Bay Area Entrepreneurs in Statistics

03/15/2025

Estimating Pi using a Monte Carlo simulation in Excel - the estimate by averaging the last 50 of 500 runs changes each time but is usually +/- 1%. This run the result was 3.14 to three significant figures.

06/03/2024

What's a couple of degrees between friends when it's already hot with an average annual temperature of 100 dF? Well if we add 2 dF so the average goes to 102 dF things get a lot hotter. For a simulation run I set a threshold of 125 dF. Yes, the 100 dF average does have days exceeding 125 dF. And the simulation indicates as many as 22! That's hot! But at 102 dF there are a projected 49 days over 125 dF. Either way it is too hot for me, but just a small increase in average can make a big increase in the frequency at the upper extreme.

In the charts that follow, blue represents the 100 dF scenario and red the 102 dF scenario. The simulation was programmed in Excel using a Monte Carlo randomization.

02/29/2024

Using a Monte Carlo Program to Define Process Control Parameters © Ken Osborn 2013
[Paper available on request from kozborn@sbcglobal.net]

Abstract: Profiler is a program written in Excel® Visual Basic® and uses a Monte-Carlo simulation to fit process data to a Normal distribution. Output includes raw data and simulation statistics and outliers are identified and flagged. If the data are not skewed and show a good fit except for the outliers, process control limits can be calculated from the Normal curve average and standard deviation.

Data plotted in red in Chart 1 (attached) are from a waste discharge stream controlling for mercury. Clearly some of the values are outliers and do not represent the process when it is in control. Chart 1: Mercury in discharge vs Monte Carlo simulation The blue line represents the Monte Carlo fit to a Normal distribution. The majority of the mercury discharge data exhibit a close fit to the simulation curve with outliers clearly visible.

08/10/2021

The U.N. report on global warming predicted a potential 7 dF increase in the average global temperatures if efforts to stop the increase in atmospheric carbon dioxide are not sufficient.

I wanted to see what impact an increase of 7 dF would have locally, say in a region where the average annual temperature was 70 dF with a standard deviation (SD) of 15 dF.

At first glance, if you have a range of temperatures from winter to summer of 40 dF to 100 dF (average +/- 2SD then a shift in the average of 7 dF given a range of 60 dF (100-40) doesn't seem like that much.

But lets do the math. I programmed a Monte Carlo simulation to provide some answers. It compares two sets: a high set with an average of 77 dF and SD = 15 and a low set with an average of 70 dF and SD = 15. I set the program to generate 364 values for each set for 20 separate runs with a run standing in for a year.

I assigned a threshold of 100 dF wanting to know:
1] Maximum temperatures in a given run for high and low
2] Number of days the threshold was exceeded

The number of days the threshold was exceeded for the 77 dF scenario are in red and for 70 dF in blue in the chart below.

The maximum temperatures ranged from 113 to 124 for the high scenario and 104 to 114 for the low scenario. While that may seem not much difference, in the 20 simulated years there were 481 days exceeding 100 dF in the high scenario and 152 in the low scenario.

08/07/2021

Fooling around with the numbers

I had a question I wanted to answer for myself: if the purpose of a vaccination is to give you a head start on the virus, how would changes in the initial antibody titer affect the progression of virus vs antibody.

So I used a logistic model for predator-prey interactions with the virus as prey and anti-body as predator.

Not surprisingly, the results show the higher the initial antibody load the faster the virus is cleared. Surprisingly, the higher the initial antibody load the lower the final antibody load at the time of viral clearance. And lower by a factor of 10,000,000. This may explain why vaccinations help keep us out of the hospital: we can still get infected but the antibody clearance is faster and the inflammatory impact is dramatically lower.

The inputs to the model were the initial infectious load, how fast the virus replicated, initial antibody titer, how fast the antibodies were generated, how many viruses an antibody would clear in a cycle, and a random factor to account for variability is these inputs.

08/03/2021

Data analysis using Photoshop

The Oura ring is a popular accessory for monitoring daily activity, sleep, heart rate and HRV (heart rate variability) during sleep. I wanted to explore the relationship between heart rate and HRV. While you can download the data, it's only the averages day by day and not data collected minute-by-minute over a single day.

The display, though, does present a continuous presentation of a night's worth of data for heart rate and HRV. So my idea was to take screenshots off my phone, load them into Photoshop, and overlay the images for a quick comparison.

Here are the results with the screenshots first then the overlay results. Red displays HRV data and blue displays heart rate data in the combined charts.

You can draw your own conclusions based on the visual presentation.

04/20/2021

A recent study from Tel Aviv University concludes that the "Coronavirus Variant Affects Vaccinated People 8 Times More Than Unvaccinated" (Source: https://nypost.com/2021/04/10/south-african-covid-variant-can-break-through-pfizer-vaccine/)

So does this mean to protect yourself from variant B1.351 you should not get vaccinated? No, it does not.

To see why, let's do the numbers.
Given: 1,350,000 vaccinated individuals and 40,000 unvaccinated individuals; B1.351 accounts for 1% of the virus population; the Pfizer vaccine is 97% effective against the original pre-mutated virus and 75% effective against the variant B1.351; the fractional case load is 1%.

