Isaiah‘s Structure from Random Forest Regression Analysis

This is the first paper to analyze the tripartite linguistic structure of Isaiah using Random Forest Regression, a supervised machine learning statistical approach. By predicting the occurrences of ‗judgment‘ and ‗hope‘ verses, we examine the threefold structure of Isaiah (section 1--chapters 1-39; section 2--chapters 40-55; and section 3--chapters 56-66) for differences in expression within and between each section. We find more inter-sectional homogeneity between sections 1 and 2 than between sections 1 and 3 or between sections 2 and 3, with respect to both judgment and hope word structures. Moreover, analysis of the judgment-vs-hope word structure indicate that section 3 heterogeneity differs significantly from sections 1 and 2 homogeneity, reinforcing the hypothesis that there is indeed a post-exilic authorship of section 3 (Isaiah 56-66).

-big data‖ analysis of accounting information (Nissim, 2022); in detecting the propensity to fall in older adults (Usmani et al., 2021); in analyzing public sentiment (Shahzad et al., 2022;Adamu et al., 2021;Angelopoulou, Mykoniatis, & Smith, 2022); and-most relevant to our analysis-in text classification (Lagutina & Lagutina, 2021;Shah, Patel, Sanghvi, & Shah, 2020;Gupta, Sharma, & Mohapatra, 2021;Khan et al., 2021;Bastian, 2022). And while this is the first RFR analysis of Isaiah, Peuriekeu et al. (2021) compare Proverbs, Ecclesiastes, and Wisdom from the Bible to the Quran, Yogasutras (India), Tao Te Ching (China) and the Upanishads after extensive pre-processing of the documents, and subsequently applying various supervised machine learning approaches, including random forest regressions (RFR), but with no formal hypothesis testing involved of the type we engage in here.
On the other hand, we do not impose any prior restrictions or pre-processing before the RFR analysis, and keep the analysis relatively simple by dividing each of the three sections into halves when analyzing the intra-sectional homogeneity of Isaiah. That is, we do not drop chapters nor restrict some verses that may be otherwise viewed as inserted or borrowed text. Rather, we take a broad view of the Isaiah chapters in order to test the usefulness of our RFR approach. This analysis of all three parts of Isaiah, with minimal a priori restrictions, will pave the way for more sophisticated analyses later on, not only of Isaiah, but also of other texts where there is controversy over the authorship. In this study, the (null) hypotheses explored include: Hypothesis 1-judgment vs hope: word instruments associated with judgment are not different from word instruments associated with hope, within each of Isaiah's three major sections (that is, the differences in the ranks of the nodal-orderings will be statistically insignificant from one another) Hypothesis 2--intra-sectional homogeneity: dividing up (into halves) and then analyzing each of the three Isaiah sections will indicate that there are no statistical differences within each section, when predicting either warnings of judgment or expressions of hope.
Hypothesis 3-inter-sectional homogeneity: H3a: section 1 will be like section 2, and also like section 3, at least with respect to judgment H3b: section 2 will be like section 3, with respect to judgment and hope if the bi-partite advocates are correct (alternative: section 3 will differ from section 2, if section 3 is a post-exilic text and sections 1 and 2 existed before Jerusalem was captured)

Random Forest Regression and the Structure of Isaiah
We do a statistical analysis of word usage in Isaiah different from Adams (1972) and Adams and Rencher (1974), in that we look at verse by verse predictors of ‗judgment' (prominent in chapters 1-39) and ‗hope' (prominent in chapters 40-55) using ‗instrumental' word associations, rather than a correlational analysis. Throughout, our source material is the New International Version (NIV) translation of Isaiah. Our data criteria for finding intra-sectional and inter-sectional homogeneity (i.e., similarity) between the Isaiah sections is the relative ordering of predictive nodes using Random Forest Regression (RFR).
