Sometimes we want only pdf of some (or one) of the components. → marginal pdf . G. Cowan, Statistical Data Analysis, Clarendon, Oxford, see also . and Statistical Data Analysis / Stat 1 21 Marginal pdf Sometimes we want only pdf of. G. Cowan, Statistical Data Analysis, Clarendon, Oxford, see also Suppose we have a pdf characterized by one or more parameters.
The technical components to do this are discussed in this section, which follows a top-to-bottom description of the classes illustrated in Figs.
Each fitConfig instance defines a PDF built from a list of channel i. Each channel owns a list of samples and each sample owns a list of systematic uncertainties.
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Correlated samples and systematics are declared by being given identical names. Otherwise they are treated as un-correlated Open image in new window Fig. When executing HistFitter, users interact with the Python interface of the configManager to define, for each data model, a fitConfig object, describing the fit configuration. The fitConfig class configures each processing step of Fig. The configuration manager can hold any number of fitConfig objects.
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By producing a list of data models, HistFitter thus introduces an additional level of abstraction which allows hypothesis tests to be performed over sets of signal models.
The design of this class allows for the creation of highly complex PDFs, describing highly non-trivial analysis setups, with only a few lines of intuitive code. This is configured by users as follows: Open image in new window where myFitConfig is a reference to a new fitConfig object owned by the configManager.
The fitConfig class logically corresponds to a PDF decorated with meta-data about the properties of the contained channels CR, SR, VR , including visualization, fitting and interpretation options. During configuration, instances of channels, samples and systematics are put together by fitConfig objects, together with links to the corresponding input histograms.
The user interface provides the methods addChannel , addSample and addSystematic to build up data models in an intuitive manner. This means that fitConfig. Similarly, sample. Since different channels often share the same samples i.
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This ensures that complex configurations of PDFs can often be described with only a few lines of code. As illustrated in Fig. A basic fit configuration can also be conveniently cloned and extended to specify new configurations, a feature which is frequently used to build data models corresponding to multiple signal hypotheses from a common background description.
Channels can represent either a simple event count i. New binned and un-binned channels can be added to a fitConfig by calling: Open image in new window where myObs is the name of an element of the input dataset, nBins, varLow and varHigh indicate the number of bins and the range of values as for a one-dimensional histogram, and mySelection specifies the selection criteria of the considered region.
For un-binned channels, cuts is a reserved keyword indicating that only the total the number of events passing the selection criteria needs to be considered. This information is configured by users as follows: Open image in new window It is possible to add an arbitrary number of channels to a given fitConfig by simply calling addChannel multiple times.
The data itself is described by a list of Sample objects owned by each channel, as discussed in the next sub-section. In a typical particle physics analysis, each sample corresponds to a specific physics process and several samples are needed to model a complete dataset. In HistFitter, samples can be defined in a specific channel or defined simultaneously in multiple channels.
The Sample class also owns a list of objects representing its systematic uncertainties.
Importantly, samples provide the link between input data and the respective components of the PDF. Three types of inputs are supported: 1.
HistFitter software framework for statistical data analysis
Float inputs tend to be used for quick tests and simple processes. For e. Define expectation mean value as Notation often: For a function y x with pdf g y , equivalent Variance: Standard deviation: Suppose we measure a set of values and we have the covariances Now consider a function What is the variance of The hard way: Often not practical, may not even be fully known.
We have said nothing about the exact pdf of the x i, e. But correlations can change this completely Then i. 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.
Tch-prob1 Chapter 4. S In some random experiments, a number of different quantities.
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Auth with social network: Registration Forgot your password? Download presentation. Cancel Download. A might be a hypothesis and B might. Principles of Parameter Estimation The purpose of this lecture is to illustrate the usefulness of the various concepts introduced and studied in.
Chap 8: Sums of Random Variables Let be a sequence of random variables, and let be their sum:.
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Download presentation. Cancel Download. Presentation is loading. Please wait. Copy to clipboard.Cowan Lectures on Statistical Data Analysis Lecture 2 page 3 Cumulative distribution function Probability to have outcome less than or equal to x is cumulative distribution function Alternatively define pdf with. Share buttons are a little bit lower.
Then, Estimate this using the 2nd derivative of ln L at its maximum: My presentations Profile Feedback Log out. The hour from 5 to 6 will be for discussion and overflow. I agree. Cowan Lectures on Statistical Data Analysis 4 Properties of estimators If we were to repeat the entire measurement, the estimates from each would follow a pdf: All rights reserved.