Put this into an Excel spreadsheet and do the calculations:
Individuals vaccinated that get infected = 435 of which 34 get B1.351. Individuals not vaccinated that get infected = 400 of which 4 get B1.351. So the vaccinated group has a 34/4=8.4 higher relative rate of variant infection.

But there is more. Out of 1,350,000 vaccinated individuals there were 435 infections for a rate of 0.03% and 400 out of 40,000 for the unvaccinated group, or 1%. That means the unvaccinated group is 33 times more likely to get infected.

04/13/2021

The date of peak Cherry Blossom bloom has trended earlier, a canary-in-the-mine metric for Global Warming.

04/13/2021

The date of peak Cherry Blossom bloom has been trending earlier, another canary-in-the-coal-mine metric following increasing global temperatures.
REF:http://www.columbia.edu/~mhs119/Temperature/Emails/March2021.pdf
https://www.ncdc.noaa.gov/paleo-search/study/26430

03/05/2021

Mask Math

Masks are not perfect! But they do reduce the risk of air born infection. When the fires in Northern California brought smoke filled skies, it was obvious: protect your lungs and wear a mask. No mandates required; compliance high. Now the risk is transmission not from smoke filled skies, but a virus transmitted from person to person. We can’t see it and we can’t smell it so the reality is existential. The decision to mask or not mask becomes a matter of collective responsibility vs perceived individual liberty.

Number One: Let’s say my belief is that the decision to wear a mask or not to wear a mask is a personal one. I’ll take the risk and you can wear a mask if you don’t want to take the risk. The problem is the risk is not partitioned that way. So educate me on why that is so.

Number Two -the Math: Even the best masks are not perfect at filtering out particulate matter. The viruses causing Covid-19 are born enveloped in water droplets and water v***r. There is variation amongst masks and especially in the way they are worn, but I’ll use a modest average of 60% as the reduction of air born particulates. That means if you wear a mask and I do not, but I am infected, your mask will filter out 60% of whatever water v***r particulates I breath in your direction. It also means that 40% will get through.

Continuing: If I now wear a similar mask, 60% of what I breath out in the way of water v***r particulates is kept from you. Again, 40% manages to escape. So if 40% escapes and then 40% of what escapes my mask gets thru your mask, by both of us wearing masks only 16% makes it to you (.4 X .4 = .16 = 16%). That reduction of risk of 40% to 16% by both of us wearing masks is not perfect but it is huge.

Summarizing: Mask filtration efficiency = FE; transmission risk TR = 1-FE; Transmission risk if both wear a mask TR2=(1-FE)x(1-FE)
Example for F=0.6: TR2 = (1-0.6)X(1-0.6) = 0.16 = 16%

Concluding: Masks are not are only way of battling the virus. Vaccinations will ultimately bring the virus down, but until then if we all wear masks, community outbreaks will decline. If community viral loads are low, businesses can reopen, on-line schools can be an option not a requirement, hugs can come back.

I conclude: Help support your local business: wear a mask!

12/20/2020

By The Numbers: modeling a way to help businesses survive while controlling the pandemic

Data from early in the pandemic reveals there’s a “sweet spot.”

12/06/2020

Back of the Envelope - Risks of Infection 201206

Scenario:
You are sitting with a friend in a room socially distanced at 10 feet and no masks. There is no forced ventilation and the windows are closed. Your friend is infected but neither of you know this. What is your risk?

Calculation inputs:
room = 15x15x8 cu ft = 1800 cu ft
VSR (viral shed rate of asymptomatic person) = 50 virons/breath
Respiratory rate = 10 breaths/min
Lung capacity = 0.5L = 0.02 cu ft
Contact time = 30 min

Calculations:
Respired virons after 30 min = 10 b/m x 50 v/b x 30 min = 15,000 virons
Virons per cu ft in room after 30 min = 15000 v/1800 cu ft = 8 v/cu ft
Virons you breath in 30 min = 10 b/m x 0.02 cu ft/m x 8 v/cu ft x 30 m = 48 virons

Now lets open the windows and place a fan in the window for an air turnover of 6/hour so after 30 min there have been 3 turnovers (based on CO2 levels) reducing the viron concentration to an approximate 5000 virons and your breathed in exposure to 16 virons.

Assumptions:
Number of virons to infect you is unknown;
VSR is not established
Minimum virons to infect highly variable
CO2 concentration is a proxy for air turnover

Bottom line: The purpose of this Back of the Envelope is to outline a process for evaluating assumptions and establishing what kinds of information are missing. The real risks have caveats, but wearing masks, keeping your distance, and clean air all reduce your risk.

ref:
1] https://heavy.com/news/2020/08/ventilation-air-filtration-coronavirus-covid19-indoors/
Outdoors, CO2 levels are just above 400 parts per million (ppm). A well ventilated room will have around 800 ppm of CO2. Any higher than that and it is a sign the room might need more ventilation.