RFR is like the monks in a huge monastery randomly exchanging their word pattern associations for judgment verses (and in separate exchanges, for hope verses) on their randomly assigned subsections of Isaiah, with other monks with different subsections, for verification of each other's findings. This is done repeatedly and impartially, without any a priori assumptions beyond the definition of a ‗judgment' (or in separate analyses, ‗hope') verse in Isaiah. The monks' instructions for this process is simple: find the instrumental words that ‗best' predict the likelihood of a judgment-type word in each verse (those word choices are given in Table 1) of your subsection, while varying the set of predictors you monks consider. (Then do the same for hope-type verses.) The monks' ultimate goal is to find what instrumental word patterns each group has found in their repeated draws-whether they vary within, and vary between Isaiah's sections 1, 2, and 3-as a means to clarify the Isaiah debates mentioned briefly in the introduction.
The accumulated summary of the overall rank ordering of the monks' independent researches provide the answers-that is, their RFR-equivalent rank ordering of instrumental words' predictive power in explaining judgment-verses or hope-verses. Instead of these repeated Monk exchanges, we look at the actual RFR nodal rank ordering of instrumental words on the basis of Out-Of-Bag Gini values (OOB Ginis, see James et al., 2013) associated with the RFR-nodes that predict a ‗judgment' word in a verse in Isaiah (or alternatively, predicting a ‗hope'). That is, we compare how these nodal-orderings (i.e., the predictive power of an instrumental word) vary within and between the three Isaiah sections. If all three sections are written by the prophet Isaiah, then the word instruments best predicting judgment ought to be somewhat similar between the sections, as well as within each section (and probably more so within sections than between sections). If it's all written by Isaiah, there should be ach.ccsenet.org Asian Culture and History Vol. 15, No. 1;2023 little statistical difference between the Isaiah sections being compared.
This approach might be criticized for ignoring the possible impact of age on the grammatical style of the prophet Isaiah, but this is a criticism that applies equally to all the linguistic (non-archeological) arguments made by all scholars, including those scholars mentioned in the introductory section.
We formally test intra-and inter-sectional differences in the generated nodal-orderings using the non-parametric Wilcoxon signed rank sum tests in alternative specifications. Since our approach is based on machine-learning, we hope to more carefully deal with pre-test biases of standard linguistic simple word-count, or correlational, approaches in our linguistic analysis of Isaiah. Such pre-test adjustments may bias the analysis, especially if the analyst's theological graduate training predisposes her to particular word associations. That is, we want our analogue monks to be impartial when examining the word associations. The left-hand column in Table 1 lists the 111 instruments we use to predict judgment (with nodal-orderings in Table 2) and hope (with nodal-ordering in Table 3). The 20 ‗judgment' variables are listed in the middle column of Table 1; the 19 ‗hope' variables are listed in the right-hand column of Table 1. The nodal-orderings were generated by Random Forest Regressions (RFR) when -regressing‖ judgment words (or, alternatively, hope words) on the 111 word-instruments. The means for these variables by Isaiah sections is given in Appendix Table  A1.
Random Forest Regression (RFR) is a random aggregation of decision trees. A decision tree is a sequential list of yes/no questions, subdividing the instrumental data to yield the predicted probability for a verse being a judgment verse (or hope verse) for given subsets of the sample defined by ‗nodes'. Figure 1 is a decision tree aligned with our word analysis of Isaiah's judgment verses, with a root node indicating whether or not the word ALMIGHTY is in the representative verse as the root node, with the initial branches (-branches‖ are those lines connecting the nodes) indicating the Yes/No response patterns starting at this root node. Each ‗internal node' indicates a sample attribute that helps divide the sample population into subsets, and each leaf node (also known as a terminal node, at the bottom of the inverted tree) defines a predicted likelihood of a given verse being a judgment verse on the basis of its containing one or more of the judgment words from the middle column of Table 1. The tree continues to subdivide at nodes, until it reaches a bottom with several terminal nodes. All members in a particular terminal node (or leaf) are assigned the probability of being a judgment verse by taking the average percentage of judgement verses that follow that respective branch in the tree (Gareth et al., 2013).
