index.ipynb

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    "# A Graduate Introduction to Probability and Statistics for Scientists and Engineers\n",
    "\n",
    "## [Philip B. Stark](http://www.stat.berkeley.edu/~stark), Department of Statistics, University of California, Berkeley\n",
    "\n",
    "## First offering: a 10-hour short course at University of Tokyo, August 2015\n",
    "\n",
    "## Software requirements\n",
    "+ Jupyter: http://continuum.io/downloads and Python 2 kernel for Jupyter; see https://ipython.org/install.html\n",
    "\n",
    "## Supplemental Texts\n",
    "+ Stark, P.B., 1997&ndash;2015. [_SticiGui: Statistical Tools for Internet and Classroom Instruction with a Graphical User Interface_](http://www.stat.berkeley.edu/~stark/SticiGui/index.htm).\n",
    "+ Stark, P.B., 1990&ndash;2010. Lecture notes for Nonparametrics, [Statistics 240](https://www.stat.berkeley.edu/~stark/Teach/S240/Notes/index.htm)\n"
   ]
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    "# Index\n",
    "**These notes are in draft form, with large gaps.**\n",
    "I'm happy to hear about any errors, and I hope eventually to fill in some of the missing pieces.\n",
    "\n",
    "1. [Overview](overview.ipynb)\n",
    "1. [Introduction to Jupyter and Python](jupyter.ipynb)\n",
    "1. [Sets, Combinatorics, & Probability](prob.ipynb)\n",
    "1. [Theories of Probability](probTheory.ipynb)\n",
    "1. [Random Variables, Expectation, Random Vectors, and Stochastic Processes](rv.ipynb)\n",
    "1. [Probability Inequalities](ineq.ipynb)\n",
    "1. [Inference](inference.ipynb)\n",
    "1. [Confidence Sets](conf.ipynb)"
   ]
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    "# Rough Syllabus for Tokyo Short Course\n",
    "\n",
    "## [Preamble: Introduction to Jupyter and Python](jupyter.ipynb)\n",
    "1. Jupyter notebook\n",
    "    + Cells, markdown, MathJax\n",
    "1. Less Python than you need\n",
    "\n",
    "## [Lecture 1: Probability](prob.ipynb)\n",
    "1. What's the difference between Probability and Statistics?\n",
    "1. Counting and combinatorics\n",
    "    + Sets: unions, intersections, partitions\n",
    "    + De Morgan's Laws\n",
    "    + The Inclusion-Exclusion principle\n",
    "    + The Fundamental Rule of Counting\n",
    "    + Combinations\n",
    "    + Permutations\n",
    "    + Strategies for counting\n",
    "\n",
    "2. Axiomatic Probability\n",
    "    + Outcome space and events, events as sets\n",
    "    + Kolmogorov's axioms (finite and countable)\n",
    "    + Analogies between probability and area or mass\n",
    "    + Consequences of the axioms\n",
    "        - Probabilities of unions and intersections\n",
    "        - Bounds on probabilities\n",
    "        - Bonferroni's inequality\n",
    "        - The inclusion-exclusion rule for probabilities\n",
    "    + Conditional probability\n",
    "        - The Multiplication Rule\n",
    "        - Independence\n",
    "        - Bayes Rule\n",
    "## Lecture 2: Probability, continued\n",
    "3. Theories of probability\n",
    "    + Equally likely outcomes\n",
    "    + Frequency Theory\n",
    "    + Subjective Theory\n",
    "    + Shortcomings of the theories\n",
    "    + Rates versus probabilities\n",
    "    + Measurement error\n",
    "    + Where does probability come from in physical problems?\n",
    "    + Making sense of geophysical probabilities\n",
    "        - Earthquake probabilities\n",
    "        - Probability of magnetic reversals\n",
    "        - Probability that Earth is more than 5B years old\n",
    "4. Random variables.\n",
    "    + Probability distributions of real-valued random variables\n",
    "    + Cumulative distribution functions\n",
    "    + Discrete random variables\n",
    "        - Probability mass functions\n",
    "        - The uniform distribution on a finite set\n",
    "        - Bernoulli random variables\n",
    "        - Random variables derived from the Bernoulli\n",
    "            * Binomial random variables\n",
    "            * Geometric\n",
    "            * Negative binomial\n",
    "        - Hypergeometric random variables\n",
    "        - Poisson random variables: countably infinite outcome spaces\n",
    "\n",
    "## Lecture 3: Random variables, contd.\n",
    "5. Random variables, continued\n",
    "    + Continuous and \"mixed\" random variables\n",
    "    + Probability densities\n",
