Archive for the ‘Statistics – Probabilities’ Category

If I test positive for COVID, am I infected?

March 10, 2021

The answer may surprise you, and it has big implications for how individuals & organizations respond to positive Covid test results.
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Originally posted 05/27/2020; updated January 17, 2022

In a prior post, we reported that “Asymptomatics” are not rushing to get tested and provided some subjective reasons why that might be (e.g. no doctor referral, high hassle factor, privacy concerns).

OK, let’s up our game a notch or two and throw some math & economics at the problem.

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I’m a fan of “Freakonomics” … the popular call sign for a discipline called Behavioral Economics … the study of the rationality that underlies many seemingly irrational decisions that people sometimes make.

And, in my strategic business analytics course, I used to teach something called Bayesian Inference … a way to calculate probabilities by combining contextual information (called “base rates” or “priors”) with case-specific observations (think: testing or witnessing).

Today, we’ll connect Freakonomics and Bayesian Inference and apply them to the COVID testing situation…

(more…)

Posted in Bayes - Bayesian Inference, Coronavirus - Covid 19, Covid-19 Testing, Statistics - Probabilities | Leave a Comment »

If I test positive for COVID, am I infected?

October 2, 2020

The answer may surprise you, and it has big implications for test & trace.
=============

In a prior post, we reported that “Asymptomatics” are not rushing to get tested and provided some subjective reasons why that might be (e.g. no doctor referral, high hassle factor, privacy concerns).

OK, let’s up our game a notch or two and throw some math & economics at the problem.

==============

I’m a fan of “Freakonomics” … the popular call sign for a discipline called Behavioral Economics … the study of the rationality that underlies many seemingly irrational decisions that people sometimes make.

And, in my strategic business analytics course, I used to teach something called Bayesian Inference … a way to calculate probabilities by combining contextual information (called “base rates” or “priors”) with case-specific observations (think: testing or witnessing).

Today, we’ll connect Freakonomics and Bayesian Inference and apply them to the COVID testing situation…

(more…)

Posted in Bayes - Bayesian Inference, Coronavirus - Covid 19, Covid-19 Testing, Statistics - Probabilities | Leave a Comment »

If I test positive for COVID, am I infected?

May 27, 2020

The answer may surprise you, and it has big implications for test & trace.
=============

In a prior post, we reported that “Asymptomatics” are not rushing to get tested and provided some subjective reasons why that might be (e.g. no doctor referral, high hassle factor, privacy concerns).

OK, let’s up our game a notch or two and throw some math & economics at the problem.

==============

I’m a fan of “Freakonomics” … the popular call sign for a discipline called Behavioral Economics … the study of the rationality that underlies many seemingly irrational decisions that people sometimes make.

And, in my strategic business analytics course, I used to teach something called Bayesian Inference … a way to calculate probabilities by combining contextual information (called “base rates” or “priors”) with case-specific observations (think: testing or witnessing).

Today, we’ll connect Freakonomics and Bayesian Inference and apply them to the COVID testing situation…

(more…)

Posted in Bayes - Bayesian Inference, Coronavirus - Covid 19, Covid-19 Testing, Statistics - Probabilities | Leave a Comment »

What are your chances of dying from ___ ?

November 8, 2019

Yesterday, we posted that men are 9 times more likely than women to be attacked by sharks … and 6 times more likely to be struck by lightning.

Continuing in that vein, here’s a test for you  …

image

Rank the the following by the odds that somebody who is in the group or who is exposed to the risk is likely to die.

Make #1 the highest risk of dying in the next year; make #7 the lowest risk circumstance

  • For women giving birth
  • For anyone thirty-five to forty-four years old
  • From asbestos in schools
  • For anyone for any reason
  • From lightning
  • For police on the job
  • From airplane crashes

And the answer is …

(more…)

Posted in Probability - certainty, Statistics - Probabilities, Uncategorized | Leave a Comment »

Is it more dangerous to be a man than a woman?

November 7, 2019

Some evidence says it is …  by far in some situations.
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According to Prof. Walter E. Williams writing about Proportional Disparities…

Men are roughly half of the population, right?

But, sharks are nine times likelier to attack and kill men than they are women.

image

Men are struck by lightning six times as often as women.

And, 82% of people killed by lightning are men.

Why is that?

(more…)

Posted in Statistics - Probabilities | Leave a Comment »

Jeopardy Math: What’s the most money that the a contestant can win on one show?

May 23, 2019

Here’s the solution to yesterday’s question.

