My Research in Statistics

CMC-Based Modeling — the Approach and Its Performance Evaluation

This post explains the central role of Continuous Monotone Convexity (CMC) in Response Modeling Methodology (RMM).

In earlier blog entries, the unique effectiveness of the Box-Cox transformation (BCT) was addressed. I concluded that the BCT effectiveness could probably be attributed to the Continuous Monotone Convexity (CMC) property, unique to the inverse BCT (IBCT). Rather than requiring the analyst to specify a model in advance (prior to analysis), the CMC property allows the data, via parameter estimation, determine the final form of the model (linear, power or exponential). This would most likely lead to better fit of the—estimated model, as cumulative reported experience with implementation of IBCT (or BCT) clearly attest to.

In the most recent blog entry in this series, I have introduced the “Ladder of Monotone Convex Functions”, and have demonstrated that IBCT delivers only the first three “steps” of the Ladder. Furthermore, IBCT can be extended so that a single general model can represent all monotone convex functions belonging to the Ladder. This transforms monotone convexity into a continuous spectrum so that the discrete “steps” of the Ladder (the separate models) become mere points on that spectrum.

In this third entry on the subject (and Article #3, linked below), I introduce in a more comprehensive fashion (yet minimally technical) the general model from which all the Ladder functions can be derived as special cases. This model was initially conceived in the last years of the previous century (Shore, 2005, and references therein) and had since been developed into a comprehensive modeling approach, denoted Response Modeling Methodology (RMM). In the affiliated article, an axiomatic derivation of RMM basic model is outlined and specific adaptations of RMM to model systematic variation and to model random variation are addressed. Published evidence for the capability of RMM to replace current published models, previously derived within various scientific and engineering disciplines as either theoretical, empirical or semi-empirical models, is reviewed. Disciplines surveyed include chemical engineering, software quality engineering, process capability analysis, ecology and ultra-sound-based fetal-growth modeling (based on cross-sectional data).

This blog entry (with the linked article given below) was originally posted on the site of the American Statistical Association (ASA), where the linked article was visible to members only.

Haim Shore_3_ASA_Jan 2014

General Statistical Applications

Determining measurement-error requirements to satisfy statistical-process-control performance requirements (Presentation, English)

On January 6th, 2014, I have delivered a talk that carried the title, as displayed above.

The talk was given in the framework of a workshop organized by the Open University of Israel (see details at the bottom of the opening screen of the presentation). It was based on my article of 2004:

Shore, H. (2004). Determining measurement error requirements to satisfy statistical process control performance requirements. IIE Transactions, 36(9): 881-890.
A link to this presentation, in PDF format, is given below:
Open University_Measurement Error and SPC_Haim Shore Presentation_Jan 2014
The lecture (in English) may be viewed at:
My Research in Statistics

The “Continuous Monotone Convexity (CMC)” Property and its ‎Implications to Statistical Modeling

In a previous post in this series, I have discussed reasons for the effectiveness of the Box-Cox (BC) transformation, particularly when applied to a response variable within linear regression analysis. The final conclusion was that this effectiveness could probably be attributed to the “Continuous Monotone Convexity (CMC)” property, owned by the inverse BC transformation. It was emphasized that the latter, comprising the three most fundamental monotone convex functions, the “linear-power-exponential” trio, delivers only partial representation to a whole host of models of monotone convex relationships, which can be arranged in a hierarchy of monotone convexity. This hierarchy had been denoted the “Ladder of Monotone Convex Functions.”

In this post (and Article #2, linked below), I address in more detail the nature of the CMC property. I specify models included in the Ladder, and show how one can deliver, via a single model, representation to all models belonging to the Ladder (analogously with the inverse BC transformation, a special case of that model). Furthermore, I point to published evidence demonstrating that models of the Ladder may often substitute, with negligible loss in accuracy, published models of monotone convexity, which had been derived from theoretical discipline-specific considerations.

This blog entry (with the linked article given below) was originally posted on the site of the American Statistical Association (ASA), where the linked article was visible to members only.

Haim Shore_2_ASA_Dec 2013

My Research on the Bible and Biblical Hebrew

Hebrew-English presentation on the Bible and on biblical Hebrew (with color ‎graphics)‎

This presentation expounds on various research findings given in my book: “Coincidences in the Bible and in Biblical Hebrew” (Shore, 2 Ed., 2012).

