204 Documenta Praehistorica XLVI (2019) Until the 1960s, typochronology of the Early and Middle Neolithic in Central Europe was mainly based on descriptive typologies and individual judgements by expert archaeologists (Tichý 1960; 1962; Meier- Arendt 1966). However, standardized typologies and combinations of the types were already used during the 1930s (Buttler, Haberey 1936), with the method being later refined by Pieter J. R. Modderman (1970). Statistics-based methods using such typologies be- came the standard for new relative chronologies since about 1970 (Dohrn-Ihmig 1974; Meier-Arendt 1975). Finally, a consensus about the relative chro- nology of the Early and Middle Neolithic was achi- eved around 1990 (Stehli 1994; Spatz 1996; Strien 2000; all PhD theses completed 1989–1991), com- bining regional seriation-based chronologies, clas- sical typological linking and sometimes additional supra-regional seriations (Stehli, Strien 1986; Steh- ‘Robust chronologies’ or ‘Bayesian illusion’| Some critical remarks on the use of chronological modelling Hans-Christoph Strien Institut für Altertumswissenschaften, Vor- und frühgeschichtliche Archäologie, Johannes Gutenberg Universität, Mainz, DE strien@uni-mainz.de ABSTRACT – The explanatory power of Bayesian chronological modelling is often overestimated, leading to an uncritical belief in the reliability of each isolated model without the necessary look at archaeological connections between different models. The methodical pitfalls of this approach, espe- cially in combination with inaccurate use of typochronological methods, are highlighted for Linear Pottery Culture (ger. Linienbandkeramik – LBK) and Middle Neolithic chronological models from Central Europe (Jakucs et al. 2016; Denaire et al. 2017; Bánffy et al. 2018). A more critical approach to Bayesian modelling, considering possible mathematical artefacts and the deficits of the actual cal- ibration curve as well as the inherent imprecision of the used typochronological dates, seems to be required. IZVLE∞EK – Mo≠, ki jo nudi Bayesovo kronolo∏ko modeliranje za razlago, je pogosto precenjena, kar vodi v nekriti≠no zaupanje v zanesljivost vsakega posameznega modela, ne da bi se pri tem upo∏te- vale arheolo∏ke povezave med posameznimi modeli. Metodolo∏ke zanke tak∏nega pristopa, predvsem ob nenatan≠ni uporabi tipolo∏ko-kronolo∏kih metod, se ka∫ejo predvsem pri preu≠evanju kulture li- nearno trakaste keramike (nem. Linienbandkeramik – LBK) in kronolo∏kih modelov za srednji neo- litik v Centralni Evropi (Jakucs et al. 2016; Denaire et al. 2017; Bánffy et al. 2018). ∞e upo∏tevamo mo∫ne matemati≠ne izdelke in primanjkljaje dejanske kalibracijske krivulje kot tudi nelo≠ljivo ne- natan≠nost uporabljenih tipolo∏ko-kronolo∏kih datumov, lahko sklepamo, da potrebujemo bolj kriti- ≠en pristop k Bayesovemu modeliranju. KEY WORDS – 14 C; Bayesian modelling; Correspondence Analysis; Central Europe; Early Neolithic; chronology KLJU∞NE BESEDE – 14 C; Bayesovo modeliranje; koresponden≠na analiza; Centralna Evropa; zgodnji neolitik; kronologija ‘Robustne kronologije’ ali ‘Bayesova iluzija'| Nekaj kriti;nih pripomb na uporabo kronolo[kega modeliranja DOI> 10.4312\dp.46.13 ‘Robust chronologies’ or ‘Bayesian illusion’| Some critical remarks on the use of chronological modelling 205 al. 2018.121) nor on the “selective use of visual in- spection of radiocarbon dates” (Bánffy et al. 2018. 128), but explicitly based on omitting all 14 C dates (Strien 2018.17–18, 27–28). The exclusive use of quantitatively modelled 14 C-data series (e.g., Strien 1989a) was proposed as a standard procedure long ago (Strien 2000.70–71). ● The succession of house generations as a base for my absolute chronology is not “identified only by study of ceramic motifs” (Bánffy et al. 2018.130), but also by detailed studies of site-formation proces- ses (Strien 2018.94–95, 97–98 and further; illustrat- ed Strien 2014.Abb. 1–2): “The knowledge of the stylistic development is fundamental for this pur- pose, but it is supplemented by other, independent information such as the position of pits relative to houses, spatial relations between houses, and stra- tigraphy” (Strien 1989b.364–365; own translation; in more detail and with comprehensive literature cf. Zimmermann 2012.12–13). ● It should be noted that using (1) the lowest exist- ing estimate for the number of inhabitants of a house, (2) a low estimate for the mean number of houses per settlement based on a model with a low dura- tion of houses (23–25 years), (3) only actually known settlements, and (4), a very high