    "        - The uniform distribution on an interval\n",
    "        - The Gaussian distribution\n",
    "    + The CDF of discrete, continuous, and mixed distributions\n",
    "    + Distribution of measurement errors\n",
    "        - The box model for random error\n",
    "        - Systematic and stochastic error\n",
    "6. Independence of random variables\n",
    "    + Events derived from random variables\n",
    "    + Definitions of independence\n",
    "    + Independence and \"informativeness\"\n",
    "    + Examples of independent and dependent random variables\n",
    "    + IID random variables\n",
    "    + Exchangeability of random variables\n",
    "7. Marginal distributions\n",
    "8. Point processes\n",
    "    + Poisson processes\n",
    "        - Homogeneous and inhomogeneous Poisson processes\n",
    "        - Spatially heterogeneous, temporally homogenous Poisson processes as a model for seismicity\n",
    "        - The conditional distribution of Poisson processes given N\n",
    "    + Marked point processes\n",
    "    + Inter-arrival times and inter-arrival distributions\n",
    "    + Branching processes\n",
    "        - ETAS\n",
    "\n",
    "## Lecture 4: Expectation, Probability Inequalities, and Simulation\n",
    "9. Expectation\n",
    "    + The Law of Large Numbers\n",
    "    + The Expected Value\n",
    "        - Expected value of a discrete univariate distribution\n",
    "            * Special cases: Bernoulli, Binomial, Geometric, Hypergeometric, Poisson\n",
    "        - Expected value of a continuous univariate distribution\n",
    "            * Special cases: uniform, exponential, normal\n",
    "        - Expected value of a multivariate distribution\n",
    "    + Standard Error and Variance.\n",
    "        - Discrete examples\n",
    "        - Continuous examples\n",
    "        - The square-root law\n",
    "        - Standardization and Studentization\n",
    "        - The Central Limit Theorem\n",
    "    + The tail-sum formula for the expected value\n",
    "    + Conditional expectation\n",
    "        - The conditional expectation is a random variable\n",
    "        - The expectation of the conditional expectation is the unconditional expectation\n",
    "    + Useful probability inequalities\n",
    "        - Markov's Inequality\n",
    "        - Chebychev's Inequality\n",
    "        - Hoeffding's Inequality\n",
    "        - Jensen's inequality\n",
    "10. Simulation\n",
    "    + Pseudo-random number generation\n",
    "        - Importance of the PRNG. Period, DIEHARD\n",
    "    + Assumptions\n",
    "    + Uncertainties\n",
    "    + Sampling distributions\n",
    "\n",
    "## Lecture 5: Testing\n",
    "11. Hypothesis tests\n",
    "    + Null and alternative hypotheses, \"omnibus\" hypotheses\n",
    "    + Type I and Type II errors\n",
    "    + Significance level and power\n",
    "    + Approximate, exact, and conservative tests\n",
    "    + Families of tests\n",
    "    + P-values\n",
    "        - Estimating P-values by simulation\n",
    "    + Test statistics\n",
    "        - Selecting a test statistic\n",
    "        - The null distribution of a test statistic\n",
    "        - One-sided and two-sided tests\n",
    "    + Null hypotheses involving actual, hypothetical, and counterfactual randomness\n",
    "    + Multiplicity\n",
    "        - Per-comparison error rate (PCER)\n",
    "        - Familywise error rate (FWER)\n",
    "        - The False Discovery Rate (FDR)\n",
    "\n",
    "## Lecture 6: Tests and Confidence sets\n",
    "12. Tests, continued\n",
    "    + Parametric and nonparametric tests\n",
    "        - The Kolmogorov-Smirnov test and the MDKW inequality\n",
    "        - Example: Testing for uniformity\n",
    "        - Conditional test for Poisson behavior\n",
    "    + Permutation and randomization tests\n",
    "        - Invariances of distributions\n",
    "        - Exchangeability\n",
    "        - The permutation distribution of test statistics\n",
    "        - Approximating permutation distributions by simulation\n",
    "        - The two-sample problem\n",
    "    + Testing when there are nuisance parameters\n",
    "13. Confidence sets\n",
    "    + Definition\n",
    "    + Interpretation\n",
    "    + Duality between hypothesis tests and confidence sets\n",
    "    + Tests and confidence sets for Binomial p\n",
