Quantum Phaith

Obviously, either I do not know how to spell “faith,” or I am making a play on words—like physics. 

A few years ago, I wrote a book with this title (still in print), ISBN 9781257904518. Since this book is about faith and physics, I just simply joined the words: physics + faith = phaith.  The content of the book explains why I joined two seemingly disparate concepts, the physical and the spiritual.

Shortly after publishing the book, I discovered that there is another book entitled Quantum Faith (probably much better than mine). In order to distinguish my work from the other, I decided to write this blog.

If you read the Foreword of the book, you might think I am rather blunt.  I should note here that what appears in the body of the book is entirely my opinion.  It does not represent the view of a Southern Baptist church, were I might be considered heretic, and not churches like Pulpit Rock, where I might be considered a traditionalist.  It does however represent many years of careful study of the mathematical nature of physics and of God’s Word.

I am not a graduate of seminary, not a pastor, or a teacher of religion.  I am a simple (really simple) mathematician.  I went to college at Mercer University in Macon, GA, where I studied Biology and Christianity.  I studied mathematics at the Colorado School of mines for my Masters education, and received my Ph.D. in mathematics at the University of Northern Colorado.  I studied New Testament Greek for a year at Fuller, and taught mathematics, statistics, and operations research at a variety of institutions.

I once had the great privilege of teaching an experimental multivariable calculus and physics course at the United States Military Academy to cadets whom I felt were smarter than I was.  In total, I taught there for six years, and one of the greatest ‘take-aways’ was that some of the nation’s finest young soon-to-be officers are men of great faith—actually of quantum phaith—who allow Christ to work through them for greatness.

I am now working in the financial industry, using logical models to predict various consumer behaviors given certain stimuli.  I have written a few, more technical books, but this one demands a larger readership.

My own faith does not come from books.  In fact, I have heard it said that belief is what someone else teaches you, while faith is something you learn for yourself.  I spent about five years commanding cavalry troops from the platoon to company level during the cold war, and I learned much of my faith while engaged in some very trying experiences on the former Czech border.  I also learned much about faith going through two graduate programs in mathematics, which I was ill prepared for.  My wife, Laurie is also responsible for contributing to my faith education (in a positive way, of course).  Together, we have been through the births of our children, death of siblings and parents, deaths of soldiers we commanded, divorces of friends we love, and many other life tragedies.  I have had two near death experiences with pulmonary emboli, so life has a different meaning for me, and death is not something of which I am afraid.

Quantum Phaith is about what I have discovered about faith, and how my interpretation of mathematics and physics has emerged from that faith.  It is what I am now calling “quantum phaith.”

The emphasis here is how faith made math and physics make sense, not the other way around.  Hence, my a priori is faith in the Lord Jesus Christ.  So not only do I write with presuppositions—imposed by life and careful study—but under the influence of the Living Savior.  Though the way I earn my living depends greatly upon mathematics and physics—I use them every day—they are not first principles, as we will see later.

Big Bang Theorist, evolutionist, and some creationist will not be happy with the content of this book—it may not be for you.  On the other hand, opponents and proponents may find it entertaining.  It is technical to some extent, but not too technical.  I have not used mathematical formulae or formal theorems—except to restate some well-known ones—and Jeff Goldblum (Jurassic Park), Jessica Rabbit (Who Framed Roger Rabbit), and Julia Roberts (Conspiracy Theory) all have parts in the story.  Other role players include George Cantor, Isaac Newton, Albert Einstein, Kurt Gödel, and Karl Heisenberg.  The Koch Snowflake, the Mandelbrot Set, Chaos Theory, Quantum Particles, and Number Theory liven up the action.  Though it may not seem, the book is about faith!

In the book I examine inductive reasoning and inductive Bible study.  I explore the Seven Weeks of Daniel, the Four Horsemen (I  mean Equestrians of Revelation), the Beginning, and more.  I lay out a Biblical Model and quantum particle model—the Standard Model—and draw analogies of spiritual things with physical things.