population growth to calculate the minimum number of immigrated people is usually termed a ‘conservative estimate’ and not (Bánffy et al. 2018.129) ‘demographic spe- culations’. What should be discussed in more detail are some other points: ‘robust chronologies’ require dates with a statistical error as small as possible, which in 14 C- dating is at first hand a technical problem. However, the statistical error of a typochronological date in the case of Neolithic ceramics is mainly a function of the number of sherds found in the feature. In con- sequence, using Correspondence Analysis (hereafter CA) is no guarantee for a ‘robust chronology’ of all dated features; a critical look at dates based on small samples is necessary. In regions not reached by mo- dern statistical methods of relative dating the uncer- tainties of individual typochronological judgement enlarge the potential errors considerably. Looking first at the Transdanubian earliest LBK (eLBK), the only available CA consists of all accessi- ble features of this phase from all over Central Eu- rope (Strien 2018). The alleged earlier date of the so-called ‘formative phase’ compared to the Bíňa phase and the expansion horizon, which plays a cen- li 1994). This was complemented by first modelling of 14 C dates, mainly aiming at estimates for the ab- solute duration of the LBK as a whole and of the house generations of the compound model (ger. Wohnplatzmodel; Stehli 1989). The estimated abso- lute date for the LBK of the lower Rhine Valley (5300–4950 cal BC) was soon confirmed by dendro- chronological dates from the Kückhoven wells (Fig. 2). Later on, other regional chronologies were added (e.g., Lefranc 2007; Denaire 2009; Pechtl 2009), but without great changes for the overall scheme. In the south-east, until recently chronologies relied mainly upon individual typochronological estima- tion (e.g., Pavúk 1980; ∞i∫mař 1998; 2002; Marton, Oross 2012.Fig. 10). While the start of the early LBK (known also as Flom- born and Notenkopf phase) somewhere around 5300 BC is widely accepted, the absolute date of the for- mation and expansion of the earliest LBK (eLBK) remains contested, with postulated dates up to 5700 BC, but rarely later than 5500 BC. The model of an at least partial parallelization of earliest and early LBK based mainly upon 14 C dates from taphonomi- cally problematic contexts (Stäuble 2005; Cladders, Stäuble 2003) has not received general approval. However, recently the previous consensus on the re- lative and absolute chronology of the beginning as well as the end of LBK was disturbed by the ap- proach of formal modelling of 14 C dates, applying Bayesian statistics. The first attempts (Jakucs et al. 2016; Denaire et al. 2017), postulating an unexpec- tedly late start of the expansion of the eLBK around 5350 cal BC, and a long-lasting hiatus between the final LBK and the beginning of the Middle Neolithic, provoked concerns (Strien 2017). Consequently, this led to a reply in which the claims of the criticized papers were restated (Bánffy et al. 2018). The prob- lems with 14 C-dates on bone collagen (as discussed in Strien 2017) were rejected by the authors, main- ly based on the conviction that 14 C dating is techni- cally mature to a degree excluding major problems. This point shall be addressed below with additional evidence. To come to an overall sound line of argument, it is helpful to briefly review some statements of Eszter Bánffy et al. (2018) concerning the alleged methodi- cal deficits of my line of argument: ● The absolute chronology proposed by Hans-Chri- stoph Strien (2017) is not “based on informal in- spection of selected radiocarbon dates” (Bánffy et Hans-Christoph Strien 206 tral role in the argument of János Jakucs et al. (2016), is in clear contradiction to the results of this CA (Fig. 1), showing an anteriority of Bí- ňa, not ‘formative phase’ in- ventories. The detailed results of the CA might be question- ed for edge effects (as discus- sed in Strien 2018.24–25), but an earlier start of Bíňa (Donau-eLBK) seems most probable, although a synchro- nous start remains possible, and the reverse sequence can be excluded 1 1 . These results are backed by maps (Strien 2018.Abb. B4-B5) showing that contemporaneity between the ‘formative phase’ and Bíňa phase, and even some early Moravian sites, all synchronized by CA, is geographically plausible. It remains to be noted that: ● The only argument for the anteriority of the ‘for- mative phase’ mentioned by the authors, the pres- ence of Star≠evo-like pottery at Szentgyörgyvölgy- Pityerdomb