A Statistical Exploration of Text Partition Into Constituents: The Case of the Priestly Source in the Books of Genesis and Exodus (2023)

Abstract: We present a pipeline for a statistical stylometric exploration of a hypothesized partition of a text. Given a parameterization of the text, our pipeline: (1) detects literary features yielding the optimal overlap between the hypothesized and unsupervised partitions, (2) performs a hypothesis-testing analysis to quantify the statistical significance of the optimal overlap, while conserving implicit correlations between units of text that are more likely to be grouped, and (3) extracts and quantifies the importance of features most responsible for the classification, estimates their statistical stability and cluster-wise abundance. We apply our pipeline to the first two books in the Bible, where one stylistic component stands out in the eyes of biblical scholars, namely, the Priestly component. We identify and explore statistically significant stylistic differences between the Priestly and non-Priestly components.

## introduction it is agreed among scholars that the extant version(s) of the hebrew bible is a result of various editorial actions (additions, redaction, and more). as such, it may be viewed as a literary patchwork quilt -whose patches differ, for example, by genre, date, and origin -and the distinction between biblical texts as well as their relation to other ancient texts from the near east is at the heart of biblical scholarship, theology, ancient israel studies, and philology. many debates in this field have been ongoing for decades, if not centuries, with no verdict (e.g., the division of the biblical text into its "original" constituents; @xcite @xcite ). while several paradigms gained prevalence throughout the evolution of this discipline @xcite @xcite , the jury is still out on many related hypotheses, such that these paradigms are prone to drastic (and occasionally abrupt) changes over time (e.g., @xcite . when scrutinized, the interrelation between various literary features within the text may shed light on its historical context. from it, one may infer the number of authors, time(s) and place(s) of composition, and even the geopolitical, social, and theological setting(s) (e.g., @xcite @xcite . such scrutiny thus serves a double purpose: (1) to disambiguate and identify features in the text that are insightful of the lexical sources of the partition (e.g., @xcite @xcite ; (2) to attempt to trace these features to the context of the text's composition (e.g., @xcite . works employing computational methods in text stylometry -a statistical analysis of differences in literary, lexical, grammatical or orthographic style between genres or authors (holmes, 1998)have been introduced several decades ago @xcite @xcite @xcite , with biblical exegesis spurring very early attempts at computerized authorship-identification tasks @xcite . since then, these methods have proved useful also in investigating ancient (e.g., @xcite @xcite , and biblical texts as well @xcite @xcite , albeit to a humbler extent. finally, statistical-learning-based research, which makes headway in an impressively diverse span of disciplines, is taking its first steps in the context of ancient scripts @xcite @xcite @xcite . in the biblical context, @xcite addressed reproducing hypothesized partitions of various biblical corpora with a computerized approach as well, using features such as orthographic differences and synonyms. in the first work -the cochran-mantel-haenszel (cmh) test was applied as a means of hypothesis testing, with the null hypothesis that the synonym features are drawn from the same distribution. while descriptive statistics were successfully applied to various classification and attribution tasks of ancient texts (see above), uncertainty quantification has been insufficiently explored in nlp-related context @xcite , and in particular -in that of text stylometry. in this work, we introduce a novel exploratory text stylometry pipeline, with which we: (1) find a combination of textual parameters that optimizes the agreement between the hypothesized and unsupervised partitions, (2) test the statistical significance of the overlap, (3) extract features that are important to the classification, the proportion of their importance, and their relative importance in each cluster. each stage of this analysis was crossvalidated (i.e., applied on many randomly-chosen sub-samples of the corpus rather than applied once on the entire corpus) and tested for statistical stability. to perform (2) in a meaningful way for textual analysis, we had to overcome the fact that labelpermutation tests do not consider correlations between units of text, which affect their likelihood of being clustered together. this results in unrealistically optimistic p-values, as, in fact, the hypothesized partition does implicitly consider such correlations (by, e.g., grouping texts of a similar genre, subject, etc.). we overcome this by introducing a cyclic label-shift test which preserves the structure of the hypothesized partition, thus conserving the implicit correlations therein. furthermore, we identify literary features that are responsible for the clustering, as opposed to intra-cluster feature selection techniques (e.g., @xcite @xcite , which seek to detect significant features within each cluster. this is also a novel approach to text stylometry. with this pipeline, we examined the hypothetical distinction between texts of priestly (p) and non-priestly (nonp) origin in the books of genesis and exodus. the priestly source is the most agreed-upon constituent underlying the pentateuch (i.e., torah). the consensus over which texts are associated with p (mainly through semantic analysis) stems from the stylistic and theological distinction from other texts in the pentateuch, streamlined across texts associated therewith (e.g., @xcite @xcite . therefore, the distinction between p and nonp texts is considered a benchmark in biblical exegesis. ## results we apply a cross-validated optimization analysis to the three representations of the book ( §2.6) by performing 2d grid searches for 20 randomly chosen sub-sets of 250 verses for each representation. we perform a cross-validated cyclic hypothesistesting analysis for the optimal overlap value ( §2.7) using five randomly-chosen sub-sets of verses, similarly to the above -and derive a p-value. finally, we perform a cross-validated feature importance analysis for every representation ( §2.8), over 100 randomly-chosen sub-sets of verses, similar to the above. in ## conclusions we examined the hypothetical distinction between texts of priestly (p) and non-priestly (nonp) origin in the books of genesis and exodus, which we explored with a novel unsupervised pipeline for text stylometry. we sought a combination of a running-window width (i.e., the number of consecutive verses to consider as a single unit of text) and n-gram size of lexemes, low-or high-resolution phrase-dependent parts-of-speech that optimized the overlap between the unsupervised and hypothesized partitions. we established the statistical significance of our results using a cyclic-shift test, which we show to be more adequate for text stylometry problems than a naive permutation test. finally, we extracted n-grams that contribute the most to the classification, their respective proportions, statistical robustness, and correlation to other features. we achieve optimal, statistically significant overlap values of 73% and 90% for the books of genesis and exodus, respectively. figure 2 : a statistical exploration of the hypothesized partition of the books of genesis and exodus into priestly and non-priestly constituents: results for the book of genesis (lexemes representation). upper left panel -optimization: cross-validated grid-search over verse running-window widths and n-gram sizes to identify the combination yielding an optimal overlap. the combination, value, and uncertainty of the optimal overlap are plotted on top of the panel, and all combinations whose overlap value is within 1σ of the optimal overlap value are marked in red cells. upper right panel -hypothesis testing: cross-validated hypothesis testing, where we simulate the null hypothesis distribution through a cyclic shift of the hypothesized p/nonp labeling. the p-value is measured with respect to the optimal overlap value minus its standard deviation. bottom panels -feature importance analysis: cross-validated important feature analysis (running-window 4 and n-gram size 1) and their statistical stability, displaying features bearing 75% of the explained variance. features in the left and right panels are important to the p-associated and nonp-associated clusters, respectively. the small numbers above each error bar indicate the cluster-wise abundance of the feature. entire book w/o 3 rd block w/o 2 nd block w/o 1 st block w/o 1 st +2 nd blocks figure 4: optimal overlap of a cross-validated optimization analysis of the book of exodus, after removing different p-associated blocks. black dots: high-res pos. red dots: low-res pos. through complementary exegetical and statistical analyses, we show that our methodology differentiates the unique generic style of the priestly source, characterized by lawgiving, cult instructions, and streamlining a continuous chronological sequence of the story through third-person narration. this observation corroborates and hones the stance of most biblical scholars.