The book is now available for free download at this blog’s home page (“About“).

Presentation is divided into eight parts:

  • “Laban – the Case of a Lost Identity” (Ch. 15 in the book; in Hebrew);
  • “Chance” and “Cold” – two separately developed scientific concepts of entropy that are actually one (and also expressed by a single word root in biblical Hebrew; Ch. 3 in the book; Hebrew);
  • Average lunar month according to Jewish sources (Ch. 18 in the book; Hebrew; See also separate blog entry on the subject);
  • “When a sample of observations are aligned on a straight line”: “A parable” about measuring temperatures on both Celsius and Fahrenheit scales (Ch. 23 in the book; English);
  • Relationships between numerical values of sets of Hebrew words and related physical traits (three consecutive examples with color plots; Hebrew-English):
    • Example 1: Time-cycles (“Day, Month, Year”; Ch. 12 in the book);
    • Example 2: Celestial diameters (“Moon, Earth, Sun”; Ch. 8 in the book);
    • Example 3: Velocity (“Light, Sound, Standstill” or “Lightening, Thunder, Silence”; Ch. 21 in the book);
  • Results from a computer simulation study aimed to estimate probabilities (Hebrew);
  • The planets example (An extensive example of relationships of size-sorted physical traits of celestial bodies to numerically sorted biblical names; Hebrew-English);
  • Genesis creation story – A statistical analysis (English);

To watch the PDF file in presentation mode, open with Adobe Reader and then go to: View -> Full Screen Mode. To manipulate slides click mouse-left to advance and mouse-right to retreat to previous slide.

Prof Haim Shore presentation_Bible and biblical Hebrew research_March 2016

My Research on the Bible and Biblical Hebrew

New Articles Related to My Research on the Bible and Biblical Hebrew

In this new blog entry, I deliver links to three new documents related mostly to the statistical analyses associated with my research on the Bible and on biblical Hebrew:

1. Three chapters from my book: “Coincidences in the Bible and in Biblical Hebrew”. These chapters mostly address the statistical perspective of my research work, as expounded in the book. Bookmarks may assist navigating between chapters:

Coincidences in the Bible and in Biblical Hebrew_Book by Haim Shore_2nd Revision_2012_Three Sample Chapters

2. An article in Hebrew, published recently in “Ha-mahapach 3”, by Rav Zamir Cohen of Hidabrut Oganization.

הידברות מקריות בתורה ובשבת הקודש

3. An article invited by Rav Zamir Cohen for the upcoming book “Ha-Mahapach 4”. The article explains how average lunar month duration can be calculated, from ancient Jewish sources (including the Hebrew Bible), to be 29.530594 days vs. NASA’s estimate of 29.530589 days.

פרופ שור_משך ירח הלבנה הממוצע_עבור המהפך 4_הידברות

My Research in Statistics

Why is Box-Cox transformation so effective?

The Box-Cox transformation and why is it so effective has intrigued my curiosity for many years. I have had the opportunity to talk both to Box and to Cox about their transformation (Box and Cox, 1964).

I conversed with the late George Box (deceased last March at age 94) when I was a visitor in Madison, Wisconsin, back in 1993-4.

A few years later I talked to David Cox at a conference on reliability in Bordeaux (MMR’2000).

I asked them both the same question, I received the same response.

The question was: What was the theory that led to the derivation of the Box-Cox transformation?

The answer was: “No theory. This was a purely empirical observation”.

The question therefore remains: Why is the Box-Cox transformation so effective, in particular when applied to a response variable in the framework of linear regression analysis?

In a new article, posted in my personal library at the American Statistical Association (ASA) site, I discuss this issue at some length. The article is now generally available for download here (Article #1 below).

Haim Shore_1_ASA_Nov 2013

My Research on the Bible and Biblical Hebrew

Free downloads at author’s personal home site

My book: “Coincidences in the Bible and in Biblical Hebrew” (2nd Ed., 2012) is available for free download at this blog’s home page (“About“).

Further Free downloads at author’s personal home site

My Research on the Bible and Biblical Hebrew

An Interview with the Author in The Jerusalem Post (Dec. 4th, 2009)

Link to an interview with professor Haim Shore, about his statistical analysis research of the Bible and biblical Hebrew, on The Jerusalem Post (Dec. 4th, 2009) :

An Interview with the Author in the Jerusalem Post (Dec., 4th, 2009)