and “the Star≠evo presence in southern Trandanubia and the Balaton, ending perhaps in the 56 th century” (Bánffy et al. 2018.128), is some- what surprising since not less than five out of the 11 authors of this paper had strongly dismissed this in another paper only a few months earlier (Jakucs et al. 2018): at Versend-Gilencsa Star≠evo and early (not ‘formative’ nor earliest!) LBK were shown to have been contemporaneous in some households, following formal modelling as late as 5200 cal BC (Jakucs et al. 2018.112), far beyond the suggested start of the Earliest LBK at about 5350 cal BC. It re- mains unexplained why Bánffy et al. (2018) never- theless claim an end date of Star≠evo anterior to the Earliest LBK and in consequence also for the ‘forma- tive phase’, in straight contradiction to their own paper. ● At Szentgyörgyvölgy-Pityerdomb, the main site of the ‘formative phase’, i.e. pit 16 and together with pit 11 forming the long pit of house 1 (house num- bers according to Lüning 2016), provided one of the earliest inventories from the site according to the CA 2 2 . One of the pots shows a motif composed of three lines, forming an arc standing on the carina- tion of the biconical bowl (Bánffy 2004.138.141, Fig. 71). The same motif in the same position on re- cipients of related form is not only well known from but most typical for the Bíňa phase (Pavúk 1980); the technical differences (narrow, smoothed and finely incised lines instead of broad deeply incised lines) at the same time link it with early Vin≠a par- allels (Horváth 2006). After all, there is no argument left for the postulat- ed anteriority of the so-called ‘formative phase’, but manifold evidence against it. Bánffy et al. (2018. 128), complain that this “simply reduces the pro- posed ‘formative phase’ to a regional variant” – in fact it simply is a regional variant. The term should in consequence be disregarded as misleading; the phase preceding the expansion of eLBK is consti- tuted not only of the earliest pits of the sites in the region between western Balaton and Vienna (only the earliest part of the so-called ‘formative phase’), but by all Bíňa phase sites, too. Changing to the Alsatian chronology, Anthony De- naire et al. (2017) tend to an uncritical optimism concerning the reliability of CA dates and at the same time to a readiness to adjust them without mathe- matical foundation, as may be shown by some exam- ples: ● In the case of Osthouse 227, a single pot is dated to a stylistic phase most probably (84% probability) 1 In fact, including the inventories from Brunn 2, published after finishing this paper (Stadler, Kotova 2019) at first sight shows a synchronisation of Brunn 2 with Biňa phase and again no anteriority. 2 I can judge the ceramic finds from Pityerdomb only from the published photographs and given descriptions. The direct access to these finds I requested for my study (Strien 2018) was unfortunately denied. Fig. 1. Projection 1./2. EV of a CA of eLBK (after Strien 2018). ‘Robust chronologies’ or ‘Bayesian illusion’| Some critical remarks on the use of chronological modelling 207 spanning not more than 10 years according to the formal modelling (Denaire et al. 2017.1106). Dating single pots poses methodical problems like possi- ble stylistic interdependencies of rim and body deco- ration (Strien 1984.23, Abb. 11) – the main reason why single pots should be excluded from a CA of features (Strien 2000.46). This weak point is com- bined with a second potential source of dating prob- lems: the assumption that ceramic from graves is re- presentative of the style in use at the time of the funeral. This assumption excludes the possibility that ceramic was produced or at least selected for funerary purposes, the decoration following rules somewhat different from those for everyday items. Indeed, there are hints in this direction at least for the Niedermerz cemetery (Frirdich 1994.336–340). The idea that typochronology based on such a nar- row and problematic base could reach a precision in the range of one decade or less is in remarkable con- trast with the negative attitude towards the much more refined identification of house generations of an estimated 25 years shown by the same authors. ● In the case of KV107 not only the small number of decorated sherds (Denaire 2013) poses problems, as its typochronological date had also been deter- mined quite arbitrarily by drawing in the projection 1./2.EV of the CA diagonal phase boundaries at strange angles, changing the position of KV107 from between phases IIB and IIC to the beginning of