The word ‗ALMIGHTY' is an important predictor in Figure 1, so the first question (root node) for this illustrative example is -Does this verse contain the word ‗ALMIGHTY' in it? The response splits the verse into two groups: the -yes‖ branch (going to the right) represent verses with ALMIGHTY in it, the -no‖ branch (going to the left from the root node), those without the word ALMIGHTY in it. The -no‖s for this split, are divided further by the next node split if it has the word ‗HEART' in it. There are 12 verses with no ALMIGHTY in them, ach.ccsenet.org Asian Culture and History Vol. 15, No. 1;2023 but with the word HEART in them. This terminal node (leaf)-with no ALMIGHTY but with the word HEART in the verse--has an average judgment rate of 33.3 percent: that is, .333 of the verses not containing the word ALMIGHTY in them but containing the word HEART in them are judgment verses. All verses in this group would be assigned a predictive probability of being a judgment verse equal to .333.
The -no‖ ALMIGHTY verses with -no‖ HEART in those verses, are then split again: -Among this set: how many have the word SWORD in it?‖-a question that creates two more terminal nodes. Hence, the ‗yes' answer to the word SWORD-20 verses without ALMIGHTY in them and without HEART in them, but with the word SWORD-has a judgment probability of .400 (40 percent), compared to those without a SWORD, without a HEART, or without an ALMIGHTY (980 verses) which has a judgment indicator only 36.3 percent of the time. On the right side of this illustrative decision tree, there are 20 verses that have both the words ALMIGHTY and EGYPT in them, and that combination is associated with more judgment verses than any other combination pictured, as 60 percent of the verses with this combination are judgment verses. On the very bottom, there are 190 verses with an ALMIGHTY in them, but no EGYPT nor PRIEST nor LORD nor SPIRIT in them, with 47.4 percent of them at this terminal node being judgment verses.
Decision trees are relatively easy to understand, and by employing all possible splits of the data, you can obviously forecast the likelihood of getting a judgment as precisely as you want. Of course, you want to employ the decision tree results (namely, the predicted probabilities within each subset needs to apply to new samples of verses) to make good predictions on new data. (You want your monks' subsection predictive model to work well on the different subsections being examined by other monks.). Unfortunately, a single tree trained on one data section (say a given subset of Isaiah's verses) usually does a very poor job predicting outcomes on a new subsection. And supervised machine learning models, such as RFR, are mostly valuable to the extent that they can predict outcomes for new data (the -testing‖ data, a holdout section of Isaiah not included in the original training data analytics), where the testing data set was not previously included in the -training‖ analysis which fit the initial RFR model.
So Random Forest Regression predicts these outcomes by averaging across several decision trees (hence, -forest‖), but it does so by randomizing the analysis in two ways. First, it randomly samples the training data points when building the trees. This is obviously an important advantage when taking averages, as such ach.ccsenet.org Asian Culture and History Vol. 15, No. 1;2023 bootstrapping helps reduce the variance in the model prediction. The second randomization comes from taking random subsets of nodal attributes (the predictor variables) when splitting the nodes.
This second randomization ‗decorrelates' the node choices otherwise made from averaging, and increases the out-of-sample usefulness of Random Forest predictions (Gareth et al., 2013, pp. 319-321). Consider Figure 1: Suppose, as is the case for our sample of verses, that the word ALMIGHTY is a very strong predictor for a judgement verse, and EYGPT is a moderately strong predictor. Then in random subsets of the data, most or all of the trees would have ALMIGHTY as the root node (top split) even when we included all the other variables in the analysis. And likely, EYPGT would most often provide one of the next internal node splits. Hence, even though we would be drawing new random samples to create new trees (for averaging), they would all look very similar to one another, so that this averaging across very similar trees would not be that different from using a single tree.
To get around this problem of generating the same nodal splits, random forests force each nodal split to consider only a subset of the possible predictor variables (say, k*<k, where k is the number of instruments-or predictor variables--in the analysis). Again, this is the second randomization. So, for example, if there are 111 instruments (k=111), then the random decorrelation would only consider 11 (k*=11) of these instruments, picked at random, in repeated draws. Hence, some trees would be constructed without even considering a split by ALMIGHTY, or a split by EGYPT, or both. Repeating this process several times leads to better out-of-sample forecasting. It also provides the researcher with access to the most predictive word instruments (how the left hand column list in Table 1 Tables 2 and 3).