    "    + Pivoting\n",
    "        - Confidence sets for a normal mean\n",
    "            * known variance\n",
    "            * unknown variance; Student's t distribution\n",
    "    + Approximate confidence intervals using the normal approximation\n",
    "        - Empirical coverage\n",
    "        - Failures\n",
    "    + Nonparametric confidence bounds for the mean of a nonnegative population\n",
    "    + Multiplicity\n",
    "        - Simultaneous coverage\n",
    "        - Selective coverage"
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    "# Rough Syllabus for complete 45-hour course\n",
    "\n",
    "---\n",
    "### Descriptive Statistics\n",
    "\n",
    "1. Summarizing data.\n",
    "    1. Types of data: categorical, ordinal, quantitative\n",
    "    1. Univariate data.\n",
    "        1. Measures of location and spread: mean, median, mode, quantiles, inter-quartile range, range, standard deviation, RMS\n",
    "        1. Markov's and Chebychev's inequalities for quantitative lists\n",
    "        1. Ranks and ordinal categorical data\n",
    "        1. Frequency tables and histograms\n",
    "        1. Bar charts\n",
    "    1. Multivariate data\n",
    "        1. Scatterplots\n",
    "        1. Measures of association: Pearson and Spearman correlation coefficients\n",
    "        1. Linear regression\n",
    "            1. The Least Squares principle\n",
    "            1. The Projection Theorem\n",
    "            1. The Normal Equations\n",
    "                1. Numerical solution of the normal equations\n",
    "                1. Numerical linear algebra is not the same as abstract linear algebra\n",
    "                1. Condition number\n",
    "                1. Do not invert matrices to solve linear systems: use backsubstitution or factorization\n",
    "            1. Errors in regression: RMS error of linear regression\n",
    "            1. Least Absolute Value regression\n",
    "        1. Principal components and approximation by subspaces: another application of the Projection Theorem\n",
    "        1. Clustering\n",
    "            1. Distance functions\n",
    "            1. Hierarchical methods, tree-based methods\n",
    "            1. Centroid methods: K-means\n",
    "            1. Density-based clustering: kernel methods, DBSCAN\n",
    "\n",
    "---\n",
    "### Probability\n",
    "\n",
    "1. Counting and combinatorics\n",
    "    1. Sets: unions, intersections, partitions\n",
    "    1. De Morgan's Laws\n",
    "    1. The Inclusion-Exclusion principle.\n",
    "    1. The Fundamental Rule of Counting\n",
    "    1. Combinations. Application (using the Inclusion-Exclusion Principle): counting derangements\n",
    "    1. Permutations\n",
    "    1. Strategies for complex counting problems\n",
    "\n",
    "1. Theories of probability\n",
    "    1. Equally likely outcomes\n",
    "    1. Frequency Theory\n",
    "    1. Subjective Theory\n",
    "    1. Shortcomings of the theories\n",
    "\n",
    "1. Axiomatic Probability\n",
    "    1. Outcome space and events, events as sets\n",
    "    1. Kolmogorov's axioms (finite and countable)\n",
    "    1. Analogies between probability and area or mass\n",
    "    1. Consequences of the axioms\n",
    "        1. Probabilities of unions and intersections\n",
    "        1. Bounds on probabilities\n",
    "        1. Bonferroni's inequality\n",
    "        1. The inclusion-exclusion rule for probabilities\n",
    "    1. Conditional probability\n",
    "        1. The Multiplication Rule\n",
    "        1. Independence\n",
    "        1. Bayes Rule\n",
    "\n",
    "1. Random variables.\n",
    "    1. Probability distributions\n",
    "    1. Cumulative distribution functions for real-valued random variables\n",
    "    1. Discrete random variables\n",
    "        1. Probability mass functions\n",
    "        1. The uniform distribution on a finite set\n",
    "        1. Bernoulli random variables\n",
    "        1. Random variables derived from the Bernoulli\n",
    "            1. Binomial random variables\n",
    "            1. Geometric\n",
    "            1. Negative binomial\n",
    "        1. Poisson random variables: countably infinite outcome spaces\n",
    "        1. Hypergeometric random variables\n",
    "        1. Examples of other discrete random variables\n",
    "    1. Continuous and \"mixed\" random variables\n",