phase III (Denaire et al. 2017.Fig. 5; one may also ask why Bisch 1735 is dated to IVa1 and not to IVa2 where its position in CA fits better) – connecting chronology in this way with 1. and 2.EV of a CA at the same time is at best unusual, and would have re- quired some solid justification. ● Another highly problematic methodical handling is shown by the last example: Talheim and the phase to which it can be dated (8A of the Württemberg chronology) had until now always been attributed to late LBK (Strien et al. 2014.Fig. 5; Lefranc 2007. Tab. 14; Jeunesse, Strien 2009.Fig. 1), correspond- ing to phases IVa2 or IVb of the Alsatian chronology – dating it without any explanation to the final LBK 3 3 is not what usually is understood under the term ‘robust chronology’, but looks more like arbitrarily arranging the relative position to fit the 14 C dates to the authors’ own chronological ideas. After all, the results of CAs are treated in very diffe- rent manners by Denaire et al. (2017) and Bánffy et 3 ‘Strien 9’ (Denaire et al. 2017.1132); phase 9 has never been found in the whole Neckar Valley; in the region Unterland/ Kraich- gau, where Talheim is, even phase 8B is not attested (Strien 2011.20). Fig. 2. Chronological table putting together different results of formal modelling (for details see text). Hans-Christoph Strien 208 al. (2018): sometimes accepted even for statistical- ly problematic inventories (Osthouse 227 in Alsace), sometimes ‘corrected’ (features KV107 and Bisch 1735 in Alsace, Talheim), sometimes completely ig- nored (‘formative phase’ of LBK) – this is far from “using a rigorous statistical methodology”, as clai- med by Bánffy et al. (2018.130), for combining 14 C dating and archaeological evidence. But ‘robust chronologies’ require reliable 14 C dates, too, not changed by later alterations of the dated material. Two thirds of the paper (Bánffy et al. 2018. 121–128) provide a lucid argument as to why on both methodological and technical grounds 14 C dates are supposedly highly reliable. In practice, things are a bit different, as some examples show. The first is the start of eLBK expansion, dated by Jakucs et al. (2016) to c. 5350 cal BC, and questioned by me on the grounds of contradictory 14 C dates. The simplest method, if my conclusions on the reliability of col- lagen dates were wrong, is a comparison of bone- based with charcoal-and-cereal-based formal model- ling, and this was not chosen – for obvious reasons, as may be shown. As the original code has not been published, the models had to be rebuilt online (Bronk Ramsey 2009a; 2009b; https://c14.arch.ox. ac.uk/oxcal/OxCal.html, Version 4.3). The recon- structed model 2 produces results that are not iden- tical but close to those of Jakucs et al. (2016) (Tab. 1). The differences may be caused by minor errors in typing and by the use of different releases of OxCal. Then the model was split in two (Appendi- ces 1–2), one version with the collagen dates and a second one with the dates on botanical material. The result is quite clear and supports my position: using collagen, the start of the expansion phase is dated to c. 5290 cal BC (the absolute dates mentioned in this paper are the median values according to OxCal; Tab. 1; Fig. 2), about the same date as for the start of Flomborn in Alsace; using botanical dates, the start goes back to c. 5395 cal BC, with a better over- all agreement for the latter. Approaching the correct archaeological model, i.e. removing the ‘formative phase’ from the botanical dates, results in a start date for the expansion of 5425 cal BC (Fig. 2). Changing the model by putting all dates from features dated by CA to the pre-ex- pansion horizon in a new ‘formative phase’ alters the results only slightly and therefore is not shown here (5290 cal BC for collagen, 5400 cal BC for cereals/ charcoal), with a date for the start of the pre-expan- sion horizon of 5325 cal BC and 5440 calBC, respec- tively. Evidently, there is a difference between the collagen and botanical dates, the latter giving a date that is more plausible, although too late compared with my archaeological findings. Anyhow, it should be noticed that none of the formal models present- ed here is meant to present a correct alternative. They are only used to highlight the problems of the disputed models. The deficits of the calibration curve, making all actually possible models insecure, will be discussed below. Another point is the end date for eLBK, left open by Jakucs et al. (2016) as the models produced dates in the 52 nd /51 st centuries cal BC. The