I hope that you will not find this too technical (my grammar checker says it is at a tenth grade reading level).  The most complex math is the Frank Equation (cabbages + some stuff = Frank) in Chapter 4.  I discuss quantum particles, such as quarks and leptons, but I explain these as clearly as possible in the text with words and pictures, or in footnotes.  I cannot pronounce words with more than two syllables, so I have reduced technical terms to the minimum and defined them.  The most difficult part may be the Greek and Hebrew, but the words are spelled out in their English phonics, for example, φωνηω = phoneo—meaning call, from which we get the English word phone.

Mainly, this book is about faith, based on Scripture—Old and New Testaments—and experience.  In speaking of the Old and New Testament, someone has stated,

The New is in the Old concealed

The Old is in the New revealed

The New is in the Old contained

The Old is in the New explained

Jeffrey S. Strickland

President

Simulation Educators

Colorado Springs, CO, “where God spends most of His time”

Bless My Hands for War

Nothing simulation about this blog. I have often told people that I felt like John Nash, a schizophrenic mathematician, but we all are just a little crazy. Have you felt the presence of other people around you that no one else felt, maybe saints, angels, demons, other spirits from another dimension in our quantum universe? Ever hear voices, audible or just barely discernible in you subconscious? Ever feel as though someone has walked past you, sensing the slight breeze left by their passing, but looking up to see no one? I would have laughed at you if you admitted any of these phenomena, and told you to not watch so many movies.

Then it started happening to me. I had been suffering from a severe sinus infections along with vertigo, and with those conditions and the medications used to treat them, I should not have been surprise if my cat started talking or I woke up with my head stapled to the carpet. However, I do not have a cat, and I am not Chevy Chase, and Cousin Eddie is not here for Christmas.

But there are some guys in my basement, real or imaginary, natural or supernatural; I see them nearly every night. We don't talk, and we barely pay attention to one another. I never see their faces, they do not seem to want me to. They sit and rise as quickly as they sat. They move back and forth. They have shown no sign of being good or evil. But if I am not in my basement at night, the call out to me with a sub-audible voice, requesting my presence.

Pretty weird so far? Well it has not gotten any weirder yet. Except tonight I thought they wanted me to bring my ammunition and consecrate it. I was not sure what that entailed and I don't know how to do it, and while I was sitting there trying to figure it out, I began to think "Bless my hands for war." Strange except I have said that many time to God between 1981 and 2005 when I was a soldier warrior. But why would God or anyone for that matter want me to have blessed war hands. War is for young people, who can do forty push-ups and not wind up in traction. War is for the young at heart and the quick at mind. But David prayed to God in Psalm 144 saying this:

1 Blessed be the Lord, ^my rock,

Who ^trains my hands for war,

And my fingers for battle;

2 My lovingkindness and ^my fortress,

My ^stronghold and my deliverer,

My ^shield and He in whom I take refuge,

Who ^subdues ^my people under me.

3 O Lord, ^what is man, that You take knowledge of him?

Or the son of man, that You think of him?

4 ^Man is like a mere breath;

His ^days are like a passing shadow.

New American Standard Bible : 1995 update. 1995 . The Lockman Foundation: LaHabra, CA

I am certainly no king fighting to gain control of a kingdom from a man whom I swore I would never bring harm to, and thus proved it many times as Saul was often within David's reach. I am not on the run from a king and his soldiers as they seek to take my life, and thus my claim to the thrown. And before you get carried away with analogies, I do not see any resemblance between this account and our current situation in America. This was specifically regarding God's chosen people, his chosen King, and His Chosen nation, Israel. Do not try to take it out of its proper context!

So what is the point? And then it hit me like a .380 hollow-point square in the forehead.

Psalm 144:3-4. "O Lord, ^what is man, that You take knowledge of him?

Or the son of man, that You think of him? ^Man is like a mere breath;

His ^days are like a passing shadow."

Well, it seems that the whole encounter has nothing to do with becoming John Nash-like (I am certain not to win a Nobel prize). It has nothing to do with weapons and ammunition, wars nor rumors of wars. It only has to do with "what is man, that God would even acknowledge his very existence, it being like a breath among an eternity of breathing. Yep, I am here for one tick on the timeline. And so are you, and so are our leaders. If our current administration were to serve five terms, it is just a breath to God.

David had figured out two important things: (1) Saul's reign as king would pass, and (2) David's own reign would pass, and even his own kingdom would pass.

