Below we provide some comment letters on some journal articles that misunderstood the MCRF approach severely or aimed to challenge, mess up, stain or plagiarize the MCRF model. The purposes were to clarify some misunderstandings and point out some studies that were mistakes and could be misleading to readers. These materials should be helpful to readers of interest who may want to sincerely work on a research topic related to geospatial statistics for categorical field simulation or multi-D Markov chain modeling conditional on spatial sample data and who want to do their research without confusions and present their results without misunderstandings. The MCRF approach may look simple, but it is at the frontier of scientific progress in geospatial statistics. It is understandable that some people may need time to understand it, even though the MCRF model is a strictly-derived unique spatial statistical model for solving existing scientific issues. Some people might misunderstand or be misled by others, probably because they did not carefully read or never read related publications and reports or they were unfamilar with the topic and related statistics or they had bias against the model proposer. Some "misunderstandings", however, were not so simple; they were intentional troublemakings or mockeries with ridiculous misleading interpretations, aiming to mislead people, mess up the MCRF model with other spatial/nonspatial models, provoke fights in geostatistics and geoinformatics, serve the internal struggles in related academic communities in some nations, etc. Maybe some people expected to get some rewards by playing gunners. Some articles may not be worth the time for writing comment letters. However, for the sake of clearing up confusions in scientific progress, we spent some time to write some comment letters on some troublemaking articles that caused serious confusions among researchers and the public.
The fundamental articles about the MCRF approach were all published on international journals (Mathematical Geology and SSSAJ) in 2007, and a further description from the Bayesian perspective with the coMCRF model was also published in Mathematical Geosciences with a land cover post-classification testing case (Li et al. 2015) after a version for soil map updating was published on an open access journal (Li et al. 2013). Whoever had problems could ask the first author or comment on them, but nobody asked or wrote a comment letter so far. In fact, the mathematical derivation procedure of the MCRF model is simple: It assumed a locally-conditioned Markov chain (using a single chain to avoid conflict transitions), and the local conditioning on nearest data in different directions within a neighborhood followed a sequential Bayesian updating process (it was done by decomposing the joint probability distribution of nearest data and the central random variable into a series of likelihoods and a prior probability using the relationship of joint probability and conditional probability). For simplifying the full solution with multi-point likelihoods, the spatial conditional independence assumption of nearest data (extended from a property of Pickard random fields) was further applied to the MCRF model. This derivation process had no relation with maximum entropy or Gibbs distribution, and the model formulas of MCRFs were unique. There was no experiential addition or elimination of any components. The MCRF sequential simulation algorithm with a quadrant neighborhood was also clearly described in Li and Zhang (2007). There was nothing hidden. Although the derivation process of the MCRF model looks simple, it was based on the configuration of neighborhoods and spatial auto/cross-correlations, which makes it thoroughly different from nonspatial statistical models such as the "linear Bayesian updating" model for integrating expert opinions and the "Naive Bayes" model for image classification (note that nonspatial models are not built on a neighborhood and contain no spatial auto/cross correlations), and it was a result of a long-term exploration in Markov chain spatial modeling for solving some specific scientific issues. It was not like that after we saw others proposed a new model and became famous, we were jealous and then we also followed to propose a new model by imitating an existing model and wanted to be famous. The initial purpose of proposing the MCRF model was to solve the defects of an existing multi-D Markov chain model (i.e., the CMC model proposed by Elfeki in his dissertation) in order to develop a practical predictive soil mapping method. We used the model in 1999 and knew it had defects (as presented in Li's postdoc report in 1999), and then we explored the issues and gradually understood the causes of the defects. In this process, we investigated almost all of the publications in Markov chain modeling in geosciences that we could obtain. The initial ideas of the MCRF model exactly targeted the defects of the CMC model. The MCRF model is not an empirical model, but a strictly-derived spatial statistical model based on some new ideas arising during the long-time effort for solving the deffects of the CMC model and extending 1-D Markov chain into a new geostatistical method. There is no ambiguity in this research, there are also no ambiguity and artificial components in the MCRF model, and our model has no conflicts with any other models (of course, competition always exists between models for similar application purposes, such as simulation of categorical spatial variables). It is unimaginable that such a strictly-derived, simple, novel, reasonable, clear, and problem-solving spatial statistical model was misunderstood and stained by some people so crazily! The MCRF model has no wrong! What is wrong must be some things irrelevant with the science!