Structuring the Analysis and Results
We test differences in the nodal-ordering between subsections of Isaiah, when the nodes are chosen randomly. For example, in a comparison of section 1 of Isaiah (chapters 1-39) with section 2 of Isaiah (chapters 40-55), suppose that a randomly generated sample of nodal identifiers are BREATH, MOON, OPPRESSORS, PROPHESY and SACRIFICE, with -section 1 nodal-ordering, section 2 nodal-ordering, and difference values‖ respectively for these nodes are -101, 95, 6‖, -70, 94, -24‖, -78, 104, -26‖, -89, 71, 18‖ and -107, 104, 3‖. Then the differences in nodal-orderings between section 1 and section 2 (those differences are the third term in each set) are statistically analyzed as a Wilcoxon signed rank test (a nonparametric test for median differences in ranks). In this case, the test statistic indicates no difference in relative ranks between section 1 and section 2 of Isaiah, based on this randomly generated five-rank comparison.
In Tables 4, 5, and 6 below, we present results for various subsets of nodes. We initially attempted to analyze the different subsections of Isaiah by choosing nodal orderings (the relative ranks of the nodes within each subset) randomly, but found that changing the random seed value (the statistic that generates the random sample subset of nodes) had unanticipatedly large impacts on the values of the Wilcoxon tests, leading to difficulties in reproducing consistent answers, and leading to conflicting conclusions within the same comparison groups. The differences in tests based on randomization seemed to be associated with how many of the top nodes were randomly included in the analysis. subsections of Isaiah-we use the top nodal ranks in Table 2 for judgment, and top nodal ranks in Table 3 for hope, with the top 75, 80, 85, 90, 95 and 100 nodes chosen to explain judgment verses in Table 5 (or hope verses in Table 6) in each comparison group.
Our dual-baseline comparison approach includes the left hand side statistic (indicated with the ‗( )' brackets in the comparison set) where the top nodes from the left-hand Isaiah section in the respective heading comparison are measured against equivalent nodal rankings of the right hand subsection. Then, on the right hand side (in the ‗[ ]' bracket comparisons) we consider the top nodal rankings given in the right hand side of the Isaiah comparison group listed in the respective headings against the equivalent nodal rankings from the left hand side. So, for example, comparing Isaiah 1-39 against Isaiah 40-55, in the left-hand side as the comparison group, would be ‗NODE(rank order)' given as: NATIONS (1), JUSTICE (2), CHILDREN (3), ZION (4), JERUSALEM (5) for Isaiah 1-39 ranks, whose nodal ranks in Isaiah 40-55 are NATIONS (46), JUSTICE (40), CHILDREN (50), ZION (60), JERUSALEM (35). These differences are statistically significant (with a probability significance of exhibiting the same nodal ordering approaching zero, and so indicate very little likelihood that they have the same structure). If we take the Isaiah 40-55 section as the baseline, then the top five nodal choices are SHAME (1), DESCENDANTS (2), ALMIGHTY (3), WORD (4), and HANDS (5) which have left hand nodal ranks of SHAME (11), DESCENDANTS (37), ALMIGHTY (6), WORD (60), and HANDS (13). Again, the comparison reveals a statistically significant difference (with low probability significance level of the null hypothesis that they are the same being true). As the number of top ranks considered approaches 111 (the total number of nodal word instruments in the far-left hand column of Table 1), the Wilcoxon test values will necessarily approach 1.00 (indicating no difference in median rank value), as the median rank will necessarily be equivalent and tests will indicate no significant difference.