    "        1. Probability densities\n",
    "        1. The uniform distribution on an interval\n",
    "        1. The exponential distribution and double-exponential distributions\n",
    "        1. The Gaussian distribution\n",
    "        1. The CDF of discrete, continuous, and mixed distributions\n",
    "    1. Survival functions and hazard functions\n",
    "        1. Counting processes\n",
    "    1. Joint distributions of collections of random variables, random vectors\n",
    "        1. The multivariate uniform distribution\n",
    "        1. The multivariate normal distribution\n",
    "        1. Independence of random variables\n",
    "            1. Events derived from random variables\n",
    "            1. Definitions of independence\n",
    "        1. Marginal distributions\n",
    "        1. Conditional distributions\n",
    "            1. The \"memoryless property\" of the exponential distribution\n",
    "        1. The Central Limit Theorem\n",
    "    1. Stochastic processes\n",
    "        1. Point processes\n",
    "            1. Intensity functions and conditional intensity functions\n",
    "            1. Poisson processes\n",
    "                1. Homogeneous and inhomogeneous Poisson processes\n",
    "                1. The conditional distribution of Poisson processes given N\n",
    "            1. Marked point processes\n",
    "            1. Inter-arrival times and inter-arrival distributions\n",
    "            1. The conditional distribution of a Poisson process\n",
    "        1. Random walks\n",
    "        1. Markov chains\n",
    "        1. Brownian motion\n",
    "\n",
    "1. Expectation\n",
    "    1. The Law of Large Numbers\n",
    "    1. The Expected Value\n",
    "        1. Expected value of a discrete univariate distribution\n",
    "            1. Special cases: Bernoulli, Binomial, Geometric, Hypergeometric, Poisson\n",
    "        1. Expected value of a continuous univariate distribution\n",
    "            1. Special cases: uniform, exponential, normal\n",
    "        1. (Aside: measurability, Lebesgue integration, and the CDF as a measure)\n",
    "        1. Expected value of a multivariate distribution\n",
    "    1. Expected values of functions of a random variable\n",
    "        1. Change-of-variables formulas for probability mass functions and densities\n",
    "    1. Standard Error and Variance.\n",
    "        1. Discrete examples\n",
    "        1. Continuous examples\n",
    "        1. The square-root law\n",
    "    1. The tail-sum formula for the expected value\n",
    "    1. Conditional expectation\n",
    "        1. The expectation of the conditional expectation is the unconditional expectation\n",
    "    1. Useful probability inequalities\n",
    "        1. Markov's Inequality\n",
    "        1. Chebychev's Inequality\n",
    "        1. Hoeffding's Inequality\n",
    "\n",
    "---\n",
    "### Sampling\n",
    "\n",
    "1. Empirical distributions\n",
    "    1. The ECDF for univariate distributions\n",
    "    1. The Kolmogorov-Smirnov statistic and The Massart-Dvoretzky-Kiefer-Wolfowitz inequality\n",
    "    1. Inference: inverting the MDKW inequality\n",
    "    1. Q-Q plots\n",
    "\n",
    "1. Random sampling.\n",
    "    1. Types of samples\n",
    "        1. Samples of convenience\n",
    "        1. Quota sampling\n",
    "        1. Systematic sampling\n",
    "        1. The importance of random sampling: stirring the soup.\n",
    "        1. Systematic random sampling\n",
    "        1. Random sampling with replacement\n",
    "        1. Simple random sampling\n",
    "        1. Stratified random sampling.\n",
    "        1. Cluster sampling\n",
    "        1. Multistage sampling\n",
    "        1. Weighted random samples\n",
    "        1. Sampling with probability proportional to size\n",
    "    1. Sampling frames\n",
    "    1. Nonresponse and missing data\n",
    "    1. Sampling bias\n",
    "\n",
    "1. Simulation\n",
    "    1. Pseudo-random number generators\n",
    "        1. Why the PRNG matters\n",
    "        1. Uniformity, period, independence\n",
    "        1. Assessing PRNGs. DIEHARD and other tests\n",
    "        1. Linear congruential PRNGs, including the Wichmann-Hill. Group-induced patterns\n",
    "        1. Statistically \"adequate\" PRNGs, including the Mersenne Twister\n",