After Allard's troublemaking article (Allard et al. 2011) came out, we were very surprised and then quickly found and carefully repeatedly read the major articles proposing the BME approach (Christakos 1990) and Bogaert's BME model (Bogaert 2002). We found that Allard's claim that he derived a simplified BME model using conditional independence assumption was incorrect (Obviously he intentionally made a joke rather than misunderstood). The conditional independence assumption that was presented clearly in Li (2007) is an assumption for spatial data (nearest neighbors in a neighborhood) and it was proposed for simplifying multi-point likelihood terms (a kind of conditional probabilities) in the full formula of the MCRF model into transition probability terms in the simplified formula of the MCRF model (see Li et al. 2015 for a clearer explanation). While Bogaert's BME model [actually a ME model derived through entropy maximization as ambiguously presented in Bogaert (2002, see p. 432, eq. (27))] even did not contain multi-point terms (let alone multi-point likelihood terms), where could Allard apply the conditional independence assumption in Bogaert's model? Actually both Christakos' BME approach and Bogaert's BME model did not contain multi-point statistics (using multi-point statistics in geostatistics was an emerging new idea after 2002 and it was proposed mainly for simulating subsurface curvilinear features; the first article was Strebelle 2002). There is no way to derive the MCRF model in any form using the entropy maximization method (Christakos' idea for the BME approach) that Bogaert used to derive his BME model, because the MCRF model based on the spatial conditional independence assumption is even not a ME model; and there is also no way to derive Bogaert's BME model using Li's ideas (spatial Bayesian updating and spatial conditional independence assumption at nearest neighbor level) for deriving the MCRF model, because the whole derivation process (which is simple and clear) of the MCRF model based on Li's ideas did not involve any intentional addition/removal of mathematical terms. The MCRF model was initially proposed as a solution to the small class underestimation tendency of the CMC model (see Li 2007, Li and Zhang 2008). All of the major ideas of the MCRF approach (especially the single-Markov-chain random field idea) aimed to solve the proved defects of the CMC model and extending 1-D Markov chain model into a new geostatistical approach (the defects of the CMC model were actually proved both by Li and Elfeki himself, although only Li explored their causes and solved them). The MCRF model has its full model formula, which is neither the Gibbs distribution nor Bogaert's BME model. MCRF also has its joint probability distribution formula (see Li and Zhang 2018), which has no application value in geostatistial modeling, because what we need in conditional simulation is the local conditional probability distribution. When Li was working on deriving his MCRF model and proposing the Markov chain geostatistics, the conditional independence assumption was even mistakenly thought to be wrong and invalid in geostatistics (see Journel 2002; but Li did agree with Journel's attitude of being careful to the assumption and testing it whenever it was possible). Li found the rationale for the spatial conditional independence assumption of nearest neighbors from a property of Pickard random fields and used the assumption to simplify the MCRF full formula to a simplified formula with only transition probabilities (Clearly there was no possibility for Allard or Bogaert to derive the MCRF model before Li did it, because Li spent a long time to explore the causes of the defects of the CMC model and their solutions, develop the novel ideas of "spatial" sequential Bayesian updating and "spatial" conditional independence assumption at nearest neighbor level for deriving the MCRF model, and test their feasibility), but its practicality depends on case study testing, which had been done in Li's articles.
