Puzzle – Gambler’s Ruin

Which is better - wealth or ability?  Fred Mosteller posed this question in his classic 1965 small compendium Fifty Challenging Problems in Probability, in the context of the Gambler’s Ruin puzzle.  Two players, M and N, engage in a game in which $1 is transferred…

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Dec 14: Statistics in Practice

In this week’s Briefing, we take a look at different strands of “purity” in AI. Our course spotlight is Jan 15 - Feb 12: Introduction to Data Literacy It's for you or anyone you know who needs to get more numerate! See you or them in…

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Oct 6: Statistics in Practice

In our Briefing this week, we take a look at unemployment insurance fraud and a statistical tool for catching the crooks. Our course spotlight is on: Oct 23 - Nov 20:  Spatial Statistics See you in class! Peter Bruce Founder, Author, and Senior Scientist Unemployment…

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Famous Errors in Statistics

“A little knowledge is a dangerous thing,” said Alexander Pope in 1711; he could have been speaking of the use of statistics by experts in all fields. In this article, we look at three consequential mistakes in the field of statistics. Two of them are famous, the third required a deep dive into the corporate annual reports of

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Puzzle: Surgery or Radiation

Several decades ago, the dominant therapies for lung cancer were radiation, which offered better short-term survival rates, and surgery, which offered better long-term rates. A thought experiment was conducted in which surgeons were randomly assigned to one of two groups and asked whether they would choose surgery. Group 1 was told: The one-month survival rate is 90%. Group 2 was told: There is 10% mortality in the first month. Yes, the two statements say the same thing. What did the two physician groups choose?

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Sept 2: Statistics in Practice

This week, our topic is Data Engineering, and we feature a guest blog by Will Goodrum, a data scientist at Elder Research. Our course spotlight is Oct 2 -30: Categorical Data Analysis See you in class! Peter Bruce Founder, Author, and Senior Scientist Four Common…

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Conversations with Data Scientists about R and Python

Died-in-the-wool software developers can get quite passionate about the relative virtues of one programming language or another, their debates sometimes threatening to transport you back to middle-school arguments about the greatest ballplayers of all time.  Though their computer passions find other outlets as well, data…

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Apr 7: Statistics in Practice

In this week’s Brief, we look in greater detail at Elder Research, Inc., which recently acquired Statistics.com.  If your organization is like most organizations, your data science initiatives may lack the direction and support they need to succeed - having a data science team does…

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Feb 10: Statistics in Practice

Tomorrow is the New Hampshire political primary in the US, and this week’s Brief looks at the statistical concept of lift.  Our spotlight is on: Feb 28 - Mar 27:   Persuasion Analytics and Targeting See you in class! - Peter Bruce, Founder Lift and…

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Aug 2: Statistics in Practice

In part 1 of this week’s brief, we looked at political analytics; in Part 2 we extend that look to commercial domains. Our course spotlight is Persuasion Analytics, taught by Ken Strasma, who pioneered the use of statistical modeling to microtarget voters in the 2004…

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Probability

You might be wondering why such a basic word as probability appears here. It turns out that the term has deep tendrils in formal mathematics and philosophy, but is somewhat hard to pin down

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Density

Density is a metric that describes how well-connected a network is

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Algorithms

We have an extensive statistical glossary and have been sending out a "word of the week" newsfeed for a number of years.  Take a look at the results

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Gittens Index

Consider the multi-arm bandit problem where each arm has an unknown probability of paying either 0 or 1, and a specified payoff discount factor of x (i.e. for two successive payoffs, the second is valued at x% of the first, where x < 100%).  The Gittens index is [...]

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Cold Start Problem

There are various ways to recommend additional products to an online purchaser, and the most effective ones rely on prior purchase or rating history -

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Autoregressive

Autoregressive refers to time series forecasting models (AR models) in which the independent variables (predictors) are prior values of the time series itself.

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Tensor

A tensor is the multidimensional extension of a matrix (i.e. scalar > vector > matrix > tensor). 

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Confusing Terms in Data Science – A Look at Synonyms

To a statistician, a sample is a collection of observations (cases).  To a machine learner, it’s a single observation.  Modern data science has its origin in several different fields, which leads to potentially confusing  synonyms, like these:

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Confusing Terms in Data Science – A Look at Homonyms and more

To a statistician, a sample is a collection of observations (cases).  To a machine learner, it’s a single observation.  Modern data science has its origin in several different fields, which leads to potentially confusing homonyms like these: 

 

 

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Rectangular data

Rectangular data are the staple of statistical and machine learning models.  Rectangular data are multivariate cross-sectional data (i.e. not time-series or repeated measure) in which each column is a variable (feature), and each row is a case or record.