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Note: Refer back to yesterdays post if you need a refresher on the question and the Jeopardy game essentials

See Jeopardy Math: What’s the most money that a contestant can win on one show?

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OK, let’s get started with the Jeopardy round’s gameboard:

image

For starters, assume that our contestant first-buzzes and correctly answers all of the gameboard’s questions.

Each category has questions totaling $3,000 … and there are 6 categories … so the gameboard has an “displayed total value” of $18,000.

That’s not the most that a contestant can win in that round because it doesn’t consider the impact of the hidden Daily Double square.

(more…)

Posted in Jeopardy, Math & Quant Skills, Sports - Games - Recreation, Statistics - Probabilities | 1 Comment »

Math Trix: So, exactly how lucky is Hillary?

February 4, 2016

I know that this doesn’t matter from a political perspective… Bernie stands zero chance of winning the nomination.

But I think that the math is interesting … made me dust off my recollections of combinatorial probabilities.

Just in case you’ve been asleep for the past couple of days (or get all of your news from the NY Times), Hillary squeaked by Bernie in Iowa … I mean, really squeaked.

The ending tally was that Hillary got credit for 701 delegates and Bernie got credit for 697.

How those final totals were concocted is very interesting.

image

Here’s the scoop … and the stats.

(more…)

Posted in 2016 Campaign, Statistics - Probabilities | Leave a Comment »

Math Trix: The case of the gifted stock-picker…

January 29, 2016

I’ve been reading a book called How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg

The author recounts a classic stock advisor scam that goes like this …

clip_image001

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One day, you receive an unsolicited newsletter from an investment advisor, containing a tip that a certain stock is due for a big rise.

A week passes, and just as the Investment advisor predicted, the stock goes up.

The next week, you get a new edition of the newsletter, and this time, the tip is about a stock whose price the adviser thinks is going to fall.

And indeed, the stock craters.

That’s good, but it gets even better …

(more…)

Posted in Math & arithmetic, Math & Quant Skills, Statistics - Probabilities | Leave a Comment »

Math Trix: The case of the gifted stock-picker…

September 30, 2015

I’ve been reading a book called How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg

The author recounts a classic stock advisor scam that goes like this …

clip_image001

======

One day, you receive an unsolicited newsletter from an investment advisor, containing a tip that a certain stock is due for a big rise.

A week passes, and just as the Investment advisor predicted, the stock goes up.

The next week, you get a new edition of the newsletter, and this time, the tip is about a stock whose price the adviser thinks is going to fall.

And indeed, the stock craters.

That’s good, but it gets even better …

(more…)

Posted in Math & arithmetic, Math & Quant Skills, Statistics - Probabilities | 1 Comment »

Flaw of Averages: 3 views on inflation …

July 23, 2015

Oftentimes, important trends are buried  in statistical averages.

You know, the thing drowning in a river with an average depth of 3 feet.

In my Strategic Business Analytics course, I harp on “decomposing” problems and statistics down to their component parts …. to simplify the problems and reveal insights.

Here’s a case in point: the Consumer Price Index (CPI).

image

For the past 10 years (really, longer), the CPI has pretty much straight-lined upward.

Case closed, steady inflation … right?

Not so fast.

Let’s look at the CPI from a couple of other angles …

(more…)

Posted in Averages - Flaw of averages, CPI, Decomposition - problems & data, Stat, Statistics - Probabilities | Leave a Comment »

Math Trix: The case of the gifted stock-picker…

April 20, 2015

I’ve been reading a book called How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg

The author recounts a classic stock advisor scam that goes like this …

clip_image001

======

One day, you receive an unsolicited newsletter from an investment advisor, containing a tip that a certain stock is due for a big rise.

A week passes, and just as the Investment advisor predicted, the stock goes up.

The next week, you get a new edition of the newsletter, and this time, the tip is about a stock whose price the adviser thinks is going to fall.

And indeed, the stock craters.

That’s good, but it gets even better …

(more…)

Posted in Math & arithmetic, Math & Quant Skills, Statistics - Probabilities | 1 Comment »

Your price sensitivity is asymmetric … and we know it.

January 29, 2015

According to TheVerge.com …

Big grocery chains are increasingly turning to big data and mathematical models to take the guessing out of the process of pricing thousands of items on their shelves,

 

image

 

The models can detect your yogurt flavor preferences and your “internal hierarchy of brands” … i.e. which brands your think are better than others.