Allard derived his MCP method (actually the MCRF model) using the same ideas (spatial Bayesian updating and spatial conditional independence assumption on nearest neighbors) that Li presented to derive the MCRF model, but he painted it as a new model while describing the MCRF model as the CMC model. Surprisingly, Allard even claimed that the MCRF model (he claimed it to be his MCP method and a simplified BME model) was known as the "Naive Bayes classifier" - a nonspatial model (which classifies a dependent variable based on some predictor/independent variables) used in machine learning and classification literature and claimed that the spatial conditional independence assumption for nearest neighbors was known as the "Naive Bayes assumption" (which assumes that the predictor variables are conditionally independent given the dependent variable) (If that was true, how could Allard claim a MCP method? Wasn't the MCP method a plagiarism to Naive Bayes classifier?). As a trained geostatistician, didn't Allard know the differences between geostatistical models and nonspatial statistical models? If he was not intentionally messing the MCRF model and mislead the public, did he also believe that kriging was the same as the multiple linear regression (MLR) and might be claimed as a "Markov-type continuous variable prediction" method of his? That might be why Allard had to describe the MCRF model as the CMC model in his article (Allard et al. 2011) and claim the spatial conditional independence assumption in Li (2007) to be wrong in his reply letter (Allard 2012) to our comment letter (Li and Zhang 2012). And that should also be why Allard claimed a MCP method for himself - he even dared not claim a new model because that was not a new model. How could one use the same ideas and the same procedure to derive a different geostatistical model for simulating categorical fields? What scientific issues did he want to solve? No matter how one write the MCRF model in different forms it is still the MCRF model, just like no matter how one write the MLR in different forms it is still the MLR rather than kriging. What is the problem with Allard's article? Real experts in geostatistics and spatial statistics can understand. It seemed that what Allard wanted were to mislead people, mess up the MCRF model, and provoke fights (e.g., provoke us to attack the BME approach and the CMC model? Maybe he wanted Bogaert to take over the MCRF model?). To distort the MCRF model, Allard had to ignore the CMC model (Elfeki and Dekking 2001) and the real contents of the related major articles (Li 2007; Li and Zhang 2008; Bogaert 2002) and say whatever nonsense he wanted to say, such as that the MCRF model was a sequential simulation algorithm built on a path (while the truth is that any spatial model needs a fixed or random path to perform stochastic simulations). Even if we assume that the simplified MCRF model might be regarded as a simplified BME model, that does not mean someone could derive it before Weidong Li (unless he had Li's experience, made similar efforts, and obtained the same ideas) and should claim it as his (that is why we believed that Allard was joking and fooling). To further mess up the MCRF model and whitewash Allard's MCP method, some people (see Sartore 2013, 2016; Huang et al. 2016; Benoit et al. 2018) had to ignore the real contents of Allard's article (Allard et al. 2011) and his reply letter (Allard 2012) to our comment letter (Li and Zhang 2012) and also had to ignore the real contents of Christakos (1990) and Bogaert (2002) (maybe they even did not have a read to these related articles?), so that they could give Allard's MCP method a distorted favorable explanation that sounds reasonable [we are not sure about some people's real purpose. Did Sartore (2013, 2016) and Benoit et al. (2018) want to embarrass Allard and the BME approach, or did they want to embarrass Li?].
No matter how some people repeatedly whitewash Allard's troublemaking, they cannot change the facts, and so far they even dared not face the truth: (i) The CMC model has defects, which were proved both by us and by Elfeki himself; (ii) the MCRF model solved the defects of the CMC model; (iii) the MCRF model is a spatial sequential Bayesian updating model (based on the initial idea of conditioning a single Markov chain on local nearest data - an idea to avoid the conflict transitions excluded in the CMC model that caused the small class underestimation tendency in simulation using the CMC model or CMC-based model); (iv) Allard apparently could not tolerate a new fundamental geostatistical model proposed by others; (v) Allard misled readers in his article (Allard et al. 2011) by distorting the MCRF model into the CMC model and the spatial conditional independence assumption for nearest neighbors into an independence assumption of two Markov chains; (vi) Allard could not understand the spatial conditional independence assumption (it seemed that he even did not know that the conditional independence formulas P(B,C|A)=P(B|A)P(C|A) and P(B|A,C)=P(B|A) given A are equivalent) and claimed his MCP method (i.e., MCRF model) to be the Naive Bayes classifier (a nonspatial model with a nonspatial conditional independence assumption); (vii) Allard could not understand the difference between the spatial sequential Bayesian updating (on nearest neighbors in a neighborhood) in the MCRF model and a sequential simulation algorithm (for simulating a whole random field using any spatial probability model, such as indicator kriging); (viii) some people tried to use Allard's mistakes to mess the MCRF model and provoke fights; and (ix) some people tried to capture the chance to propose their "new" transition probability-based geostatistical models/theories by ridiculously imagining nonspatial statistical models into geostatistical models [e.g., imagining opinion experts in a nonspatial linear Bayesian updating model or different predictor variables in Naive Bayes classifier to be nearest neighbors of a neighborhood (see Huang et al. 2016; Huang and Wang 2018). The former was a mimic to transition probability indicator kriging (TPROGS) (see Carle and Fogg 1996), and the latter was the same as the MCRF model. Were these also jokes made for messing the MCRF model and fooling the public? What scientific issues did they solve or want to solve?]. When we wrote our comment letters in 2011 and 2012, we tried our best to be polite and did not refute their articles sentence by sentence - we only focused on clarifying their misunderstandings to our MCRF model (i.e., mainly explaining the MCRF model and its relationship with the CMC model, how we solved the defects of the CMC model, and why we proposed the MCRF model and developed the MCRF approach) and avoided any personal accusations and any attacks on other models. Any researcher who made a comparison between the main related articles (Li 2007; Elfeki and Dekking 2001; Bogaert 2002) can see the differences of the models and the joking nature of Allard et al. (2011). Normally, even if there were really some misunderstandings, troublemaking should stop in 2012 or 2013 after our comment and further clarification letters were published. However, after that, troublemaking not only continually occurred round by round but even escalated (especially with Sartore's troubmaking spMC software for misinterpreting the MCRF approach using Allard's viewpoints, and Huang's series of articles for reinterpreting the MCRF/coMCRF models and proposing new geostatistical models/theories), trying to scare people all over the world and give Li no chance to survive. We don't know what the problems were behind the long-lasting campaign (since the beginning of 2004). If some people had problems with the BME approach, why didn't they directly deal with it? If some people determinedly believed that the CMC model did not have the defects that Li said and solved, we are afraid that they had to explain why both Li's case studies (e.g., Li 1999; Li et al, 2004; Li 2007; Zhang and Li 2008) and Elfeki's case studies (e.g., Elfeki and Dekking 2001, 2005; Park et al. 2005) demonstrated similar features (in simulated realizations generated by the CMC model and the CMC-based TMC model) and had to prove theoretically that Li was wrong about the CMC model. It was unimaginable that our effort to modify the CMC model and theoretically solve its small class underestimation problem by proposing the MCRF model caused so much anger and hatred.
It seemed that some people (e.g., Sartore 2013, Sartore et al. 2016, Benoit et al. 2018) wanted to promote Allard's article (plus his reply letter to our comment letter?) to a "masterpiece", solidify his joking (or misunderstanding-based) MCP method to a real geostatistical model, and force people to accept it and his viewpoints about the MCRF model. We are afraid that the more whitewashing to Allard's mistakes, the more embarrassing to the geostatistical community. That is not something we expected and would like to see. If deer could be claimed to be horse and black could be claimed to be white in the geostatistical field, kriging could also be regarded as a plagiarism to the MLR (a nonspatial linear model) or some filters, isn't it? In order to trouble the MCRF model, some people even tried to deny the proved small class underestimation tendency of the CMC model and paint the CMC model as a theoretically-perfect and practical model in geological engineering (so that people were confused and angry at Li and refused to recognize the MCRF model, or so that we had to fight them and write a specific comment letter to prove the defects of the CMC model again) (Is it necessary? The fact that the CMC model has defects does not deny its contribution to multi-D Markov chain modeling and also does not deny the fact it may work under some special situations. For example, if there is no small class, of course it has no small class underestimation; if patches of all layer types are straight and long, there won't be clear layer inclination in simulated realizations. On the contrary, denying its defects would only put the proposers of the CMC model on an embarrassing situation). If such kind of things could be done and could be successful, any suppression and/or plagiarism could occur in the scientific field and could be justified, isn't it?
