Categories
My Research on the Bible and Biblical Hebrew Podcasts (audio)

“Diber” or “Dever” – Two Modes of Divine Dialogue with Humankind in a World of Free-Will (Podcast)

The Ten Commandments, in their original biblical Hebrew, are — The Ten Devarim, or Ten Dibrot (the singular of which is Diber); The Holy of Holies, where the tablets with the Ten Commandments were held in the Jewish temple, is — Dvir; A plague is — Dever.

All these share a common root in biblical Hebrew — D.B.R (ד.ב.ר).

What does this root mean?

Categories
Historical Coincidences My Research on the Bible and Biblical Hebrew Shorties

A Succinct Description of Current Status of Israel

Deuteronomy 32:21:

“They have made Me jealous with Lo-El (literally, “No-God“),

provoked Me to anger with their vanities (Havalim, literally, “Nonsense“);

And I will move them to jealousy with Lo-Am (literally, “Non-people“),

with Goy-Naval (literally, “vile-nation“) will I provoke them to anger”.

Categories
My Research in Statistics Podcasts (audio)

Where Statistics Went Wrong Modeling Random Variation (Podcast)


To-date, within the Statistics literature, one may literally find thousands of statistical distributions.  

Is this acceptable?

Or perhaps we are wrong in how we model random variation?

The related post, with references:

Where Statistics Went Wrong Modeling Random Variation

References:

My Trilogy of Articles on Surgery Times – Now Complete (Published)

Categories
My Research in Statistics

Where Statistics Went Wrong Modeling Random Variation

(Related podcast: Where Statistics Went Wrong Modeling Random Variation (Podcast) )

A model of random variation, generated by a “random variable”, is presented in Statistics in the form of a statistical distribution (like the normal or the exponential).

For example, the weight of people at a certain age is a random variable, and its observed variation may be modeled by the normal distribution; Surgery duration is a random variable, and its observed variation may, at a specified circumstance, be modeled by the exponential distribution.

In the Statistics literature, one may find statistical distributions modeling random variation directly observed in nature (as the above two examples), or random variation associated with a function of random variables (like a sample average calculated from a sample of n observations).

To-date, within the Statistics literature, one may literally find thousands of statistical distributions.  

Is this acceptable?

Or perhaps we are wrong in how we model random variation?

Pursuant to a large-scale project, where I have modeled surgery times (a research effort reported in three recent publications, Shore 2020ab, 2021), I have reached certain conclusions of how random variation should be modeled as to be more truthful to reality. The new approach seems to reduce the problem of the insanely gigantic number of distributions, as currently appearing in the Statistics literature.

I have summarized these new insights in a new paper, carrying the title of the post.

The Introduction section of this paper is posted below. Underneath it, one may find a link to the entire article.

Where Statistics Went Wrong Modeling Random Variation

  1. Introduction

The development of thousands of statistical distributions to-date is puzzling, if not bizarre. An innocent observer may wonder, how in most other branches of science the historical development shows a clear trend towards unifying the “objects of enquiry” (forces in physics; properties of materials in chemistry; human characteristics in biology), this has not taken place within the mathematical modelling of random variation? Why in Statistics, as the branch of science engaged in modeling random variation observed in nature, the number of “objects of enquiry” (statistical distributions) keeps growing?

In other words: Where has Statistics gone wrong modeling observed random variation?

Based on new insights, gained from a recent personal experience with data-based modeling of surgery time (resulting in a trilogy of published papers, Shore 2020ab, 2021), we present in this paper a new paradigm to modeling observed random variation. A fundamental insight is a new perception of how observed random variation is generated, and how it affects the form of the observed distribution. The latter is perceived to be generated not by a single source of variation (as the common concept of “random variable”, r.v., implies), but by two interacting sources of variation. One source is “Identity”, formed by “identity factors”. This source is represented in the distribution by the mode (if one exists), and it may generate identity-variation. A detailed example for this source, regarding modeling of surgery times, is presented in Shore (2020a). Another source is an interacting error, formed by “non-identity/error factors”. This source generates error variation (separate from identity variation). Combined, the two interacting sources generate the observed random variation. The random phenomenon, generating the latter, may be in two extreme states: An identity-full state (there is only error variation), and an identity-less state (identity factors become so unstable as to be indistinguishable from error factors; identity vanishes; no error can be defined). Scenarios, residing in between these two extreme states, reflect a source of variation with partial lack of identity (LoI).