authors bypas- sed the problem by claiming that “for that, a much better data set is required” (Jakucs et al. 2016.318). It remains unexplained why the same dataset should produce robust estimates for the start, but obvious- ly unrealistic ones for the end of eLBK. On the other hand a very simple method for estimating an end date was omitted: the 14 C dates from Vedrovice and Kleinhadersdorf from phase Ib were included as eLBK – why not take phase IIa from these sites plus Alsatian Phases IIb/IIc as post-eLBK? The explana- tion might be the unwelcome result: Using the mo- del of Jakucs et al. (2016), as above, but excluding all eLBK dates later than 6100 BP as intrusions and including the dates of seven graves from Vedrovice and Kleinhadersdorf and 11 pits from Alsace as LBK II (Appendix 3), the new model shows low overall agreement (A = 36), mainly caused by the two ear- liest Alsatian dates (SUERC-46497, OxA-27805). Re- Jakucs et al. 2016 reconstructed model collagen only botanical material only median probability start formative c. 5500 5518 – 5516 – boundary formative\earliest c. 5350 5357 5291 5395 5427 end earliest 5113 5190 5052 5040 overall agreement (A) 79 63 85 104 95.4% range start formative 5625–5480 5590–5479 – 5610–5477 boundary formative\earliest 5395–5320 5397–5322 5340–5231 5442–5351 5517–5348 end earliest 5164–5043 5224–5127 5152–4950 5142–4933 Tab. 1. Formal modelling of eLBK. Variants of Model 2 from Jakucz et al. 2016 (see text): own online reconstruction and separate modelling of collagen and botanical dates (dates cal BC). ‘Robust chronologies’ or ‘Bayesian illusion’| Some critical remarks on the use of chronological modelling 209 moving them, the overall agreement is much better (A = 71), without changing the results (Fig. 2): the end of eLBK/ start of LBK II is dating to 5161 cal BC (95.4%: 5201–5106 cal BC), the end of LBK II to 5018 cal BC (95.4%: 5135– 4948; 68.2%: 5046–4985 cal BC). In other words: the end of LBK II in this model is with a probability of more than 85% later than the second well from Kückhoven, dating to late LBK, and the start of LBK II in this model is later than the end of it in the model of Denaire et al. (2017), although 9 and 11, respectively, of the 16/18 measure- ments are the same. Beyond this obvi- ous difference we need not discuss the implications of an end date of eLBK about the same time as the late LBK phase IVa1 in Alsace (‘around 5160 cal BC’ according to Denaire et al. (2017.1106)) to realize a contradiction between the archaeological and 14 C chronologies, which had been denied by Bánffy et al. (2018). The last example relates to the question of the inter- nal chronology of Großgartach in Alsace. Here for- mal modelling produced a result according to which the typochronological phases could not be establi- shed as chronological units 4 4 . Denaire et al. (2017. 1114) concluded that “alternative explanations have now to be found for contemporary variation”. With a bit more scepticism a possible methodological ex- planation can be found: running separate models with the Oxford, Poznan and SUERC dates (Brue- bach-Oberbergen and BORS not included) highlights differences between laboratories (Tab. 2). The Ox- ford dates are nearest to the usual expectations, with boundaries between main phases 40–70 years ear- lier compared to SUERC dates (except the end of Bi- schheim), which on the other hand are the only se- ries in accordance with the typochronology of Groß- gartach. The reason for the laboratory differences as well as for the lack of chronological differentia- tion of the Großgartach sequence might admittedly be haphazard, but problems with collagen dates can- not be excluded, which regrettably cannot be check- ed without 14 C dates from botanical material. In addition, the SUERC dates (Appendices 4–5) de- monstrate another factor, the influence of purely mathematical effects on the results, seemingly com- pletely ignored by the authors: ● Comparing the difference between the median of the boundaries (as an estimate of phase duration), there are important differences between a model se- parating the Großgartach phases and the model tak- ing Großgartach as one phase (Tab. 3; Fig. 3). The question of how fine-grained the development of ce- ramic styles is differentiated in the regional chrono- logy is of greater importance for the modelled start and end dates of the typochronological units, and even more for the relation between their time spans. This may be an extreme case as the number of dates is quite low, but first experiments with other data sets