We had been keeping silence because we knew little about the things (the attitudes and actions of some people) that occurred behind the scenes about our research in multi-D Markov chain modeling of categorical spatial variables during last fifteen years [since 2003, after we modified the impractical (actually theoretically incorrect) coupled Markov chain (CMC) model proposed in Elfeki (1996) and Elfeki and Dekking (2001)]. If not because some people messed up the MCRF appproach and insulted us again during 2014 to 2016, we even would not have had the intention to set up this website in 2015. We do not have so much energy and interest to repeatedly write comment letters to clarify those "misunderstandings" in some ridiculous/irrational troublemaking, cheating/joking or even plagiarizing articles with misleading interpretations about the MCRF model and some nonspatial models. It seemed that troublemaking/joking reached a new peak again at the end of 2017 with several misleading/cheating articles being published in journals (most published in formal issues in 2018) and some people did not want to stop so far (in 2019), but we ignored it so far, except for making above explanations. We have clarified enough. After the "wheel" was invented, any reinvention of the "wheel" in modern days is not a glorious thing, let alone reinventing it by improper manners. If some people have so strong interests to show off themselves and trouble/insult others by playing tricks, making fallacies and committing scientific frauds, let them continue!!! Scientific frauds won't be unseen forever. Fallacy-based frauds are still frauds. The following comment letters (plus the contents of this website) were sufficient to clarify the misunderstandings, though they were focused on pure scientific issues.
Comment and clarification letters published on journals:
4. Li, W. and C. Zhang, 2017. Comments on "Spatial hidden Markov chain models for estimation of petroleum reservoir categorical variables". Journal of Petroleum Exploration and Production Technology, 7(3): 905-909. doi: 10.1007/s13202-016-0312-0. [Note: This comment letter clarified the following facts: (1) The SHMC model they suggested based on the MCRF theory is exactly the same as the collocated coMCRF model with one auxiliary dataset that was proposed by Li and his coauthors years ago. (2) The case study they used to support the publication of their article is false and the results were generated by the CMC model. (3) They messed up the MCRF model with other models by tricks with wrong and irrational statements. This is not their first troublemaking article with false data]
3. Li, W. and C. Zhang. 2013. Some further clarification on Markov chain random fields and transiograms. International Journal of Geographical Information Science, 27(3): 423-430. [Note: This short communication article further clarified some major misunderstandings to the MCRF approach and stopped the arguments, after Allard et al. and Cao et al. responded to our polite comment letters with further misunderstandings in their response letters (e.g., they further challenged/attacked the MCRF model in their responses with improper excuses), because following the suggestions of editors we did not want to continuously argue with them. This letter talked about or mentioned the relationships of the MCRF model with conventional geostatistics, Markov random fields, Markov chains, and Bayes' theorem, as well as the conditional independence assumption, random field concept, and the validity of transiogram models]
2. Li, W. and C. Zhang, 2012. Comments on 'Combining spatial transition probabilities for stochastic simulation of categorical fields' with communications on some issues related to Markov chain geostatistics . International Journal of Geographical Information Science, 26(10): 1725-1739. [Note: Before we wrote this comment letter, we communicated with Cao twice (in 2009 and 2011) by emails about their misunderstandings on the MCRF approach. This comment letter was initially published as a technical communication. In this communication letter, we only clarified their misunderstandings on the MCRF approach, and did not say anything about their researches]
1. Li, W. and C. Zhang, 2012. Comments on 'An efficient maximum entropy approach for categorical variable prediction' by D. Allard, D. D'Or & R. Froidevaux. European Journal of Soil Science, 63(1): 120-124. [Note: This is the first comment letter we ever wrote. This comment letter aimed to clarify the misunderstandings by pointing out the following facts: (1) The MCRF model is not the CMC model or its extension, but rather a different spatial statistical model based on different statistical theories and ideas, although its initial purpose was to correct the small class underestimation tendency of the CMC model. (2) The MCRF model is not a simulation algorithm, but rather a model for estimating local conditional probability distributions. (3) The MCP method suggested in the commented article is the same as the simplified MCRF model based on the conditional independence assumption of nearest data (actually figure 1 in Li 2007a has expressed it). (4) The MCRF model is a Bayesian updating spatial model at the neighborhood nearest data level, rather than a maximum entropy model. Bogaert did not derive a MCRF model or any formulas of MCRF model through maximizing entropy. The MCRF model has its specific research motivations, problem-solving process, neighorhood designs, supporting theories, detailed model derivation process, model formula, spatial correlation measure, and implementation methods. It is different from Bogaert's BME model in every aspect. While some people wanted to provoke fights between us and others, we had no interest to fight anybody and also have no desire to claim anybody's achievement as ours. As to whether Boagert's BME model was generalized from Elfeki's CMC model as repeatedly hinted by some people (e.g., Allard et al.), that was/is not an issue for us to deal with!]
