Statistics for physical scientists short course

In this section we will cover:

� The process of science

� Common uses of statistics

� Summary statistics and their errors

� Estimators and bias

� Optimal combination of data

� Probability distributions: Binomial, Poisson, Gaussian

� The Poisson error

� Special role of the Gaussian distribution, central limit theorem

� Confidence regions and tails

� Comparing the Frequentist and Bayesian frameworks

� Monte Carlo simulations

  VIDEO WOULD GO HERE!   Here is the accompanying python�Jupyter notebook for Class 1�(this is for python3) -- python2 version�here�ADD Jupyter notebooks to be spun up through GitHub

In this section we will cover:

Correlation versus independence

� Pitfalls when searching for correlations

� Correlation coefficient

� Pearson product-moment correlation

� Significance of correlation

� Hypothesis tests and -values

� Student -distribution, tailed tests

� Non-parametric correlation tests; Spearman rank correlation

� Bayesian correlation methods

� Are the means of two samples consistent?

� Kolmogorov-Smirnov test

  Video and Class 2 Notebook here!!

In this section, we will cover:

� Comparing data and models

� The 2�statistic

� 2�probability distribution, degrees of freedom

� Reduced 2

� Use of 2�statistic as hypothesis test

� Modification for correlated data

� Use of 2�statistic for parameter fitting

� Errors in parameters from ?2; joint confidence regions

  PLACEHOLDER FOR VIDEO AND NOTEBOOK

In this section, we will cover:

� Introduction to regression

� Least-squares linear regression

� Quantifying the regression fit

� The case of errors in both co-ordinates

� Principal component analysis, eigenvalues and eigenvectors

� Interpolation

� Gaussian processes (kriging)

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In this section, we will cover:

� What is an error?

� Statistical versus systematic errors

� Error estimation using approximate sampling procedures

� Jack-knife errors

� Bootstrap errors

� Combining and propagating errors, linear and non-linear cases

� Fisher matrix forecasts

� Monte Carlo simulations

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In this section we will cover:

� Bayesian Methods: conditional probability, Bayes� Theorem

� Role of the prior and likelihood

� Posteriors and confidence limits

� Marginalization

� Use of likelihood for parameter fitting

� Monte Carlo Markov Chains

� Model selection; is adding another parameter justified?

� Bayes factor and Jeffreys scale

� Akaike information criteria

VIDEO WOULD GO HERE!