What a dreary thought. Someone has said that we begin to die the moment we are born. Perhaps they had insight into the quantum.

If you look at the remainder of Psalm 144, David cries out to be rescued from his desperate situation. But by the time he reached verse 15, something has changed, and he requites saying: "How blessed is the people whose God is the Lord."

God need not bless my hands to war, my country to greatness, my works to Pulitzer caliber. God has already blessed me, forgiven me, accepted me, and the rest is just a breath...

I don’t know if my “friends will be returning”, it looks like they have left for the night and I feel like I have permission to go to bed. I hope the guys in white jackets will not be here when I awake.

 

Jeffrey Strickland, Ph.D.

 

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Uplift (Netlift) Modeling

This blog describes basic concepts, benefits and challenges of implementation of Net Lift Models in direct marketing campaigns.  Net lift models predict which customer segments are likely to make a purchase ONLY if prompted by a marketing undertaking.  The modeling work was conducted using stepwise logistic regression in SAS Enterprise Miner ®.

The paper provides examples how net lift probability decomposition models leveraged differences between purchasers in test group and control group to predict which customer segments need a marketing contact and which customers segments are likely to make purchasing decision without a nudge.

TRADITIONAL APPROACH TO DIRECT MARKETING LIST MODELING

Majority of direct marketing campaigns are based on purchase propensity models, selecting customer email, paper mail or other marketing contact lists based on customers’ probability to make a purchase.

 

Scoring Rank	Response Rate	Lift
1	28.1%	3.41
2	17.3%	2.10
3	9.6%	1.17
4	8.4%	1.02
5	4.8%	0.58
6	3.9%	0.47
7	3.3%	0.40
8	3.4%	0.41
9	3.5%	0.42
10	0.1%	0.01
Total	8.2%

 

Table 1. Example of standard purchase propensity model output used to generate direct campaign mailing list at 1800Flowers.com

This purchase propensity model had a ‘nice’ lift (rank’s response rate over total response rate) for the top 4 ranks on the validation data set. Consequently, we would contact customers included in top 4 ranks. After the catalog campaign had been completed, we conducted post analysis of mailing list performance vs. control group. The control group consisted of customers who were not contacted, grouped by the same purchase probability scoring ranks.

Sample campaign post analysis results:

	Mailing Group
Scoring Rank	Response Rate
1	27.0%
2	20.3%
3	10.7%
4	8.9%
Total	16.7%

Control Group

Response Rate

27.9%

20.9%

10.0%

7.5%

16.5%

Incremental Response Rate

-0.91%

-0.56%

0.66%

1.38%

0.15%

 








Table 2. Campaign Post analysis

As shown the table 2, the top four customer ranks selected by propensity model perform we and control group. However, even though mailing/test group response rate was at decent le incremental response rate (mailing group net of control group) for combined top 4 ranks was low incremental response rate, our undertaking would be likely generating a negative ROI.

What was the reason that our campaign shown such poor incremental results? The purchase propensity model did its job well and we did send an offer to people who were likely to make a purchase. Apparently, modeling based on expected purchase propensity is not always the right solution for a successful direct marking campaign. Since there was no increase in response rate over control group, we could have been contacting customers who would have bought our product without promotional direct mail. Customers in top ranks of purchase propensity model may not need a nudge or they are buying in response to a contact via other channels. If that is the case, the customers in the lower purchase propensity ranks would be more ‘responsive’ to a marketing contact.

We should be predicting incremental impact – additional purchases generated by a campaign, not purchases that would be made without the contact. Our marketing mailing can be substantially more cost efficient if we don’t mail customers who are going to buy anyway.

Since customers very rarely use promo codes from catalogs or click on web display ads, it is difficult to identify undecided, swing customer based on the promotion codes or web display clickthroughs.

Net lift models predict which customer segments are likely to make a purchase ONLY if prompted by a marketing undertaking.

Purchasers from mailing group include customers that needed a nudge, however, all purchasers in the holdout/control group did not need our catalog to made their purchasing decision. All purchasers in the control group can be classified as ‘need no contact’. Since we need a model that would separate ‘need contact’ purchasers from ‘no contact’ purchasers, the net lift models look at differences in purchasers in mailing (contact) group versus purchasers from control group.