The new “Random Identity Paradigm”, attributing two contributing sources to observed random variation (rather than a single one, as to date assumed), has far reaching implications to the true relationships between location, scale and shape moments. These are probed and demonstrated extensively in this paper, with numerous examples from current Statistics literature (relate, in particular, to Section 3).

In this paper, we first introduce, in Section 2, basic terms and definitions that form the skeleton for the new random-identity paradigm. Section 3 addresses implications of the new paradigm in the form of six propositions (subsection 3.1) and five predictions (presented as conjectures, subsection 3.2). The latter are empirically supported, in Section 4, with examples from the published Statistics literature. A general model for observed random variation (Shore, 2020a), bridging the gap between current models for the two extreme states (normal, for identity-full state; exponential, for the other), is reviewed in Section 5, and its properties and implications probed. Section 6 delivers some concluding comments.

A link to the complete article:

Categories
Historical Coincidences My Research on the Bible and Biblical Hebrew Shorties

Shorty: When was an Earlier Climate Change and What Caused it?

Earlier Climate Change:

“In the sixth hundredth year of Noah’s life, in the second month, the seventeenth day of the month, on that day all the fountains of the great deep burst forth, and the floodgates of the heavens were opened. And rain fell on the earth for forty days and forty nights” (Genesis 7:11-12).

What Caused It:

“Now, the earth was corrupted in front of God, and the earth was filled with Chamas” (plunder, extortion). “And God looked upon the earth, and, behold, it was corrupted because all flesh had corrupted its ways upon the earth” (Genesis 6:11-12).

Categories
General My Research on the Bible and Biblical Hebrew

How to Build a GAG (Roof) in Two Steps

In an earlier post, we have addressed the significance of GAG (roof in biblical Hebrew). The word comprises two appearances of the second most rare letter in the Hebrew alphabet, the third letter, Gimmel (corresponding to the letter g in English).

In an added comment, I have observed that the two major sins of the Israelites, on their way to the Promised Land, are denoted, in Hebrew, the Sin of The Egel (Sin of the Golden Calf), and the Sin of The Meraglim (Sin of the Spies). For both sins, the Hebrew names include Gimmel as their middle letter. Combined, the two sins form a particular version of Gag, the Israelite Gag.

As the Bible tells us, both sins were responded by extreme Divine wrath.

Reacting to the sin of the Egel, God said to Moses:

“Now, therefore, let me alone, that my wrath may burn against them and that I may consume them; and I will make of thee a great nation” (Exodus 32:10).

Reacting to the sin of the Meraglim, God said to Moses:

“..How long will this people provoke me and how long will they not believe in me for all the signs which I have performed amongst them? I will smite them with the pestilence (Dever), and disinherit them, and will make of thee a great nation and mightier than them” (Numbers 14:11-12).

Moses prayed to God, and his prayer mitigated the severity of the intended Divine punishment.

According to Jewish tradition, as reflected in Talmud and affiliated interpretations, the Jewish people, for generations to come, had to pay dearly for these two sins. For example, the sin of the Meraglim occurred, according to Jewish tradition, on the ninth of the Hebrew month of Av. This date is known in Jewish tradition (and possibly also historically) to be also the date when the First Temple and The Second Temple of Jerusalem were destroyed. Other catastrophes that befell the Jewish people throughout history (like the expulsion from Spain, 1492) had also taken place on that date.

Reading these two episodes in the Bible, the Egel episode and the Meraglim episode, one cannot escape the conclusion that with these two sins, combined, the Israelites have created their own particular form of Roof (Gag), namely, a disconnect between The Heaven and The Earth.

Unlike the Gag of Agag, king of Amalek, Hamman the Agagite, Gog and Magog, a Gag formed with an explicit intention to disconnect The Heaven and The Earth (Genesis 1:1; refer to the earlier linked post), the Israelites formed a particular version of Gag, one that is not deliberately pre-planned, one that is not intentional.

What can we learn from this particular form of Gag? Can we construct a similar Gag?

The two sins teach us a powerful lesson of how to construct own personal Gag. We detail herewith a two-step procedure to achieve this goal.

Step 1: Repeat The First Sin (of the Egel): “Dancing around a Golden Calf”.

Explanation: Build your whole life around a materialistic objective, like gold (money), fame, territory and other similar materialistic assets.