Since we want a relative assessment of the likelihood of similarity within and between Isaiah sections (taking, of course, Isaiah 1-39 judgments as the authentic baseline), using RFR in a way that it has never been used before, we examine those top-ranked node sample sizes, where we switch from statistical significance (always significant in smaller samples) to statistical insignificance which will necessarily be the case as the number of nodes approaches this sample's maximum number of nodes, 111. Statistical significance indicates different nodal patterns (different -authorship‖), while insignificance indicates similar -authorship‖ patterns (maybe Isaiah, or one of his attentive disciples). In the analysis presented in Tables 4, 5 and 6 below, we found those sample sizes that can differentiate relative authorship (going from statistical significance to insignificance) to generally be in the range between the top 75 nodes and the top 100 nodes. Table 4 compares the nodal-orderings of judgment verses in the three sections of Isaiah (J_1_39, J_40_55, J_56_66) against the nodal-orderings of the hope verses from the same sections (H_1_39, H_40_55, H_56_66), using our dual-baseline approach. Again, the dual-baseline approach examines top nodal orderings from the RFR analysis using the right-hand group as one baseline, with significant values indicated inside the ‗( )' bracket; then using the left-hand group as the other baseline with significant values indicated inside the ‗[ ]' bracket.

Judgment vs. Hope Comparisons
Probability significance values closer to one indicates no statistical difference between the sections being compare-accepting the null hypothesis, given these sections and the indicated ranks considered. Probability significance values closer to zero indicates that the relevant sections being compared are statistically different-a rejection of the null hypothesis for similarity, given these sections and the indicated ranks considered. Overall, Table 4 indicates judgment nodes are the same as hope nodes for Isaiah 1-39 (the J_1_39 vs H_1_39 comparison column) since the probability significant levels are high-ranging from .3661 to .6626 for rank comparisons based on the top judgment ranks, and ranging from .0951 to .5845 for rank comparisons based on the top hope ranks. By contrast, for Isaiah 56-66, the probability significant levels are relatively low (and generally reject the idea of a similar intra-sectional structure): for the top hope ranks comparisons (the -[ ]‖ values) for Isaiah 56-66, the probability significance levels are always significant (rejecting a similar construction), ranging from .0003 to .0197. The Isaiah 40-55 section is mixed: showing similarity in authorship structure when using the judgment verses as the baseline for comparing ranks, (J_40_55, given by the -( )‖ values) but a profound difference in authorship structure when using the hope verses as the baseline for comparing ranks (H_40_55, given again as the right hand column baseline comparison in the -[ ]‖ notation).
Using Isaiah judgment nodes from section 1, the chapters 1-39 (the J_1_39) section in the far left-hand column, we find all the comparisons of nodal differences between judgment and hope verses are statistically insignificant (same authorship) with values from ‗(0.3661)' to ‗(0.6626)' in the far left-hand column of Table 4. Using the hope nodal ranks, instead of the judgment nodal ranks, as the baseline, we again find strong evidence for a same authorship structure of the judgment and hope verses, with values ranging from just barely significant at the 10 percent level, ‗[0.0951]' to overwhelming similar authorship ‗[0.5845]'. Either baseline analysis concurs that there is a similar authorship structure in the hope/judgment nodal structure, whether using a hope baseline for analysis, or a judgment baseline for analysis of the verses in Isaiah 1-39.
The far right-hand column of Table 4 looking at the similarity of judgment and hope verses in the third section of Isaiah finds just the opposite pattern from the section 1 pattern discussed above: the structure of judgment verses in section 3 of Isaiah is different than the structure of hope verses in section 3. Using judgment verses as the baseline, four of the six comparison values are less than 10 percent: (0.0158), (0.0221), (0.0330), (0.0743). Even the significant sample size values are much smaller than the judgment comparisons in the other sections: (0.1819) in section 3 is much smaller than (0.6331) in section 1, or than the (0.6896) in section 2 for the top 95 rank comparisons; and (0.2507) in section 3 is much smaller than (0.5870) in section 1, or the (0.8968) value in section 2. Whoever wrote section 3 of Isaiah, did not use the same template for judgment and hope verses, contrary to Isaiah section 1 (chapters 1-39).