In order to classify our customers into these groups we need mailing group and control group purchases results from similar prior campaigns. If there are no comparable historic undertakings, we have to create a small scale trial before the main rollout.

All models described in this project used stepwise logistic regression on data partitioned into test and validation sets. All data prep work was done in base SAS ® and all modeling was done in SAS Enterprise Miner ®.

NET LIFT MODELS

There has been recent mentions of a target selection (i.e., case selection) technique referred to as net lift, uplift, incremental response, differential response, and possible other names.  When posed as a return maximization problem, net lift and the usual target selection practice coincide.  Net lift applies to target selection in situations with a binary treatment; return maximization provides direction on how to handle problems in situations with more than one treatment.

Definition of Uplift modeling: Analytically modeling to predict the influence on a customer's buying behavior that results from choosing one marketing treatment (customer-facing action) over another. The secondary treatment is often passive – make no contact – as evaluated over a control group. The uplift model answers the question, “How much more likely is this treatment to generate the desired outcome than the alternative treatment?” For each customer, the model's prediction drives the decision of which treatment to apply [3].

Problem statement

Given the following data [2]:

·         Cases P = {1,…,n},

·         Treatments J = {1,…,U},

·         expected return R(i,t) for each case  and treatment ,

·         non-negative integers n₁,…,n_U  such that

n₁ + … + n_U = n

find a treatment assignment

f: P→J

so that the total return

∑_{[i=1 to n]} R_if(i)

is maximized, subject to the constraints that the number of cases assigned to treatment j is not to exceed n_j (j=1,…,U) [2].

Example 1: Mailing campaign

·         P: a group of customers,

·         two treatments:

1.       treatment 1: send a promotional coupon; R_i1  is the expected return if a coupon is sent to customer i,

2.       treatment 2: no coupon is sent; the expected return is zero: R_i2 = 0

Solution to the maximization problem:

•         assign treatment 1 to the customers with the n₁  largest values of R_i1

•         assign treatment 2 to the remaining customers

This solution can also be derived from the Neyman-Pearson lemma.

Example 2: Marketing action case

•         P: a group of customers,

•         two treatments:

•         treatment 1: exercise some marketing action; R_i1 is the expected return if treatment 1 is given to customer i,

•         treatment 2: exercise no the marketing action; let R_i2 be the expected return if treatment 2 is given to customer

Solution to the maximization problem:

The second sum does not involve f, so maximizing total return is equivalent to maximizing the first term

As for to the solution to Example 1, to attain the maximum return:

•         assign treatment 1 to the customers with the n₁ largest values of R_i1 – R_i2  

•         assign treatment 2 to the remaining customers

The difference R_i1 – R_i2   is called net lift, uplift, incremental response, differential response, etc.

If one considers only the response to treatment 1, bases targeting on a model built out of responses to previous marketing actions, one is proceeding as if the situation were as in Example1. One would mistakenly maximize

Such maximization would not yield the maximum return. One needs to consider the return from cases subjected to no marketing action.

Example 3: A toy example

Consider the following toy example with a population of n = 3 cases, and U = 3 treatments, n₁ = n₂ = n₃ = 1  and returns:

This  assignment is one that maximizes total return under the given constraints:

 

 
Note that neither case 2 nor case 3 were assigned the treatment that maximize their return.

Although the possibility of a return of 18 exists, this possibility is not realized, since case 2 is not assigned treatment 2.

 (In a case like this, one would probably advice that more resources be allocated to treatment 2, so that n₂ > 1.)

 

Example 4: General case

The problem can be cast as a standard integer linear programming problem. If we let

 

then the problem can be written as:

 

subject to the constraints:

 

Note:

In general, the best assignment that solves the linear programming problem does not vary continuously with the coefficients:

•         small changes in the returns R_ij  result in only small changes in the best total return,

•         but, the assignment that yields the best return may vary considerably.

Example 5: A (n almost real) example and variation

Each week, a call center is responsible for contacting a group of customers. The length n of the list is not fixed, but it does not vary much from week to week.

Based on what is known of the customers, and on historical observations, it is possible to estimate the expected probability of successfully contacting each customer at different combinations of time of the day and call type (“home” or “other”).