Other comment and clarification letters:
10. Li, W., 2019. Review comments on the manuscript "Subsoil Reconstruction in Geostatistics beyond Kriging: A Case Study in Veneto (NE Italy)". [Note: This review report pointed out the misunderstandings and misleading interpretations of Sartore and his coauthors to the MCRF model as well as the trouble-making nature of his spMC package]
9. Li, W. and C. Zhang, 2018. Some misunderstandings on the transiogram as a spatial correlation measure of categorical data. [Note: This note aimed to clarify some misundrstandings on the transiogram as a spatial correlation measure of categorical data and reduce some confusions caused by some recent distractions messing up the MCRF model]
8. Li, W., 2017. Review report on the manuscript "Simulating Reservoir Lithologies by an Actively Conditioned Markov Chain Model". [Note: I would like to share this manuscript review I made for a journal with publics. The small class underestimation tendency of the CMC model had been a proved fact both in theory and in real simulation cases a decade ago, not only proved by us but also demonstrated by the proposers of the CMC model. The MCRF model had solved the problem by using a single Markov chain locally-conditioned on nearest data in different directions (i.e., the MCRF model). This manuscript used improper parameters to conceal the problem of the CMC model because the improperly-set parameters (horizontal transition probabilities) represented wrong proportions and correlation ranges of classes (By calculating idealized transiograms and checking their sills (approximately equal to class proportions) and correlation ranges or simply by calculating the equilibrium probability vector (approximately equal to class proportions) using the input transition probability matrices, one can find that the horizontal transition probability values are largely inconsistent with both the original images (assumed real data) and simulated realization data). The authors published their manuscript in another journal later with the same data. If one does not know how to compute idealized transiograms or equilibrium probability vector, here is the computer program - "Idealized transiograms from TPM". No matter whether the authors themslves had the intention or not, this kind of articles actually passed a wrong message to their readers - "The CMC model was theoretically correct and perfect, but it was ruined by W. Li who claimed the CMC model has defects and then proposed a MCRF model". Such a wrong and misleading message (ignoring the facts and implicitly staining Li as a bad guy) has been repeatedly used to support the troublemaking/suppressing actions to Li and the MCRF approach (and also serve some infightings in the academic world of China) since 2004. We could guess that the 2017-2018 attack/troublemaking on the MCRF model might be planned to occur in geology or hydrogeology journals, with this misleading article playing the lead role. However, probably because this manuscript was rejected by Computational Geosciences in Summer 2017, other troublemaking articles that aimed to confuse readers (or stain the MCRF model) all went to environmental journals (mainly SERRA) and got published at the end of 2017 or beginning of 2018.]
7. Li, W. and C. Zhang, 2016d. Comments on "Response to 'Comments on "Spatial hidden Markov chain models for estimation of petroleum reservoir categorical variables"'". [Note: This further comment letter responded to the response letter of Huang et al. to our comment letter. While their reponse letter served as their review to our initial comment letter, this further comment letter served as our review to their response letter. We disagreed with their attitude and arguments in their response letter. If not because they had gone too far and caused serious problems, we would not have spent the time to write the comment letters. We do not know what their real purpose was and even did not know who they are. In order to mislead the public, trouble us and mess up the MCRF approach, they published a series of cheating articles around 2016]
6. Li, W. and C. Zhang, 2016c. Comments on "Spatial hidden Markov chain models for estimation of petroleum reservoir categorical variables". [Note: This comment letter pointed out the false case study and the cheating+plagiarism nature of the commented article. In fact, Zhizhong Wang never worked on geostatistics, geostatistical application, or spatial data, before they (Wang and his graduate student - Xiang Huang) suddenly jumped out to mess up the MCRF approach with misleading tricks and false data from various angles in their multiple troublemaking articles since 2014. They are too irrational, and their behaviors caused severe problems during 2014 to 2016. We delayed the revision of our comment letter for about half year to give them a chance to withdraw their wrong article, but they insisted on publishing it]
5. Li, W. and C. Zhang, 2016b. Comments on "Theoretical generalization of Markov chain random field from potential function perspective". [Note: This comment letter pointed out the tricks and the false case study in the article authored by Zhizhong Wang and his graduate student Xiang Huang]
4. Li, W. and C. Zhang, 2016a. Comments on "Reservoir lithology stochastic simulation based on Markov random fields". [Note: This comment letter pointed out the wrong data and the misleading nature of the article authored by Zhizhong Wang and his graduate student.]