showed that it is a common effect. ● Even more, sometimes the addition of more pha- ses at the end of a sequence also influences the start date of the whole sequence (Tab. 3). The changes usually seem to be in a range that is at first sight ne- gligible (rarely more than 40 years), but the moment the start or end of the model are inflicted by a pla- teau the consequences might be quite significant. ● And finally OxCal does not produce absolutely sta- ble results: changing the input order of dates within one phase sometimes slightly changes the results. Even without laboratory differences the three poten- tial mathematical artefacts identified here further weaken the illusion of ‘robust chronologies’. In the light of the aforementioned problems, the se- ries from Szederkeny should be reconsidered: here the displayed LBK finds show a clear typochronolo- gical sequence, from Bíňa in the eastern part (Jakucs, 4 Nevertheless Denaire et al. (2017.1128), claim: “The radiocarbon dates are in good agreement with the sequences suggested by the seriations in both the LBK and Middle Neolithic periods”, although for the latter this obviously is not the case. Oxford Poznan SUERC median of probability Start Hinkelstein 4827 4795 4764 Hi\Großgartach 4737 4740 4696 GG\Planig-Friedberg 4701 4653 4644 PF\Rössen 4651 4582 4580 Rössen\Bischheim 4563 4492 4494 End Bischheim 4195 4390 4256 95% range Start Hinkelstein 4990–4726 4919–4721 4901–4698 Hi\Großgartach 4785–4712 4791–4700 4729–4627 GG\Planig-Friedberg 4723–4673 4707–4582 4689–4595 PF\Rössen 4697–4589 4667–4508 4646–4526 Rössen\Bischheim 4559–4400 4570–4409 4545–4412 End Bischheim 4326–3912 4489–4246 4324–4146 Tab. 2. Laboratory differences in Alsatian Middle Neolithic models (dates cal BC). Dates from Denaire et al. 2017.Tab. 2; Oxford Hinkelstein dates from Trebur (Spatz 1999.214). Hans-Christoph Strien 210 Voicsek 2015.Fig. 10, 11) to a probably late eLBK in the middle (Jakucs et al. 2016.Fig. 8, 8.9) and post-eLBK in the western part (Jakucs et al. 2016. Fig. 9, 1.2; even Notenkopf decoration is mentioned, Jakucs et al. 2016.281). The formal modelling nev- ertheless shows no chronological difference (Jakucs et al. 2016.293–298). This implies that three or four different typochronological or geographical units of the LBK (earliest phase – Bíňa in the eastern part, Milanovce there and/or in the central part – Noten- kopf and Malo Korenovo in the western settlement), plus Vin≠a A and Ra∫i∏te are all present at the same time within a few hundred meters, but with restrict- ed contacts between them. Here again the Oxford dates show no sequence of the different parts, whe- reas modelling only SUERC and MAMS dates (Appen- dix 6) produces a different picture similar to that de- veloped at Balatonszarszo (Tab. 4; Fig. 4). A sequence for the eastern-central-western part is in sufficient overall agreement with the dates (A = 73). Of course the low number of dates per part of the settlement (and as a consequence that the differences between the laboratories might as well be pure chance) ex- cludes any definite conclusion on the contempora- neity or sequence of the three parts based exclusive- ly on 14 C, as both models are in accordance with the dates. Nevertheless we should take into account prob- lems with collagen dates, as seen for the Alsatian Mid- dle Neolithic, possibly based on diagenetic processes and the resulting difficulties in removing later conta- minations, as typochronology postulates a sequence. The two last examples clearly reveal the major me- thodical deficit of the TOTL project, the refusal to date botanical material for the sake of minimizing taphonomic risks at the cost of lack of control for possible problems with collagen dates. Given the very small number of dates the question of the start date of the Central European Middle Neo- lithic will not be discussed here in detail, as a hand- ful of new dates – especially based on botanical ma- terial – from early Hinkelstein contexts might change the picture entirely. It should only be remarked, that: ● Even Bánffy et al. (2018.130) had to admit that there is at least one contact between late LBK and Hinkelstein (Köln-Lindenthal) – the overall number of contacts is irrelevant the moment this single con- tact is undisputed, so a contemporaneity between late LBK and Hinkelstein cannot be rebutted. ● The alleged “evi- dence for contacts be- tween users of late LBK and Hinkelstein pottery” in the Worms region has never been shown; the cited pa- pers and books did not present anything of this kind, only Walter Meier-Arendt (1975) postulates, based on merely typological ar- guments, a develop- ment from LBK IV (!) to Hinkelstein I, a view Fig. 3. Percentage of each cultural unit compared to the duration of the whole sequence Hinkelstein- Rössen (SUERC dates only), with (right column) and without (left) subdivision of Grossgartach (vi- sualisation of Table 3, long model without Bisch- heim). Tab. 3. SUERC dates for Alsatian Middle Neolithic: models with different num- ber of phases and difference fine-grained vs. coarse-grained typochronology. Großgartach 1: no dates. short model> short model> long model> difference Hinkelstein- Großgartach- Hinkelstein- highest\ Planig-Friedberg Bischheim Bischheim lowest all dates calBC fine- coarse- fine- coarse- fine- coarse- grained grained grained grained grained grained Start Hinkelstein 4734 4752 4753 4763 29 Hi\Großgartach 4710 4696 4715 4688 4712 4697 27 Großgartach 2\3 4688 4685 4686 3 Großgartach 3\4 4670 4661 4661 9 Großgartach 4\5 4653 4639 4639 14 GG\Planig-Friedberg 4633 4655 4619 4632 4619 4645 36 PF\Rössen 4614 4611 4576 4579 4576 4580 38 Rössen\Bischheim 4495 4495 4495 4494 1 End Bischheim 4265 4252 4267 4256 15 ‘Robust chronologies’ or ‘Bayesian illusion’| Some critical remarks on the use of chronological modelling 211 adopted by other authors only by cit- ing it. For the undeniable typological connections between late LBK and Hinkelstein (Spatz 1996.474–475) examples from Worms and its imme- diate surroundings are missing, they are more general late and latest Northwestern LBK – so within the same time range as the ‘mixed as- semblages’ rejected by the authors. Even when interpreted as an evolu- tionary sequence instead of contacts they are no argument for a hiatus. ● A phase ‘VI’, in any case indispensable to render possible the alleged contacts in the Worms region when postulating a hiatus between LBK V and Hin- kelstein in the neighbouring regions, has never been described by any author familiar with the LBK around the estuaries of Neckar and Main 5 5 . The only inven- tories of late LBK from Worms which have been claimed to be near the beginning of Hinkelstein (Me- ier-Arendt 1972) can be dated to Phase IV (Strien 2000.66). ● The use of CA and more generally the typochro- nological approach does in no way “tend … to gloss over any possible disruptions or hiatuses” (Bánffy 2018.131). This statement reflects an obvious mis- understanding of the two cited articles (Shennan, Wilkinson 2001 6 6 ; Pechtl 2015), which do not sug- gest anything like this. In contrast, CA tends to over- estimate any disruptions, as experiments with test data sets have shown (Strien 2000.41–47). Rapid in- novations are such disruptions, causing larger dis- tances on the 1.EV between stratigraphically imme- diately neighbouring units, as demonstrated at Vin- ≠a-Belo Brdo (Schier 2001) – a well-known effect that has served for the differentiation of stylistic pha- ses for some decades (e.g., Schmidgen-Hager 1993. 89), disproving speculations about “default perspec- tives of slow change”. It may be remarked that a slow change from the Early to Middle Neolithic has never been discussed, although the question of how to explain the obviously rapid change between LBK and Hinkelstein has been noted (e.g., Spatz 2003; Strien et al. 2014.254–255). And when typological similarities and – be it a single one – contact finds suggest it, continuity is indeed and should be the de- fault perspective compared to a large-scale and long- time hiatus (the whole Rhine Valley and its tributa- ries, deserted for up to two centuries: Denaire et al. 2017.1132, 1136), especially if the only argument for this hiatus is a handful of 14 C dates. 5 Phase VI of the chronology (Lindig 2002) is synchronized with Phase IVb in Lower Alsace, Phase 8A/B in Württemberg (Lefranc 2007.Tab. 14). 6 The observed effects have recently been interpreted as indicators of social diversity (Gronenborn et al. 2017; 2018; Peters, Zim- mermann 2017). Fig. 4. Two different chronological models for Szederkény (see text; dates cal BC) and the Balatonszarszo chronology (after Marton, Oross 2012, 14 C dates from Jakucz et al. 2016). Tab. 4. Szederkèny: median and ranges of the dates (cal BC) of the boundaries between the three parts of the settlement based on SUERC and MAMS dates only. m 68.3% 95.4% Start East 5321 5335–5305 5374–5241 East\Central 5286 5309–5268 5311–5238 Central\West 5253 5272–5227 5300–5224 End West 5182 5209–5162 5217–5018 Fig. 5. Correlation between number of 14 C-dates per phase and phase lengths of Alsatian LBK (diffe- rence between