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Selection Bias

Selection bias is a sampling or data collection process that yields a biased, or unrepresentative, sample.  It can occur in numerous situations, here are just a few:

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Likert Scale

A "likert scale" is used in self-report rating surveys to allow users to express an opinion or assessment of something on a gradient scale.  For example, a response could range from "agree strongly" through "agree somewhat" and "disagree somewhat" on to "disagree strongly."  Two key decisions the survey designer faces are

  • How many gradients to allow, and

  • Whether to include a neutral midpoint

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Dummy Variable

A dummy variable is a binary (0/1) variable created to indicate whether a case belongs to a particular category.  Typically a dummy variable will be derived from a multi-category variable. For example, an insurance policy might be residential, commercial or automotive, and there would be three dummy variables created:

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Things are Getting Better

In the visualization below, which line do you think represents the UN's forecast for the number of children in the world in the year 2100? Hans Rosling, in his book Factfulness, presents this chart and notes that in a sample of Norwegian teachers, only 9%…

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Conditional Probability Word of the Week

QUESTION:  The rate of residential insurance fraud is 10% (one out of ten claims is fraudulent).  A consultant has proposed a machine learning system to review claims and classify them as fraud or no-fraud.  The system is 90% effective in detecting the fraudulent claims, but only 80% effective in correctly classifying the non-fraud claims (it mistakenly labels one in five as "fraud").  If the system classifies a claim as fraudulent, what is the probability that it really is fraudulent?

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“out-of-bag,” as in “out-of-bag error”

"Bag" refers to "bootstrap aggregating," repeatedly drawing of bootstrap samples from a dataset and aggregating the results of statistical models applied to the bootstrap samples. (A bootstrap sample is a resample drawn with replacement.)

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BOOTSTRAP

I used the term in my message about bagging and several people asked for a review of the bootstrap. Put simply, to bootstrap a dataset is to draw a resample from the data, randomly and with replacement.

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Same thing, different terms..

The field of data science is rife with terminology anomalies, arising from the fact that the field comes from multiple disciplines.

 

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HYPERPARAMETER

Hyperparameter is used in machine learning, where it refers, loosely speaking, to user-set parameters, and in Bayesian statistics, to refer to parameters of the prior distribution.

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SAMPLE

Why sample? A while ago, sample would not have been a candidate for Word of the Week, its meaning being pretty obvious to anyone with a passing acquaintance with statistics. I select it today because of some output I saw from a decision tree in Python.

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SPLINE

 

The easiest way to think of a spline is to first think of linear regression - a single linear relationship between an outcome variable and various predictor variables. 

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NLP

To some, NLP = natural language processing, a form of text analytics arising from the field of computational linguistics.

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OVERFIT

As applied to statistical models - "overfit" means the model is too accurate, and fitting noise, not signal. For example, the complex polynomial curve in the figure fits the data with no error, but you would not want to rely on it to predict accurately for new data:

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Week #18 – n

In statistics, "n" denotes the size of a dataset, typically a sample, in terms of the number of observations or records.

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Week #17 – Corpus

A corpus is a body of documents to be used in a text mining task.  Some corpuses are standard public collections of documents that are commonly used to benchmark and tune new text mining algorithms.  More typically, the corpus is a body of documents for…

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Week #2 – Casual Modeling

Causal modeling is aimed at advancing reasonable hypotheses about underlying causal relationships between the dependent and independent variables. Consider for example a simple linear model: y = a0 + a1 x1 + a2 x2 + e where y is the dependent variable, x1 and x2…

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Week #10 – Arm

In an experiment, an arm is a treatment protocol - for example, drug A, or placebo.   In medical trials, an arm corresponds to a patient group receiving a specified therapy.  The term is also relevant for bandit algorithms for web testing, where an arm consists…

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Week #9 – Sparse Matrix

A sparse matrix typically refers to a very large matrix of variables (features) and records (cases) in which most cells are empty or 0-valued.  An example might be a binary matrix used to power web searches - columns representing search terms and rows representing searches,…

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Week #8 – Homonyms department: Sample

We continue our effort to shed light on potentially confusing usage of terms in the different data science communities. In statistics, a sample is a collection of observations or records.  It is often, but not always, randomly drawn.  In matrix form, the rows are records…

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Week #7 – Homonyms department: Normalization

With this entry, we inaugurate a new effort to shed light on potentially confusing usage of terms in the different data science communities. In statistics and machine learning, normalization of variables means to subtract the mean and divide by the standard deviation.  When there are…

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Week #43 – HDFS

HDFS is the Hadoop Distributed File System.  It is designed to accommodate parallel processing on clusters of commodity hardware, and to be fault tolerant.

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Week #42 – Kruskal – Wallis Test

The Kruskal-Wallis test is a nonparametric test for finding if three or more independent samples come from populations having the same distribution. It is a nonparametric version of ANOVA.

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Week #32 – False Discovery Rate

A "discovery" is a hypothesis test that yields a statistically significant result. The false discovery rate is the proportion of discoveries that are, in reality, not significant (a Type-I error). The true false discovery rate is not known, since the true state of nature is not known (if it were, there would be no need for statistical inference).

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Week #23 – Netflix Contest

The 2006 Netflix Contest has come to convey the idea of crowdsourced predictive modeling, in which a dataset and a prediction challenge are made publicly available.  Individuals and teams then compete to develop the best performing model.