3. Li, W. and C. Zhang, 2015. A comment on Sartore's "spMC: Modelling spatial random fields with continuous lag Markov chains". [Note: Sartore's articles (Sartore 2013, Sartore et al. 2016) were misleading and messy, aiming to whitewash Allard's troublemaking. It seemed that Sartore, as an inexperienced young researcher, was not familiar with geostatistics and spatial statistics, of which the fundamental models should be neighborhood-based. Similar to kriging, MRF and GWR, the MCRF model also represents an unique way (i.e., a spatial sequential Bayesian updating way) to deal with the nearest neighbors in a neighborhood, irrelevant with whether they have maximum entropy (ME) or not. The simplified MCRF model based on the spatial conditional independence assumption for nearest neighbors was neither a ME model nor a spatial model derived using entropy maximization. It even cannot fit the BME framework proposed by Christakos (1990), which requires a ME spatial model serving as its base model (i.e., the basic model for dealing with a neighborhood of a random field). Entropy maximization is the basic requirement of Christakos (1990) for the BME approach and its base model. Using the entropy maximization method, Christakos (1990) derived his ME base model in the linear form and found that it was coincidently equivalent to simple kriging. The MCRF model was initially proposed as a solution to the small class underestimation tendency of the CMC model. All of the major ideas of the MCRF approach aimed to solve the proved defects of the CMC model and extending 1-D Markov chain model into a new geostatistical approach. It has its full model formula and its joint probability distribution formula, but the latter has no application value. The development of the MCRF model had its clear scientific issues (e.g., small class underestimation, patch inclination with fixed path, transition probability parameter estimation, optimal simulation algorithm) to solve and it had/has nothing to do with the BME approach. The defects of the CMC model was proved both by us and Elfeki himself (some people later attempted to mess up the MCRF model with the CMC model together, or repeatedly promoted the CMC model as a perfect model by using tricks or special cases; their behaviors only made the scientific field more messy, but cannot change the truth). The spatial condition independence assumption proposed in Li (2007) was proposed for spatial data (nearest neighbors of a neighborhood) and for simplifying the multi-point likelihood terms in the full formula of the MCRF model into transition probability terms in the simplified formula of the MCRF model. Both Christakos' BME approach (Christakos 1990) and Bogaert's BME model (Bogaert 2002) do not contain multi-point terms (let alone multi-point likelihoods), how could Allard use conditional independence assumption to simplify them into the MCRF model (claimed to be a simplified BME model and his MCP method)? Allard used Li's new ideas for deriving the MCRF model to derive his MCP method (that is still the MCRF model) and then irrationally connected it with Bogaert's model. Given the strong disagreements between the kriging group (i.e., Matheron clan) and the BME group, Allard's behavior (he was a trained expert in kriging) was abnormal. Sartore's articles following Allard's nonsense and Sartore's improper software aiming to whitewash Allard's mistakes only could/can serve the further troublemaking to the MCRF model and mess the whole scientific field. Nobody can or should justify a mistake or wrongdoing in scientific research by publishing more mistaken articles]
2. Li, W. and C. Zhang, 2012. Further comments on "Combining spatial transition probabilities for stochastic simulation of categorical fields". [Note: This comment letter was not submitted to avoid further arguments]
1. Li, W. and C. Zhang, 2011. Comments on "Generalized coupled Markov chain model for characterizing categorical variables in soil mapping". [Note: Although we were not happy with the purpose of Park's article published on SSSAJ in 2007 in the same issue with our papers (It was not much reasonable for them to write a manuscript in predictive soil mapping and submit it to SSSAJ while they worked on hydrogeology), following the suggestions of the SSSAJ editors we kept silent. We thank the editors of SSSAJ for giving our papers very careful editing]