Step 2: Repeat The Second Sin (of the Meraglim): “Slander and refusal to go to the Promised Land” (for whatever excuses).

 Explanation: The latter involves two elements:

  • The spies spoke ill of the Promised Land. The Israelites spoke ill of God (Deuteronomy 1:27). Therefore, Prescription A:

“Speak ill of all, all the time” (whether people, Promised Land, God or otherwise);

  • The Israelites refused to “go up” to the Promised Land, giving excuses (Deuteronomy 1:26-27). Therefore, Prescription B:

“Refrain from any attempt to gain blessing awaiting you; Generate your own personal justification to stay passive, idle, to stay lazy” (Example: “…in Jehovah’s hatred of us He had brought us forth out of the land of Egypt..”, Deuteronomy 1:27).

Articulated more succinctly, Step 2 to owning a Gag involves rejecting any possible blessing by avoiding necessary work to be done (”And Elohim blessed the seventh day and sanctified it, because in it He ceased from all his work which Elohim had created to be done”; Genesis 2:3).

We have outlined in this post a two-step prescription to becoming happy by pursuing the two sins of the Israelites, on their way to the Promised Land. The Israelites constructed their own version of Gag, namely, disconnecting the physical dimension of life, The Earth, from the spiritual dimension, The Heaven. As related in the Bible, over and over again, constructing the Gag is guarantee to stop “pouring down” of blessing.

If, to the contrary, the idea of building a personal Gag does not seem that appealing, we may wish to re-consider how Eretz Israel is described in the Bible, which also becomes a faithful description, so we believe, of the most basic human condition on Planet Earth (Deuteronomy 11:11):

“And the land, into which you go to possess it, is a land of hills and valleys; By the rain of the heaven will you drink water”.

Categories
My Research on the Bible and Biblical Hebrew Shorties

Shorty*: How Do the Ten Commandments Comport with Free-Will?

A Divine Commandment is always fulfilled, to the letter.

An example:

“And Elohim said: “Let there be light”, and there was light” (Genesis 1:3).

If that is so.

If divine command, by definition, is always fulfilled:

  • How is it that the same has not materialized with regard to another set of Divine Commandments, the Ten Commandments?
  • How come that since its inception at Mount Sinai, about three thousand and three hundred years ago, we are witnessing violating of the Ten Commandments by the human species throughout history, abundantly, continuously, right, left and center?

And more generally:

How do the Ten Commandments comport with free-will, endowed by The Creator onto humankind, the created?

Free-will is emphasized in the Bible, again and again:

  • “See, I set before you today life, and that which is good; and death, and that which is bad” (Deuteronomy 30:15);
  • “I call Heaven and earth to witness this day against you that I have set before you life and death, blessing and cursing; Therefore, choose life that both you and your seed may live” (Deuteronomy 30:19).

Hebrew prophets, likewise, do not cease to insist (emphasized mine):

  • “He has told thee, O man, what is good and what does Jehovah requires of you, but to do justice and love mercy, and to walk humbly with your God” (Micah 6:8).

If emphasis on free-will is so prevalent throughout the Bible, and given the wide-spread ignoring of the Ten Commandments, throughout history, how should we account for this seeming inconsistency in the Bible?

The answer to this intriguing question is simple and straightforward:

In its original biblical Hebrew, the Bible does not have a concept of “Ten Commandments”.

Instead, biblical Hebrew for the Ten Commandments is “Devarim”.

The root of this word, in its verbal form, means to speak. “Devarim”, literally, implies divine utterances.

A thorough discussion of this concept, with biblical quotes, is delivered in:

“Diber” or “Dever” – Two Modes of Divine Dialogue with Humankind in a World of Free-Will .

* Shorty is a short post

Categories
General Statistical Applications Podcasts (audio)

Why Predictions of Surgery-Duration are So Poor, and a Possible Remedy (Podcast)

Accurate prediction of surgery-duration is key to optimal utilization of operating theatres. Yet, current predictions, based on best available statistical and AI techniques, are highly inaccurate. This causes operating rooms worldwide to operate in a sub-optimal mode. Based on personal experience, supported by recently published three peer-reviewed articles, we believe that the poor state-of-the-art of current predictive methods for surgery-duration is traceable to a single cause. What is it? What is the remedy?