Section 2 has very mixed results. Using judgment verses as baseline, hope and judgment verses appear to have a similar nodal structure and hence, the same template for hope verse construction as for judgment verse construction, as was the case with Isaiah section 1. However, the hope verse nodal rankings of section 2 indicate very different templates, just like Isaiah section 3. However, row-by-row comparisons by the number of top nodal ranks employed in testing reinforce our relative ranking: section 1 is most similar in linguistic construction, and section 3 the least similar in linguistic construction. Comparing the judgment-hope similarity for any given number of ranks by going across the rows in Table 4, the linguistic structure of hope-verses is most like judgment-verses for Isaiah section 1 (chapters 1 through 39) and least alike for Isaiah section 3 (chapters 56 through 66). Take the first-row, top 75 ranks as illustrative of the rows in Table 4, -[ ]‖-with top ranked hope-nodes as the baseline, then going from left to right the relative significance values are .0951 (9.51 percent chance that judgment and hope verses are similar) for section 1; .0099 for section 2; and only .0003 for section 3. That is, for section 3, there is virtually no chance that the judgment and hope verses have a similar linguistic structure; but very likely that they do have a similar linguistic structure for section 1.
Overall, the author of section 1 of Isaiah (Isaiah himself) uses a similar template for hope verses as for judgment verses, reflecting the same authorship (or at least, the same nodal structure for predicting a hope verse as for predicting a judgment verse). Section 3 results indicate the opposite: the judgment and hope nodal structures are different whatever baseline is used. With these strong results in judgment compared to hope nodal patterns for Isaiah's three sections, we next examine the intra-sectional and inter-sectional template construction of Isaiah first for judgment verses, and then for hope verses. Hypothesis 1 is accepted for Isaiah section 1 and rejected for Isaiah section 3.

Intra-Sectional and Inter-Sectional Analysis of Isaiah's Judgment Verses
Intra-sectional Judgment Homogeneity. While the overall Random Forest Regression (RFR) predicted judgement word patterns are very much like the overall hope word patterns for Isaiah section 1, as indicated in Table 4, predicted judgment word patterns vary considerably within Isaiah section 1 (upper left-hand 6 rows in Table 5) and within Isaiah section 2 (upper central 6 rows in Table 5)-that is, there is intra-sectional heterogeneity for Isaiah sections 1 and 2 up until the 95 and 100 top ranks results. Isaiah section 3 (upper ach.ccsenet.org Asian Culture and History Vol. 15, No. 1;2023 right-hand 6 rows) indicate relatively more intra-sectional homogeneity than either Isaiah sections 1 and 2: that is, for any top rank row examination, the significance levels are always higher for section 3 than for sections 1 and 2. On the intra-sectional judgment analysis in the upper rows of Table 5 (as well as judgment vs hope comparisons in Table 4) section 3 differs from sections 1 and 2. In Table 5, Isaiah sections 1 and 2 reject the null hypothesis of a relatively homogeneous judgment word pattern within each of these subsections, except at the 100 top rank level. This is a rejection of hypothesis 2, the homogeneity of judgment word patterns within each respective section of Isaiah. Section 3, however, seems to provide some relative support for intra-sectional homogeneity. Hypothesis 2 for judgment is supported only in Isaiah section 3. Inter-sectional comparisons of the judgment verses by section in the last six rows of Table 5, tests differences between section 1 and 2 in the left-hand column, bottom left hand 6 rows; test differences between section 1 and section 3 in the bottom central columns; and tests differences between sections 2 and 3 in the bottom right hand column of the Table. Examining the significance values as the number of top ranks considered increases (going from 75 top ranks to 100 top ranks), it appears that section 1 vs. section 2 (bottom left-hand comparisons) have a relatively homogeneous word structure as does sections 2 vs. 3 (bottom right hand side comparisons). However, the bottom central comparisons indicate heterogeneity in the judgment word structures between section 1 vs section 3-statistically significant differences persist up to, and including, the top 95 rank comparisons. The third null hypothesis is supported in the section 1 vs section 2 comparison and in the section 2 vs section 3 comparison. However, the