And, there’s more …

(more…)

Posted in Grocery Stores, Mathematical Models, Pricing analytics, Statistics - Probabilities | Leave a Comment »

Math Trix: The case of the gifted stock-picker…

August 21, 2014

I’ve been reading a book called How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg

The author recounts a classic stock advisor scam that goes like this …

clip_image001

======

One day, you receive an unsolicited newsletter from an investment advisor, containing a tip that a certain stock is due for a big rise.

A week passes, and just as the Investment advisor predicted, the stock goes up.

The next week, you get a new edition of the newsletter, and this time, the tip is about a stock whose price the adviser thinks is going to fall.

And indeed, the stock craters.

That’s good, but it gets even better …

(more…)

Posted in Math & arithmetic, Math & Quant Skills, Statistics - Probabilities | Leave a Comment »

Your price sensitivity is asymmetric … and we know it.

May 23, 2014

According to TheVerge.com …

Big grocery chains are increasingly turning to big data and mathematical models to take the guessing out of the process of pricing thousands of items on their shelves,

 

image

 

The models can detect your yogurt flavor preferences and your “internal hierarchy of brands” … i.e. which brands your think are better than others.

The models can identify the precise price point at which you would switch between brands or how much incentive you’d need to buy the bigger pack.

It’s not enough to simply know that a 12-pack should cost less per item than a six-pack, nor that branded yogurts should command a price premium … the models try to calculate exactly how much each of those prices should vary.

The models recognize that people are really price-sensitive when buying cold desserts and that a “buy one, get one free” offer is more cost efficient than a straight 50 percent price cut (that’s because some people will still take just one).

And, the models can also detect more nuanced dynamics such as “asymmetric cross-price elasticity” … e.g. an eight-pack’s price affects sales of four-packs more strongly than vice versa.

Think about it next time you swipe your store’s loyalty card.

#HomaFiles

Follow on Twitter @KenHoma             >> Latest Posts

Posted in Grocery Stores, Mathematical Models, Pricing analytics, Statistics - Probabilities | Leave a Comment »

Nums: How to win at Monopoly …

June 22, 2013

Everybody knows that Blackjack is a game of probabilities and that card-counting can get you kicked out of casinos – because it helps slightly with the odds.

Did you know that math and statistics can also improve your odds in Monopoly?

Business Insider posted a fun (and thorough) pitch re: how to win in Monopoly … a great practical (?) application of math and statistics.

 

image

 

Here are a couple of takeaways and a link to the entire pitch … worth browsing, even if you’re not a Monopoly aficionado.

(more…)

Tags:
Posted in Math & Quant Skills, Predictive Analytics, Statistics - Probabilities | Leave a Comment »

What does this map represent?

January 7, 2013

Take a guess …

image

No good reason for anybody to know.

It’s a mapgraphic depicting the 1,540 Walmart stores in 1990.

So what?

Here’s what makes it interesting.

For a cool, dynamic visual showing how & where Walmart has grown over the years, click the link to view FlowData.com’s Walmart growth map.

The content is interesting, and it’s a nice way to present geo-time series data over time.

* * * * *
Follow on Twitter @KenHoma         >> Latest Posts

Posted in Big data, Data analysis, Data base marketing, Statistics - Probabilities, Visualizations | 1 Comment »

I was struck by a Volt of lightning …

September 13, 2012

What are the odds?

I actually (not virtually, actually) passed a Chevy Volt on the road

Note that “I passed” not “I was passed by”

image

Again I ask, what are the odds?

Well, according to the Detroit News, there have been about 16,000 Volts sold from its birth to date.

Note: about 2,000 have been bought by the gov’t and GE – pandering to the Feds

According to the Dept. of Transportation, There are about 250 million registered vehicles in the U.S.

So, the statistical likelihood of the next car I pass being a Volt is about .0064% … or, less than 1 in 15,000, given the geographic distribution of Volts. 

According to the NOAA, the odds of being struck by lighting in your lifetime are 1 in 10,000.

Hmmm.

* * * * *

Side Note

Reuters reports that nearly two years after the introduction of Volt, GM is still losing as much as $49,000 on each one it builds

It currently costs GM “at least” $75,000 to build the Volt,

According to experts, GM’s basic problem is that “the Volt is over-engineered and over-priced,”

Weak sales are forcing GM to idle the Detroit-Hamtramck assembly plant that makes the Chevrolet Volt for four weeks starting September 17

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Tags:, ,
Posted in Autos - Travel, Statistics - Probabilities | 4 Comments »

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