Un-adjusted probabilities of successful contact are not constant in time…

Problem: make a (calling time, weekday) assignment so that expected total number of contacts is maximized, subject to the constraint that the call centre capacity is limited.

Remarks:

•         in general, we will only know an estimate of R_ij:

which suggests that insisting on solving the full maximization problem is an over-kill

•         in practice, proper call optimization is carried dynamically

A solution sketch:

•         segment customers, including the probabilities of successful contact at different times as segmentation variables, so that the probability of contact is approximately constant for the segment

•         solve the optimization problem for the fraction of each segment that has to be contacted at each time

NET LIFT MODELING APPROACH – PROBABILITY DECOMPOSITION MODELS

Segments used in probability decomposition models:

	Contacted Group	Control Group
Purchasers prompted by contact	A	D
Purchasers not needing contact	B	E
NonPurchasers	C	F

 

Figure 2. Segments in probability decomposition models

Standard purchase propensity models are only capable of predicting all purchasers (combined segments A and B). The probability decomposition model predicts purchasers segments that need to be contacted (segment A) by leveraging two logistic regression models, as shown in the formula below [1].

P(A I AUBUC) =	P(AUB I AUBUC) x	(2 - 1/P(AUB I AUBUE))
Probability of purchase prompted by contact	Probability of purchase out of contact group	Probability of purchaser being in contact group out of all purchasers

 

Summary of probability decomposition modeling process:

1.       Build stepwise logistic regression purchase propensity model (M1) and record model score for every customer in a modeled population.

2.       Use past campaign results or small scale trial campaign results to create a dataset with two equal size sections of purchasers from contact group and control group. Build a stepwise regression logistic model predicting which purchasers are from the contact group. The main task of this model will be to penalize the score of model built in the step 1 when purchaser is not likely to need contact.

3.       Calculate net purchasers score based on probability decomposition formula

Results of the probability decomposition modeling process for marketing offer mailing.

 

S co ring R a nk	Co nta ct Gro up R e sp o nse %	Co ntro l Gro up R e sp o nse %	Incre me nta l R e sp o nse R a te
1	18.8%	12.9%	5.9%
2	7.8%	5.4%	2.4%
3	6.9%	4.5%	2.5%
4	4.3%	3.6%	0.7%
5	3.9%	3.5%	0.4%
6	4.1%	4.1%	0.0%
7	3.7%	4.0%	-0.2%
8	4.7%	4.1%	0.6%
9	5.0%	6.7%	-1.7%
10	11.0%	15.7%	-4.7%

 

Table 3. Post analysis of campaign leveraging probability decomposition model

Scoring Ranks 1 thru 6 show positive incremental response rates. The scoring ranks are ordered based on the incremental response rates.

CONCLUSION

The probability decomposition model is just one in a group of methods known as net lift models. The net lift models help maximize ROI of marketing campaigns as they let us avoid contacting customers or prospects who are highly likely to buy a product or service anyway. The traditional purchase propensity model may do a good job ranking customers based on their probability to make a purchase but it does not have the ability to select the true responders, the customers who will only make a purchase if contacted. The probability decomposition model has its challenges; it is relatively difficult to interpret as it combines scores of two separate model scores. Following is a list of conditions required for net lift model:

•         presence of randomized control group

•         analyzed marketing contact is not the only communication leading to purchase

•         purchase rate is not correlated to lift, purchase propensity model is not sufficient

•         presence of similar/repetitive marketing campaigns or small scale tests

•         variation in average lift across scoring ranks

References

1.       Jun Zhong, VP Targeting and Analytics, Card Services Customer Marketing, Wells Fargo in the presentation: “Predictive Modeling & Today’s Growing Data Challnges” at Predictive Analytics World in San Francisco, CA in 2009.

2.       Lo, Victor S.Y. “The True Lift Model - A Novel Data Mining Approach to Response Modeling” in Database Marketing, SIGKDD Explorations. Volume 4 (2002), Issue 2, pg 78-86

3.       Siegel, Eric, “Uplift Modeling: Predictive Analytics Can’t Optimize Marketing Decisions Without It”, Predictive Impact, Inc., 2011.