upper and lower boundary; visuali- sation of Table 5). Hans-Christoph Strien 212 A last point to be mentioned is the high degree of confidence in the actual cali- bration curve demonstrated by the au- thors. Looking at known problems, e.g., inaccuracies of the calibration curve around the time of the Thera eruption (Pearson et al. 2018) and within the LBK plateau (Weninger 2019), a more modest judgement concerning the al- legedly ‘robust’ models would perhaps have been appropriate. The low density of measurements (IntCal13: 483 dates for the range 4050–6050 cal BC), low density of interlaboratory dating, and the extreme smoothing of the IntCal13 curve com- pared to IntCal98 – all well-known facts – exclude any reliable dating, especially within plateaus. In consequence the idea that the duration of the styl- istic phases of Alsatian LBK, all boundaries between them laying within the plateau around the 52 nd cen- tury cal BC, could be reliably estimated at the actual state is highly dubious, so doubts concerning, for example, the duration of phase IVa2 of “only 1–15 years (95% probability)” (Denaire et al. 2017. 1106), based on two (!) 14 C dates (plus one outlier and two old charcoal dates, another date arbitrarily put to Phase IVa1, as shown above), seem to be nei- ther overcautious nor overcritical but self-evident, even when neglecting the fact that the stylistic pha- ses are found by a CA with its inherent statistical dat- ing errors, consisting of inventories from several sites and different functional and social contexts, with individual filling histories, which makes typo- chronological divisions at this fine-grained level high- ly improbable. Even more, further OxCal mathema- tical artefacts become visible: (1) for unknown rea- sons the given estimates for the duration (e.g., “pro- bably for 5–35 years (68% probability)” for phase IIb; Denaire et al. 2017.1104) are evidently too short, even the sum of the upper boundaries of the 68%-ranges lying slightly below the estimated over- all duration (Tab. 5), and (2) there is a correlation between the number of 14 C dates per phase and their length according to Bayesian modelling. Using the means of the modelled boundaries between phases for calculation of durations (Tab. 5) the correlation is clearly significant (Spearman’s rank correlation coefficient: rs = 0.8857, n = 6, p = 0.01; Fig. 5); using the above mentioned modelled phase lengths, rs is even higher (Tab. 5). Oxcal seemingly distributes the dates more or less evenly along the plateau of the IntCal13 curve. Using even numbers of dates per phase would not cure the fault but produce equal phase lengths. A robust estimate of phase lengths in the plateau, using the IntCal13 curve, is mathemat- ically impossible. A completely new model for settle- ment organisation, based on so slippery ground (Le- franc, Denaire 2018) will necessarily be highly spe- culative and no serious alternative to existing models. The models of Jakucs et al. (2016) and Denaire (2017), suffering from methodological deficits in the typochronologies on the one hand, and an uncritical attitude towards the reliability of 14 C dates and de- ficits of the present calibration curve as well as a lack of awareness of mathematical artefacts in Baye- sian modelling on the other, are far from being ‘ro- bust chronologies’, as claimed by Bánffy et al. (2018). A patchwork of contradictory chronologies for different parts of the Danubian sequence in diffe- rent regions and even at single sites (as shown in Fig. 2) is no chronological model of any explanato- ry value. The conclusion of the authors concerning the greater effectiveness of “our collective efforts … if the strengths of the various approaches review- ed in this paper were to be applied more regularly and more systematically” (Bánffy et al. 2018.131) can only be underlined. Bayesian statistics will pro- vide a highly valuable instrument for absolute chro- nology once the main requirements are fulfilled: a precise calibration curve, better control of factors in- fluencing dates, better knowledge of mathematical properties – presently this instrument only produces an illusion of robustness. Appendices 1–6 are available at http://dx.doi.org/10.4312/dp.46.13 stylistic modelled phase length difference number of phases –1σ σ mean +1σ σ start\end (medians) 14 C dates IVb 30 50 70 67.5 15 IVa2 1 5.5 10 12.5 2 IVa1 5 15 25 32.5 4 III 15 32.5 50 40 9 IIc 1 13 25 25 5 IIb 5 20 35 50 6 sum 57 136 215 227.5 rs 0.8571 0.9429 0.9857 0.8857 Tab. 5. 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