Literature

[1] Shore, H (1986). An approximation for the inverse distribution function of a combination of random variables, with an application to operating theatres. J. Statist. Com. Simul. 1986; 23:157-81. Available on Shore’s ResearchGate page.

[2] Shore, H (2020). An explanatory bi-variate model for surgery-duration and its empirical validation, Communications in Statistics: Case Studies, Data Analysis and Applications, 6:2, 142-166, DOI: 10.1080/23737484.2020.1740066 .

[3] Shore, H (2021a). SPC scheme to monitor surgery-duration. Qual Reliab Eng Int. 37: 1561– 1577. DOI: 10.1002/qre.2813 .

[4] Shore, H (2021b). Estimating operating room utilisation rate for differently distributed surgery times. International Journal of Production Research. DOI: 10.1080/00207543.2021.2009141

[5] Shore, H (2021c). “Predictive Methods for Surgery Duation”Wikipedia. April 16, 2021.

Categories
General Statistical Applications

Why Surgery-Duration Predictions are So Poor, and a Possible Remedy

(Related podcast:  Why Predictions of Surgery-Duration are So Poor, and a Possible Remedy (Podcast)  ).

Operating theatres are the most expensive resource at the disposal of hospitals. This renders optimizing scheduling of surgeries to operating rooms a top priority. A pre-condition to optimal scheduling is that accurate predictions of surgery-duration be available. Much research effort has in recent years been invested to develop methods that improve the accuracy of surgery-duration predictions. This ongoing effort includes both traditional statistical methods and newer Artificial Intelligence (AI) methods. The state-of-the-art of these methods, with relevant peer-reviewed literature, have recently been summarized by us in a new entry on Wikipedia, titled “Predictive Methods for Surgery Duation”.     

Personally, I was first exposed to the problem of predicting surgery-duration over thirty years ago, when I was involved in a large-scale project encompassing all governmental hospitals in Israel (at the time). Partial results of this effort had been reported in my published paper of 1986, and further details can be found in my more recent paper of 2020. Both articles are listed in the literature section at the end of this post (for podcast listeners, this list may be found on haimshore.blog).

My second involvement in developing predictive methods for surgery-duration was in more recent years, culminating in three peer-reviewed published papers (Shore 2020, 2021 ab; see references below).

Surgery-duration is known to be very highly volatile. The larger the variability between surgeries, the less accurate the prediction may be expected to be. To reduce this variability, newly devised predictive methods for surgery-duration tend to concentrate on subsets of surgeries, classified according to some classification system. It is assumed that via this classification, prediction accuracy may be enhanced. A common method to classify surgeries, implemented worldwide, is Current Procedural Terminology (CPT®). This coding system delivers, in a hierarchical fashion, particular codes to subsets of surgeries. In doing so, variability between surgeries sharing same CPT code is expected to be reduced, allowing for better prediction accuracy.

A second effort to increase accuracy is to include, in the predictive method, certain factors, known prior to surgery, which deliver variability to surgery-duration. It is hoped that by taking account of these factors, in the predictive method, unexplained variability in surgery-duration will be reduced, thereby enhancing prediction accuracy (examples will soon be given).

A third factor that influence accuracy is the amount of reliable data, used to generate predictions. Given recent developments in our ability to process large amounts of data, commonly known as Big Data, Artificial Intelligence (AI) methods have been summoned to assist in predicting surgery times.

These new methods and others are surveyed more thoroughly in the aforementioned entry on Wikipedia.

The new methods notwithstanding, current predictive methods for surgery-duration still deliver unsatisfactory accuracy.

Why is that so?

We believe that a major factor for the poor performance of current predictive methods is lack of essential understanding of what constitute major sources of variability to surgery-duration. Based on our own personal experience, as alluded to earlier, and also on our professional background as industrial engineers, specializing in analysis of work processes (of which surgeries are an example), we believe that there are two sets of factors that generate variability in surgery-duration: A set of major factors and a set of secondary factors. We denote these Set 1 and Set 2 (henceforth, we refer only to variability between surgeries within a subset of same code):

Set 1 — Two Major Factors:

  • Factor I. Work-content instability (possibly affected by variability in patient condition);
  • Factor II. Error variability.

Set 2 — Multiple Secondary Factors, like: patient age, professional experience and size of medical team, number of surgeries a surgeon has to perform in a shift, type of anaesthetic administered. 