    "        1. Cryptographic quality PRNGs, including cryptographic hashes\n",
    "    1. Generating pseudorandom permutations\n",
    "    1. Taking pseudorandom samples\n",
    "    1. Simulating sampling distributions\n",
    "\n",
    "---\n",
    "### Estimation and Inference\n",
    "\n",
    "1. Estimating parameters using random samples\n",
    "    1. Sampling distributions\n",
    "    1. The Central Limit Theorem\n",
    "    1. Measures of accuracy: mean squared error, median absolute deviation, etc.\n",
    "    1. Maximum likelihood\n",
    "    1. Loss functions, Risk, and decision theory\n",
    "    1. Minimax estimates\n",
    "    1. Bayes estimates\n",
    "    1. The Bootstrap\n",
    "    1. Shrinkage and regularization\n",
    "\n",
    "1. Inference\n",
    "    1. Hypothesis tests\n",
    "        1. Null and alternative hypotheses, \"omnibus\" hypotheses\n",
    "        1. Type I and Type II errors\n",
    "        1. Significance level and Power\n",
    "        1. Approximate, exact, and conservative tests\n",
    "        1. Families of tests\n",
    "        1. P-values\n",
    "            1. Estimating P-values by simulation\n",
    "        1. Test statistics\n",
    "            1. Selecting a test statistic\n",
    "            1. The null distribution of a test statistic\n",
    "            1. One-sided and two-sided tests\n",
    "        1. Null hypotheses involving actual, hypothetical, and counterfactual randomness\n",
    "        1. Multiplicity\n",
    "            1. Per-comparison error rate\n",
    "            1. Familywise error rate\n",
    "            1. The False Discovery Rate\n",
    "    1. Approaches to testing\n",
    "        1. Parametric and nonparametric tests\n",
    "        1. Likelihood ratio tests\n",
    "        1. Permutation and randomization tests\n",
    "            1. Invariances of distributions\n",
    "            1. Exchangeability\n",
    "            1. Other symmetries\n",
    "            1. The permutation distribution of test statistics\n",
    "            1. Approximating permutation distributions by simulation\n",
    "    1. Confidence sets\n",
    "    1. Duality between hypothesis tests and confidence sets\n",
    "    1. Conditional tests, conditional and unconditional significance levels\n",
    "\n",
    "1. Tests of particular hypotheses\n",
    "    1. The Neyman model of a randomized experiment.\n",
    "        1. Strong and weak null hypotheses\n",
    "        1. Testing the strong null hypothesis\n",
    "            1. The distribution of a test statistic under the strong null\n",
    "        1. \"Interference\"\n",
    "        1. Blocking and other designs\n",
    "            1. Ensuring that the null hypothesis matches the experiment\n",
    "    1. Tests for Binomial p\n",
    "    1. The Sign test\n",
    "        1. The sign test for the median; tests for other quantiles\n",
    "        1. The sign test for a difference in medians\n",
    "    1. Tests based on the normal approximation\n",
    "        1. The Z statistic and the Z test\n",
    "        1. The t statistic and the t test\n",
    "        1. 2-sample problems, paired and unpaired tests\n",
    "        1. Tests based on ranks\n",
    "            1. The Wilcoxon test\n",
    "            1. The Wilcoxon signed rank test\n",
    "        1. Tests using actual values\n",
    "    1. Tests of association\n",
    "        1. The hypothesis of exchangeability\n",
    "        1. The Spearman test\n",
    "        1. The permutation distribution of the Pearson correlation\n",
    "    1. Tests of randomness and independence\n",
    "        1. The runs test\n",
    "    1. Tests of symmetry\n",
    "        1. Tests of exchangeability\n",
    "        1. Tests of spherical symmetry\n",
    "    1. The two-sample problem\n",
    "        1. Selecting the test statistic: what's the alternative?\n",
    "            1. Mean, sum, Student t\n",
    "            1. Smirnov statistic\n",
    "            1. Other choices\n",
    "        1. The permutation distribution of the test statistic\n",
    "        1. The two-sample problem for complex data\n",
    "            1. Test statistics\n",
    "        1. The k-sample problem\n",
    "    1. Stratified permutation tests\n",
    "    1. Fisher's Exact Test\n",
    "    1. Tests of homogeneity and ANOVA\n",
    "        1. The F statistic\n",
    "        1. The permutation distribution of the F statistic\n",
    "        1. Other statistics\n",
    "        1. Ordered alternatives\n",
    "    1. Tests based on the distribution function: The Kolmogorov-Smirnov Test\n",
    "        1. The universality of the null distribution for continuous variables\n",
    "        1. Using the K-S test to test for Poisson behavior\n",
    "    1. Sequential tests and Wald's SPRT\n",
    "        1. Random walks and Gambler's ruin\n",
    "        1. Wald's Theorem\n",
    "\n",
    "1. Confidence intervals for particular parameters\n",
    "    1. Confidence intervals for a shift in the Neyman model\n",
    "    1. Confidence intervals for Binomial p\n",
    "        1. Application: confidence bounds for P-values estimated by simulation\n",
    "        1. Application: intervals for quantiles by inverting binomial tests\n",
    "    1. Confidence intervals for a Normal mean using the Z and t distributions\n",
    "    1. Confidence intervals for the mean\n",
    "        1. Nonparametric confidence bounds for a population mean\n",
    "            1. The need for a priori bounds\n",
    "            1. Nonnegative random variables\n",
    "            1. Bounded random variables\n",
    "    1. Confidence sets for multivariate parameters\n",
    "\n",
    "1. Density estimation\n",
    "    1. Histogram estimates\n",
    "    1. Kernel estimates\n",
    "    1. Confidence bounds for monotone and shape-restricted densities\n",
    "    1. Lower confidence bounds on the number of modes\n",
    "\n",
    "1. Function estimation\n",
    "    1. Splines and penalized splines\n",
    "        1. Polynomial splines\n",
    "        1. Periodic splines\n",
    "        1. Smoothing splines as least-squares\n",
    "        1. B-splines\n",
    "        1. L1 splines\n",
    "    1. Constraints\n",
    "        1. Balls and ellipsoids\n",
    "            1. Smoothness and norms\n",
    "            1. Lipschitz conditions\n",
    "            1. Sobolev conditions\n",
    "        1. Cones\n",
    "            1. Nonnegativity\n",
    "            1. Shape restrictions\n",
    "                1. Monotonicity\n",
    "                1. Convexity\n",
    "        1. Star-shaped constraints\n",
    "            1. Sparsity and minimum L1 methods\n",
    "\n",
    "---\n",
    "### *Sketchy from here down*\n",
    "### Experiments\n",
    "\n",
    "1. Experiments versus observational studies\n",
    "    1. Controls and the Method of Comparison\n",
    "    1. Randomization\n",
    "    1. Blinding\n",
    "\n",
    "1. Experimental design\n",
    "    1. Blocking\n",
    "    1. Orthogonal designs\n",
    "    1. Latin hypercube design\n",
    "\n",
    "\n",
    "\n"
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        {
         "module": "pandas",
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        {
         "module": "matplotlib",
         "version": "1.4.3"
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       ]
      },
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>2.7.10 64bit [GCC 4.2.1 (Apple Inc. build 5577)]</td></tr><tr><td>IPython</td><td>3.2.1</td></tr><tr><td>OS</td><td>Darwin 14.5.0 x86_64 i386 64bit</td></tr><tr><td>scipy</td><td>0.14.0</td></tr><tr><td>numpy</td><td>1.9.2</td></tr><tr><td>pandas</td><td>0.14.1</td></tr><tr><td>matplotlib</td><td>1.4.3</td></tr><tr><td colspan='2'>Sun Aug 23 17:00:13 2015 PDT</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 2.7.10 64bit [GCC 4.2.1 (Apple Inc. build 5577)] \\\\ \\hline\n",
       "IPython & 3.2.1 \\\\ \\hline\n",
       "OS & Darwin 14.5.0 x86\\letterunderscore{}64 i386 64bit \\\\ \\hline\n",
       "scipy & 0.14.0 \\\\ \\hline\n",
       "numpy & 1.9.2 \\\\ \\hline\n",
       "pandas & 0.14.1 \\\\ \\hline\n",
       "matplotlib & 1.4.3 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Sun Aug 23 17:00:13 2015 PDT} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 2.7.10 64bit [GCC 4.2.1 (Apple Inc. build 5577)]\n",
       "IPython 3.2.1\n",
       "OS Darwin 14.5.0 x86_64 i386 64bit\n",
       "scipy 0.14.0\n",
       "numpy 1.9.2\n",
       "pandas 0.14.1\n",
       "matplotlib 1.4.3\n",
       "Sun Aug 23 17:00:13 2015 PDT"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Version information\n",
    "%load_ext version_information\n",
    "%version_information scipy, numpy, pandas, matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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