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Week #20 – R

This week's word is actually a letter.  R is a statistical computing and programming language and program, a derivative of the commercial S-PLUS program, which, in turn, was an offshoot of S from Bell Labs.

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Week #16 – Moving Average

In time series forecasting, a moving average is a smoothing method in which the forecast for time t is the average value for the w periods ending with time t-1.

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Week #15 – Interaction term

In regression models, an interaction term captures the joint effect of two variables that is not captured in the modeling of the two terms individually.

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Week #14 – Naive forecast

A naive forecast or prediction is one that is extremely simple and does not rely on a statistical model (or can be expressed as a very basic form of a model).

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week #9 – Overdispersion

In discrete response models, overdispersion occurs when there is more correlation in the data than is allowed by the assumptions that the model makes.

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Week #8 – Confusion matrix

In a classification model, the confusion matrix shows the counts of correct and erroneous classifications.  In a binary classification problem, the matrix consists of 4 cells.

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Week #5 – Features vs. Variables

The predictors in a predictive model are sometimes given different terms by different disciplines.  Traditional statisticians think in terms of variables.

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Week # 52 – Quasi-experiment

In social science research, particularly in the qualitative literature on program evaluation, the term "quasi-experiment" refers to studies that do not involve the application of treatments via random assignment of subjects.

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Week #48 – Structured vs. unstructured data

Structured data is data that is in a form that can be used to develop statistical or machine learning models (typically a matrix where rows are records and columns are variables or features).

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Word #39 – Censoring

Censoring in time-series data occurs when some event causes subjects to cease producing data for reasons beyond the control of the investigator, or for reasons external to the issue being studied.

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Work #32 – Predictive modeling

Predictive modeling is the process of using a statistical or machine learning model to predict the value of a target variable (e.g. default or no-default) on the basis of a series of predictor variables (e.g. income, house value, outstanding debt, etc.).

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Week #29 – Goodness-of-fit

Goodness-of-fit measures the difference between an observed frequency distribution and a theoretical probability distribution which

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Week #53 – Effect size

In a study or experiment with two groups (usually control and treatment), the investigator typically has in mind the magnitude of the difference between the two groups that he or she wants to be able to detect in a hypothesis test.

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Week #51 – Type 1 error

In a test of significance (also called a hypothesis test), Type I error is the error of rejecting the null hypothesis when it is true -- of saying an effect or event is statistically significant when it is not.

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Week #49 – Data partitioning

Data partitioning in data mining is the division of the whole data available into two or three non-overlapping sets: the training set (used to fit the model), the validation set (used to compared models), and the test set (used to predict performance on new data).

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Week #42 – Cross-sectional data

Cross-sectional data refer to observations of many different individuals (subjects, objects) at a given time, each observation belonging to a different individual.  A simple...

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Week #32 – CHAID

CHAID stands for Chi-squared Automatic Interaction Detector. It is a method for building classification trees and regression trees from a training sample comprising already-classified objects.

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Week # 29 – Training data

Also called the training sample, training set, calibration sample.  The context is predictive modeling (also called supervised data mining) -  where you have data with multiple predictor variables and a single known outcome or target variable.

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Churn Trigger

Last year's popular story out of the Predictive Analytics World conference series was Andrew Pole's presentation of Target's methodology for predicting which customers were pregnant.

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Congratulations to Thomas Lumley!

Newly elected American Statistical Association (ASA) Fellow, and recognized for his outstanding professional contributions to and leadership in the field of statistical science.

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Julian Simon birthday

February 12 was the 80th anniversary of the birth of Julian Simon, an early pioneer in resampling methods.

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Statistics for Future Presidents

Statistics for Future Presidents - Steve Pierson, Director of Science Policy at ASA wrote interesting blog wondering how statistics for future presidents (or policymakers more generally) would compare with the recommended statistical skills/concepts for others. Take a look and let him know!

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The Data Scientist

The story of the prospective Facebook IPO, and prior IPO's from LinkedIn, Pandora, and Groupon all involve "data scientists".  Read an interview with Monica Rogati - Senior Data Scientist at LinkedIn to see the connection.

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Coffee causes cancer?

"Any claim coming from an observational study is most likely to be wrong." Thus begins "Deming, data and observational studies," just published in "Significance Magazine" (Sept. 2011).

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The sacrifice bunt

I was watching a Washington Nationals game on TV a couple of days ago, and the concept of "expected value" ...

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Epidemiologist joke

A neurosurgeon, pathologist and epidemiologist are each told to examine a can of sardines on a table in a closed room, and present a report.

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The Power of Round

Advertisers shy away from round numbers, believing that $99 appears significantly cheaper than $100...

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Bees on the attack

What does Matt Asher's article "Attack of the Hair Trigger Bees" have to do with global warming? Matt Asher runs statisticsblog.com ...

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Catastrophe Modeling Assistant

Thinking about careers that use statistics? The job title "catastrophe modeling assistant" caught my eye recently in a job announcement. ...

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