alternative hypothesis H3b appears to be supported for the section 1 vs section 3 comparison: section 1 definitely differs from section 3 in its linguistic structure. Table 6 for hope verses is structured just like Table 5 for judgment verses. The upper 6 rows of Table 6 offer intra-sectional comparisons of Isaiah's hope verses, again by contrasting the RFR nodal-orderings of the instruments using the dual-baseline comparisons of top ranks (top 75, top 80, top 85, top 90, top 95 and top 100 ranks), within the three sections of Isaiah in the upper rows, and between the three sections in the lower rows. Table 6 indicates that Isaiah sections 2 and 3 are quite similar in their intra-sectional similarity with respect to the hope word patterns, indicating relative homogeneity within each section respectively (intra-sectional homogeneity). On the other hand, Isaiah section 1, with greater average levels of statistical significance, indicates a bit more heterogeneity within its section. These sectional distinctions, however, are not quite as pronounced as the judgment differences in the upper 6 rows of Table 5.  As for inter-sectional homogeneity in the lower 6 rows of Table 6, the most consistent result is the relative homogeneity between section 1 and section 2 of Isaiah in the sense that these comparisons are more statistically insignificant than for section 1 vs section 3 comparisons in the central bottom rows, or the section 2 vs section 3 comparisons in the bottom right-hand rows.

Intra-Sectional and Inter-Sectional Analysis of Isaiah's Hope Verses
Overall, the results from these judgment and hope analyses indicate that sections 1 and 2 are generally more alike each other (bottom, left-hand rows in Tables 5 and 6) than they are to section 3. The hypotheses of inter-sectional homogeneity that includes section 3 of Isaiah is rejected.
In an Appendix available from the author upon request, we provide another analysis, where the ‗judgment' and ‗hope' indicators are expanded further to see if that clarifies the resulting patterns: judgment indicators in that extended version now include 37 words (up from 20 here), and hope now includes 31 words (up from 19 here). The results follow the same general patterns as exhibited here, based on hope-verses' top ranks. But the overall pattern suggesting section 3 differs particularly from section 1, continues to hold.

Conclusions
The judgment discourses in Isaiah 1-39 have always been the fundamental building block for scholarly structures of Isaiah, as indicated by the research references to it listed in the introductory section and by our Random Forest Regression analysis of it. While we find that judgment RFR word structures are not always internally consistent in Isaiah 1-39 (section 1), there is more general inter-sectional homogeneity between (internally RFR-consistency) between sections 1 and 2 than between 1 and 3 or between 2 and 3, with respect to both judgment and hope word structures. Moreover, analysis of judgment vs hope word structure in Table 4 indicate that section 3's heterogeneity differs significantly from sections 1 and 2's homogeneity, suggesting that there is indeed a post-exilic authorship of Isaiah 56-66.
Margaret Barker notes: -[The third section of Isaiah] raise several questions of date and authorship. There is great variety of tone and material within them, and several parts resemble the Second Isaiah… If they were written by another [author other than Second Isaiah], he was a prophet who reused the earlier writings as a basis for his polemic. We know from the dated and parallel prophecies of Haggai and Zechariah that it was possible for one prophet to comment upon another. It is possible the Third Isaiah was doing this. It is also possible that he spoke for a later generation. If the Second Isaiah had seen the end of the exile, then these final chapters probably came from the period of the return to Jerusalem, and the question which must be answered by anyone attempting to reconstruct the period is ‗How did the bitterness in these prophecies arise from the events of the period?' The earlier prophecies have been reused in an extraordinary way, yet they survived as an appendix to the Isaiah corpus.‖ (Barker, 1985, p. 201).
Perhaps with a little more scholarship-based analyses employed for ‗judgment', ‗hope', and instrumental word predictor choices, more refined analyses of Isaiah will be under taken to examine more specific hypotheses. At the least, however, the Random Forest Regression approach suggested here may well be found useful elsewhere in future literary and scriptural analyses.

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