Let us explain why, in contrast to current practices, we believe that work-content instability has critical effect on prediction accuracy, and why accounting for it, in the predictive method, is crucial to improving current accuracy, obtained via traditional methods.

To prepare predictions for any random phenomenon, assumed to be in steady-state, the best approach is to define its statistical distribution and estimate its parameters, based on real data. Once the distribution is completely defined, various statements about the conduct of the random phenomenon (like surgery-duration) can be made.

For example:

  • What is the most likely realization (given by distribution’s mode);
  • What is the middle value, which delivers equal probabilities, for any realization, to be larger or smaller than that value (expressed by distribution’s median);
  • What is the probability that any realization of the random phenomenon exceeds a specified value (calculated by the cumulative density function, CDF)?

Understanding that complete definition of the distribution is the best approach to predict surgery-duration, let us next explain what type of distributions can one expect in the two extreme states, regarding the two major factors of Set 1:

State 1. There is no variability in work-content (there is only error variability);

State 2. There is no error (error variability is zero; there is only work-content variability).

The two states define two different distributions for surgery-duration.

The first state, State 1, implies that the only source of variability is error. This incurs the normal distribution, for an additive error, or the log-normal distribution, for a multiplicative error (namely, error expressed as a percentage).

State 2, lack of error variability, by definition can only materialize when there is no typical value (like the mode), on which error can be defined. Since no definition of error is feasible, error variability becomes zero. For work-processes, like surgery, this can happen only when there is no typical work-content. In statistical terms, this is a state of lack-of-memory. An example is the duration of repair jobs at a car garage, relating to all types of repair. The distribution typical to such situations is the memoryless exponential.

We learn from this discussion, that any statistical model of surgery-duration, from which its distribution may be derived, needs to include, as extreme cases, both the normal/lognormal distributions and the exponential distribution.

This is a major constraint on any model for the distribution of surgery-duration. It has so far eluded individuals engaged in developing predictive methods for surgery-duration. Lack of knowledge of basic principles of industrial engineering, as well as total ignorance regarding how instability in work-content of a work process (like surgery) influences the form of the distribution, these probably constitute the major culprit for the poor current state-of-the-art of predicting surgery-duration.

In Shore (2020), we have developed a bi-variate model for surgery-duration, which delivers not only the distributions of surgery-duration in the extreme states (State 1 and State 2), but also the distributions of intermediate states, residing between the two extreme states. The two components of the bi-variate model represent work-content and error as two multiplicative random variables, with relative variabilities (standard deviations) that gradually change as surgery-duration moves from State 1 (normal/lognormal case) to State 2 (exponential case).

What do we hope to achieve with publishing of this post (and the accompanying podcast)?

We hope that individuals, engaged in developing predictive methods for surgery-duration, internalize the grim reality that:

  1. Unless their predictive method allows for the normal/lognormal and for the exponential to serve as exact distributions of surgery-duration at the extreme states;
  2. Unless their predictive method allows intermediate states, spanned on a continuous spectrum between the two extreme states, to converge smoothly to these states (as in Shore, 2020),

unless these two conditions be met, the likelihood for the accuracy of predictive methods for surgery-duration to improve anytime soon, this likelihood would remain, as it is today, extremely slim.

Literature

[1] Shore, H (1986). An approximation for the inverse distribution function of a combination of random variables, with an application to operating theatres. J. Statist. Com. Simul. 1986; 23:157-81. Available on Shore’s ResearchGate page.

[2] Shore, H (2020). An explanatory bi-variate model for surgery-duration and its empirical validation, Communications in Statistics: Case Studies, Data Analysis and Applications, 6:2, 142-166, DOI: 10.1080/23737484.2020.1740066 .

[3] Shore, H (2021a). SPC scheme to monitor surgery-duration. Qual Reliab Eng Int. 37: 1561– 1577. DOI: 10.1002/qre.2813 .

[4] Shore, H (2021b). Estimating operating room utilisation rate for differently distributed surgery times. International Journal of Production Research. DOI: 10.1080/00207543.2021.2009141

[5] Shore, H (2021c). “Predictive Methods for Surgery Duation”. Wikipedia. April 16, 2021.

Categories
My Research on the Bible and Biblical Hebrew Podcasts (audio)

Agag, Haman the Agagite, Gog, Magog, Gag — What binds them all together? (Podcast)

On the general concept of “Roof” in the Hebrew Bible, and what does it really signify: