Bayesian Inference - Science topic

mostly they are replaced by the GTR models. It is better to use Iqtree where the models are automatically set according to the dataset.

As Ray Kidd mentioned, filtering data is futile. First, the noise is part of the data. In some cases noise can be informative. Filtering can not increase the information content of the data. The information content is an unalterable state of nature. Second, if the filter happens to be inappropriate, the parameter estimates can be meaningless. Third, sometimes the data information content is too low to compute meaningful parameter estimates. Using a filter tells you nothing about parameter estimate uncertainties.

One approach is to include a model for the noise in the parameter estimate model. If you know a lot about the noise, include all that information in the model for the data instead of using a data filter. Never include ad-hoc, indefensible assumptions about the noise (or the parameters).

I noticed Bayesian terms in your keywords. Under no circumstance should you filter the data with Bayesian methods. Bayesian methods include one or more models for the noise in the model for the data. This means there will be well-designed, prior probability, distributions for the noise. Objective, prior probability distributions consistent with maximum entropy principles are the best one can do.

The width of the posterior probability distributions for the parameters will tell you if the data information content is simply too low to compute meaningful parameter estimates.This can be explored by adding noise to simulated data (or empirical data). At some point the signal-to-noise ratio will no longer support meaningful parameter estimates.

For those who were following this question, after a long search I couldn't find any package that implements the CIR model under a Bayesian framework. So I wrote up a Python script to do that. Interested readers can find the code in my GitHub repository https://github.com/Kwabena16108/CIR-Bayesian-Estimation.

Hope this helps.

When you combine MMM and MTA methodologies, you arrive at a unified measurement approach one in which multiple types of data sets, techniques, and approaches illustrate not only each channel’s impact on sales but also how the interaction between channels and non-media variables can influence buying decisions. In turn, these insights allow you to know where to invest your ad spend for the greatest incremental impact, as well as which creative, copy, and messaging will resonate best on each channel. This allows you to be more strategic and to improve tactical decisions.

Dear Prakash Chandra ,

A very excellent blog article on this topic can be found at https://towardsdatascience.com/probability-concepts-explained-bayesian-inference-for-parameter-estimation-90e8930e5348

Some other short articles that will be extremly helpful to you are

Is it possible to do a Bayesian reanalysis, from OR data, which are converted to r-correlation values to estimate the Bayes factor?

Bayesian inference usually produces a consensus tree likely to contain multifurcations, especially at the basal branches and for the data containing low numbers of variable sites. On the contrary, NJ tries to infer a binary tree and inserts short internal branches almost unsupported. Slight changes in the model of molecular evolution in this case are likely to change the whole topology. But it is highly probable to find an NJ tree among the top topologies in the MrBayes (or its likes :) output. For the same reason BI is more resistant to long branch attraction (seemingly not your case, still..)

# load packages library(extRemes) library(xts) # get data from eHYD ehyd_url <- "http://ehyd.gv.at/eHYD/MessstellenExtraData/nlv?id=105700&file=2" precipitation_xts <- read_ehyd(ehyd_url) # mean residual life plot: mrlplot(precipitation_xts, main="Mean Residual Life Plot") # The mean residual life plot depicts the Thresholds (u) vs Mean Excess flow. # The idea is to find the lowest threshold where the plot is nearly linear; # taking into account the 95% confidence bounds. # fitting the GPD model over a range of thresholds threshrange.plot(precipitation_xts, r = c(30, 45), nint = 16) # ismev implementation is faster: # ismev::gpd.fitrange(precipitation_xts, umin=30, umax=45, nint = 16) # set threshold th <- 40 # maximum likelihood estimation pot_mle <- fevd(as.vector(precipitation_xts), method = "MLE", type="GP", threshold=th) # diagnostic plots plot(pot_mle) rl_mle <- return.level(pot_mle, conf = 0.05, return.period= c(2,5,10,20,50,100)) # L-moments estimation pot_lmom <- fevd(as.vector(precipitation_xts), method = "Lmoments", type="GP", threshold=th) # diagnostic plots plot(pot_lmom) rl_lmom <- return.level(pot_lmom, conf = 0.05, return.period= c(2,5,10,20,50,100)) # return level plots par(mfcol=c(1,2)) # return level plot w/ MLE plot(pot_mle, type="rl",      main="Return Level Plot for Oberwang w/ MLE",      ylim=c(0,200), pch=16) loc <- as.numeric(return.level(pot_mle, conf = 0.05,return.period=100)) segments(100, 0, 100, loc, col= 'midnightblue',lty=6) segments(0.01,loc,100, loc, col='midnightblue', lty=6) # return level plot w/ LMOM plot(pot_lmom, type="rl",      main="Return Level Plot for Oberwang w/ L-Moments",      ylim=c(0,200)) loc <- as.numeric(return.level(pot_lmom, conf = 0.05,return.period=100)) segments(100, 0, 100, loc, col= 'midnightblue',lty=6) segments(0.01,loc,100, loc, col='midnightblue', lty=6) # comparison of return levels results <- t(data.frame(mle=as.numeric(rl_mle),                      lmom=as.numeric(rl_lmom))) colnames(results) <- c(2,5,10,20,50,100) round(results,1)

I think that your answer may vary depending on what you consider as better results. In your case, I will assume that you are referring to better results in terms of smaller bias and mean square error. As stated above, if you have poor knowledge and assume a prior that is very far from the true value, the MLE may return better results. In terms of Bias, if you work hard you can remove the Bias of the MLE using formal rules and you will get better results in terms of Bias and MSE. But if you would like to look at as point estimation, the MLE can be seen as the MAP when you assume a uniform distribution.

On the other hand, the question is much more profound in terms of treating your parameter as a random variable and including uncertainty in your inference. This kind of approach may assist you during the construction of the model, especially if you have a complex structure, for instance, hierarchical models (with many levels) are handled much easier under the Bayesian approach.

Please have a look at this article on multilevel analysis

First, p-values have nothing to do with design of studies but lots to do with interpretation. There are as u point out already other possible ways to look at things many involving Bayesian ideas. Many in the social sciences. As a statistics professor I have not seen an increased demand for such studies this makes me think that the people abusing p-values would probably abuse Bayesian ideas too We must,IMO get away from the idea that there's some magic thing that makes a study publishable which is what drives p-hacking in my view. I suppose people like that are not interested in good science but rather in body count of papers. In any case education is part of the answer. BTW, greater power is achieved by finding better methods that would make power obsolete perhaps. In any case as you might've expected I will call for increased statistical research and education. I don't however expect the people that are abusing p-values to have much interest. Thus better education in both methods and ethics may be the best hope for future researchers. Best wishes, D. Booth

Great, I hope everything goes well with snp-sites. If you can obtain the .vcf file, take a look in both these resources, they may help you to analyze your data in terms of structure: https://grunwaldlab.github.io/Population_Genetics_in_R/TOC.html https://popgen.nescent.org/index.html From my experiences, after having a .vcf, and with the help of PGDSpider, you can go for many different analyzes. Good luck and sure, tell me how everything is going.

bnlearn package in R should do the job. Maybe you need to change how your binary data is represented such as using yes/no text instead of 0/1 or something like that. I have never experienced any issues using bnlearn package for binary data

If you have performed the analysis separately it may be an indirect inference that can be reported, although with the evidence the second predictor does not have any significant frequency effect, in case it is significant and you have performed the regression including both predictors you can refer a possible mediating effect of the first predictor.

https://cran.r-project.org › webPDF

Package 'EpiILM' - CRAN

If you have a sample from the marginal or the conditional distribution with closed-form expression, you can compute directly the posterior estimates, such as posterior mean and variance. If you are using some approach such as the metropolis-hastings algorithm you have to check the convergence of your chains before compute your posterior estimates. Just remember that if you want to make predictions, you have to sample for the predictive posterior distribution.

Let me point at the core difference between the "usual" Bayes' and the Jeffreys' proposal.

1. usual Bayes uses prior info in the form of a FINITE weight, reducible without loss of gnerality to probability distribution, called then prior pd.

2. Jeffreys' algorithm - also possible to be named Bayesian - uses the prior info in a form of INFINITE measure, which is a product of

2.1. (obviously finite) normal pd for the mean and

2.2. (obviously infinite) Lebesgue mesure on positive reals R₊ = (0, oo).

3. In the case under considerations the resulting a posteriori info is a finite weight and it can be for further needs used in the "usual" Bayes' as a prior probability distribution.

Hopefully, this explains the acceptability ofJeffreys' formulas when there is NO INFO A PRIORI ABOUT THE SIGMA.

PS1. One can use any other algorithm, since statistics is based on our "impression" that we have about existence of some probabilities. In every case the results of the statistical inferrence are subject of a CONVENTION BETWEEN USERS; the mathematical derivation of algorithms is only a tool to transform principles into concrete formulas. But the principles (e.g. maximum likelihood) are our free choice supported by some elegant consistency with our image.

PS. Moreover, in every case when applying the probabilities to a single event, we are completely lost wondering why the things do not happen according to our expectations. The answer is: For a single event no probability calculus can help predict the result.

The sign of a relationship can change when you put in random slopes. In standard regression the fixed slope is the general slope, but when random slopes are used, the associated estimate of the fixed slope is the precision-weighted slope averaged across all the allowed to vary slopes . see

I suggested you to search the main papers in this area and then call the authors or co-authors to start a conversation.

Relics of Phylowar II can be found in this thread.

Let me play the devil's advocate:

You have data for the past 50 years. However, you say that there is a mayor break or change in the pattern around 1990, so that you want to use only the more recent 30 years ... to predict what will be in 30 or 50 years in the future?

I doubt that this makes any sense. Toss some dice. It will be as reliable as your model predictions.

If "phase changes" like around 1990 can happen, they can happen in the future, too. Additionally, many other things can happen that we are not even aware of today. The uncertainty about such things must be considerd. Further, as you don't have any model that might be justifed by subject matter arguments, there is a universe of possibilities, again adding to the uncertainty of the prediction. If you consider all this, you will almost surely find that the predcition interval 30 or 50 years ahead will be so wide that it can't have any practical benefit.

You can surely grab one possible model, select some subset of your data, and neglect anything else, then you can make a possibly sufficiently precise forecast, which applies to this model fitted on this data, assuming that nothing else happens or can impact the dependent variable. Nice. But typically practically useless. It's a bit different when you has a model, based on a theory. Then you could at least say that this theory would predict this and that. But if you select a model just because the data looks like it's fitting, you actually have nothing.

It's important to think about all this before you invest a lot of work and time in such projects! It may turn out, in the end, that your approach is still good and helpful. But many such "data-driven forecast models" I have seen in my life have benn completely worthless, pure waste. Good enough to give a useful forecast for the next 2-3 years, but not for decades.

@LaHim, I think that approach makes sense overall. I would also suggest including the actual support values on the summary tree that are over some threshold (e.g. 60%). With the subtrees, it sounds like there is a trade-off between including additional sequence data vs. not including some taxa within the presumed clades because data are not available. There's no single right answer to how to make that decision, but I would avoid simply picking the combination that gives you the highest support values.

My practical experience suggests that that different priors do not usually make much difference unless there is very liitle information in the data. indded different results could be seen as a feature and not a problem so that you could do a sesnitivity analysis with different priors. There is a nice eaxmple of this in Clayton and Hills Statsitical Methods in epidemiology

You have a fairly larger dataset so I would try with more generation time. On other hand I would check a modeltest for the 1st and 2nd as often they have the same model when tested (I don't have much experience but that is what I have seen).

I am not sure you need to you need to unlink the 3 partition and then set the priors as variable. Have you tried to remove:

unlink statefreq=(all) revmat=(all) shape=(all) pinvar=(all);

prset applyto=(all) ratepr=variable;

Finally, I don't see in the code where do you set the 2 independent runs (nrun=Number or independent analysis with the same dataset and script) so I guess you run 8 chains but in a single run. So how come they don't converge? All the chains are dependent.

Try to add nrun=2 [usual for Bayesian] each run has 4 chains by default so no need to set that up.

mcmc ngen= 24000000 append=yes samplefreq=1000 nrun=2;

No neighbor doing is not best except for getting a rough first view of the quality of your data an a preview of what you might find with a better method of maximum likelihood. So many advantages to likelihood. Salmi please cite some reasons that you think NJ is best. See my earlier response.

You can dear brother, Çağatay Çetinkaya use the Approximative bayesian methods like: Integrated Nested Laplace Approximation developped bay Rue, H. and Martino, S. and Chopin, N. (2009). a package named "INLA" is available in R cran , or simply you will find a lot about it in http://www.r-inla.org

First, note that the distribution of IVs does not matter in regression models.

The brms package in R provides Bayesian negative binomial regression. The command for a full model would be:

brm(DV ~ IV1 * IV2, family = "negbinomial", data = YourData)

You can extract and interpret the results in much the same way as Poisson regression, which I describe in chapter 7.4 of my book draft:

If I understand you correctly, you want to concentrate the density of your prior distribution about that parameter on a single point. In other words, the prior will be a point mass distribution. Then your posterior will also be a point mass distribution and concentrates all density on that point. I highly doubt that is what you really want, since your data will not influence the posterior at all. If you are really confident, put a informative prior on that parameter that will also allow some uncertainty.

I am not sure that I am right but lets add something to the discussion.

As likelihod is the joint prob (prodct of pdfs)of the sample and also prior/posterior predictive is the prob fnctn of xnew, therefore, to me, the liklihood fntn of x and xnew is the product of likelihood of x and prior/posterior predictive of xnew. U have the likelihood fnctn u can derive the posterior p(mu/D’).

The question posed by David Baum in the title of his book review, "Does the future of systematics really rest on the legacy of one mid-20th-Century German entomologist?" is deliberate distortion of our book's title, :The future of phylogenetic systematics: the legacy of Willi Hennig." The book is comoosed of contributions from a Linnean Society symposium that celebrated Willi Hennig's 100th birthday, and it was the organizers' intent to mark his legacy with a book that both looked back at Hennig's historical impact on phylogenetics, and tried to assess how his contributions are still relevant today. All the plesion discussion above is a distraction that has nothing to do with either our book or with Baum's review.

Does the future of evolutionary biology rely on the contributions of one 19th Century English biologist? Does the future of physics rely on the contributions of a 17th-Century English physicist/astronomer? Probably not. But that does not mean that we do not honor the contributions of Darwin or Newton or deny that subsequent work "rests on their legacies." As Newton himself said, "if I see further, it is because I stand on the shoulders of giants."

The fact that people are still arguing about whether or not classifications ought to be based on monophyletic (in the Hennigian sense) groups is a pretty clear indication that Hennig's ideas remain pertinent in the 21st Century.

Many thanks to Luca, Jochen, and Christopher. You three have made it quite easy to understand!

Hi Manuel,

Concerning Bayesian analyses there are some parameters that can be checked to see if the analyses have been run for enough time. You can check the “average standard deviation of split frequencies” (if you run MrBayes for example). You can check it in the program screen log while the analyses are running. Usually values below 0.01 are considered acceptable.

Which program are you using?

Alternatively, you can check the output files in Tracer. If you have values of ESS above 200 for the different parameters, the analyses are ok.

I hope it helps,

Salvatore

As Gelman says on the BDA book, model selection still is a on going subject of research. I would trust more on the posterior intervals, given that they were grounded on probability axioms.

If the answer is useful, please recommend for others,

magnitude-based inference(MBI) is an interpretation that clinicians need in their evidence-based approach. Due to clinical heterogeneity and small sample sized, clinicians' decision-making about an treatment is not only based on statistical significance, but an overall interpretation of effects including benefits and harms of a treatment, confidence interval (range of uncertianty).

I like this one: http://szeliski.org/Book/

However, if you are more interested in low-level image processing, I would suggest

MESQUITE is a phylogenetic analysis package (as are MEGA, PHYLIP, PAUP, DAMBE and a few others).   A package such as MESQUITE has many advantages such as having built-in functions for consistency index scoring, but a disadvantage is that you need to leard how to use the package, such as importing your data file, importing your treefile, and running the job you want.  It can sometimes be frustrating to figure out exactly what data format is needed for each type of data.

Anyway, MESQUITE does have a consistency index module built in.  I do not find this built in to DAMBE or MEGA. 

Before you go to a lot of trouble calculating the consistency index value for your data and tree, I think you should find out if you will gain any useful information from this value.  Do you know what a "good" value should be for your type of data, for example?  The Consistency Index can be very useful for morphological character data sets in some organisms where morphology evolves nicely.  For DNA and amino acid sequence data the consistency index usually does not give us much information about the quality of the data or the tree.

I haven't touched Lisrel for maybe 6 years, but in my knowledge its output includes the number of parameters and AIC (not sure if it also prints -2ln(L) or L in the output). You can use these two equations:

AIC= 2t - 2ln(L) and BIC = tln(N)- 2ln(L)

where t is the number of parameters.

As Geoffrey pointed out, the BIC penalizes more heavily for complex models.  So the context certainly matters here.

Ok. I will keep then. I think it is important to show if there is "morphological long branch". Even in parsimony it is interesting if there is a branch full of "autapomorphies", because it highlights that the taxon is very different from the others, and taxa such as these are usually "wildcards" too;

Hi! If you are not familiar with mathematical modeling, there are three resources I would recommend above all:

Bishop - Pattern recognition and machine learning (a real classic in Bayesian machine learning)

Hastie, Tibshirani, Friedman - The elements of statistical learning (a frequentist view on learning)

Murphy - Machine learning (a modern book with a lot of applications)

Hi Laura, 

The problem is not so much with MrBayes, but rather with MEGA as a tree viewer. MrBayes does include the Translate block to store all the sampled and consensus trees from mcmc run in a more efficient way. Most tree viewer programs (FigTree, TreeGraph, TreeView, Mesquite, etc.) have no problems reading tree files with such Translate blocks and show your OTUs with the original taxa labels; MEGA only reads the newick trees from your tree files but not the Translate block, so it shows your trees with numbered OTUs as they appear in the newick format. I've been using Mesquite and FigTree to visualise trees from the new MrBayes and had no problems with taxa labels (these programs also offer more options to edit, format, and analyse trees).

Cheers,

Oksana

Okay, then ideally, these variance components should be exactly what I have explained above:

Now I don't know SAS (I mostly use R) and I don't know exactly what method they use in this procedure. If your data are not balanced, the order of the explanatory variables in the model can change the variance components, or not, depending on the type of sum of squares used. So the interpretation of the variance components is conditional on the previous components ("how much variation does Y explain after accounting for X? how much variation does Z explain after accounting for X and Y?...)

If it is not clear for you, I recommend you read more about ANOVA (similar enough to ANCOVA but better documented), sum of squares and F-tests; and the SAS documentation.

Cheers,

Timohée

Compare deviance of both. Smaller deviance is better.  Moreover,  smaller  posterior SD will be better approximation, which often seen with simulations.

a a khan

Hello,

Thoroughly designed experiments where preferably only independent variables are being manipulated. 

Regards, Witold

Ideally Bayesian analysis should get the same results but the two search processes are quite different and the tree criteria are different.

Maximum likelihood analysis searches specifically for the globally optimal (highest likelihood) tree estimate. Bayesian analysis yields a consensus tree of all the sampled trees after the burnin period. Usually (if the priors are well chosen) the set of Bayes trees will include the ML tree but not always.

The paper by Siu and Kelly from 1998 for example explains this nicely in my opinion.

Straight foreward: use the old data and some reasonable "flat" prior and calculate the posterior for that data. This will be the prior for your new data.

You might consider a hierarchical model, where you have n independent Dirichlet distributions with common parameter (like in your reply to Hamideh Sadat Fatemi Ghomi), and then put a prior on the common parameter.  This would typically require MCMC to estimate. But you could also use empirical Bayes to come up with a point estimate for the common prior and solve this model exactly.

What about CARBayes?

Hello,

The answer to your first question is here :

Its a complex and interesting subject !

# If we want inference to be driven solely form data, why do we even bother specifying a prior?

Inference neccesarily goes beyond data, and information is a quantity or entity that exists only in the relation of data and a context (what is here the current "state of conviction" [you may call it "konwlege"], the assumed models, and the kown circumstances of the experiment/study/survey/data collection).

So data alone is and cannot not enough or the only thing to make inference. One needs a model and a context to assert the information of the data (relevant to and related to the model and the context). The model can often be described in some formal way, like a statistical model, either being "obviousely reasonable" or derived from "obviousely reasonable" basic assumptions. The likelihood is the a function that relates the data to the model. This still is not enough to make inference. We still need a context to interpret this function (or likelihood ratios, or p-values from likelihood-ratio tests, etc.). An example can demonstrate this:

If I play lotto (the experiment) the event of winning the lottery has a very small probability under the hypothesis (model) that the result was just a wild guess. The probability of winning would get a mconsiderably higher probability if I had psychic powers so that I could foresee the next lotto numbers. Now I perform the experiment and I win. Wow :) The p-value of this result P(win|guessing) is very small. But would I take this result to conclude that I have psychic powers? Certainly not. But this conclusion is not driven by the data but by the context, by what all we know (or belive) about how the world works. In this context the result remains a "lucky" incident, nothing else, because there is no other data that would be simpler/better be explained from such an assumption and there is such a lot of data that is much more likely if we do not assume that I had psychic powers.

This was quite an extreme example, because we are so sure that psychic powers do not exist (what only means that we would need a hell lot of good data obtained from adequate experiments to reconsider its existence). There are other examples where the influence of the prior knowledge (or believe) is not that drastic.

What is the sense of a so called "uninformative prior"?

Priors are essentially arbitrary. There is no law that would prohibit that two people (agents, social groups, scientific communities) have considerably different priors. Several aspects of the priors can be attributed to (or be seen as consequences of) considering particular (prior) nformation. The above example uses an extremely "informative" prior because there is very much experience about people obviousely lacking psychic powers and because we have no idea how we would integrate the existence of psychic powers into the body of our other models. But if we could not agree on how this information is to be weigted, in other words: if we could not agree on a common wager in a bet for/against the existense of psychic powers? A hoped-for solution is to eliminate all the impact of our former experiencees and of the rest of our models, what would lead to a "non-informative prior".

A sensible non-informative prior is the uniform prior, what says that one considered all possible hypotheses as equally likely. It makes sense in a way that it expresses that we don't see any reason to prefer one of the hypotheses over any other (this is related to Laplaces principle of indifference). However, the hypothesis space may be transformed. But a uniform prior in one space is non-uniform in a transformed space. Here Jeffreys proposed priors that are invariant against transformations.*

# Isn't one of the Bayesian goals that of allowing to systematically incorporate prior information into inference?

No, you turned this around a bit. It is not to incorportae prior information into inference, it is to incorparate the current information into our beliefs (or knowledge). So we do have some beliefs before seeing the data, and the data exhibits a momentum to change our beliefs to a state after accounting for the new data. The data does not tell us where we *are*, it just tells us how far we have to move into which direction. You can see data as being a "force" that acts on masses. Defining a force makes sense only in relation to masses. No masses, no forces. The data changes the impulses, but it does not determine what impulse any mass has to have. This depends on the inpulse the mass had before the force was acting on it.

The Bayesian goal is to provide an objective and systematic way to calculate apply the "force" on a given "impulse".

---

* you may imagine a binomial experiment to infer a proportion (p). You may argue that the uniform for p in [0;1] is an uninformative prior. You can express the proportion as an odds ratio, or = p/(1-p). The prior chosen above won't be uniform on the scale of the odds ratio. Which one is correct? Jeffrey's prior for the binomial is invariant under this transformation. So giving the posterior obtained via Jeffrey's prior would be convertible between the proportion and the odds ratio. Hence, "non-informative" means that the posterior won't depend on the way the data is interpreted (as proportion or as odds ratio). I personally doubt that there is any "really objective" non-informative prior. That would be like attempt to describe the frequency of a wave without giving any time scale ("fequency" is an entity that exists only in conjunction with "time"; as soon as I remove "time" from my model it makes no sense or it is impossible to talk about "frequency").

Check this link :

The best friendly book on Baeysian statistics I have red so far. Probably easier as a first read while containing loads of information plus some code.  You can also find some stuffs on the website.

Good luck with that

Hello Charles,

There are a lot of different methods for making a phylogeny. Below is an answer I had to another question asking about different methods for making trees. But in short maximum likelihood and Bayesian methods are the two most robust and commonly used methods. Neighbor joining is just a clustering algorithm that clusters haplotypes based on genetic distance and is not often used for publication in recent literature.

"Neighbor joining and UPGMA are clustering algorithms that can make quick trees but are not the most reliable, especially when dealing with deeper divergence times. These method are good to give you an idea about your data, but are almost never acceptable for publication. 

Maximum parsimony and minimum evolution are methods that try to minimize branch lengths by either minimizing distance (minimum evolution) or minimizing the number of mutations (maximum parsimony). The major problem with these methods is that the fail to take into account many factors of sequence evolution (e.g. reversals, convergence, and homoplasy). Thus, the deeper the divergence times that more likely these methods will lead to erroneous or poorly supported groupings.

Maximum likelihood and Bayesian methods can apply a model of sequence evolution and are ideal for building a phylogeny using sequence data. These methods are the two methods that are most often used in publications and many reviewers prefer these methods. The main downside of these methods is that they are computational expensive. However, with the today's computers this is not too much of a problem (except for some next-generation sequencing methods).

For maximum likelihood MEGA is not the fastest method out there. For example, if you have a hundred samples for 16S, RAxML will complete is a matter of minutes whereas MEGA will take hours. This will become more of a problem with the more data you include. MEGA also does not have Bayesian method, thus, if you choose to use a Bayesian method you will have to look elsewhere.

If the phylogeny is the main focus of your work, my suggestion is to make both maximum likelihood and Bayesian trees. For these methods you will need to choose a model of sequence evolution. The best way to do this is to use JModelTest, in which you simply input your alignment and it will tell you the best model for your data (you will have to do this if you use MEGA or other software to make your tree). From there you can run a maximum likelihood tree (I would use PhyML or RAxML) and a Bayesian tree (I would use Mr.Bayes or BEAST). 

If you do not want to download these programs or do not have access to a computer that you can dedicate to making trees I would suggest using the CIPRES online portal. 

This portal will give you access to fast computers that can run in parallel and has all of the software I have mention above in an easy to use point and click environment. This is a great resource to use and is free (they just ask that you cite them).

Hope this helps and if you have any questions please ask.

Max"

What is the best phylogenetic tree construction method for bacterial identification? - ResearchGate. Available from: https://www.researchgate.net/post/What_is_the_best_phylogenetic_tree_construction_method_for_bacterial_identification [accessed Aug 24, 2015].

Which tree model (Maximum Likelihood or Neighbor Joining) is better to use with mitochondrial control region haplotypes? - ResearchGate. Available from: https://www.researchgate.net/post/Which_tree_model_Maximum_Likelihood_or_Neighbor_Joining_is_better_to_use_with_mitochondrial_control_region_haplotypes [accessed Oct 27, 2015].

Increasing thinning intervals could help to reduce autocorrelation, although some authors discourage thinning technique.

Inclusion of parameter extensions is probabbly what you`re looking for. Some packages, as MCMCglmm (in R), already include easy ways to implement parameter extensions in the variance structure.

I think the Taguchi-Maharanobis strategy is proper for your inquiry.

We consider each reference samples as each classes and one individual as the other class. This is the same as one-class SVM.

I developed the optimal LDF on the minimum number of misclassisications (MNM).

We discriminate the data consists of reference samples with one individual.

We evaluate the discriminant scores by obtained LDFs and choose reference calass with the most biggest t-value.

I am willing to co-work.

Are you trying to identify gene families? Or do you already have families and are trying to understand the relationships therein?

If you are trying to find the families to explore you can use a clustering algorithm, such as OrthoMCL, to create the families.

To parse the relationships within the gene families, I would think the best approach would include blasting all of the organisms/genomes of interest with known members of the family, aligning the hits with the queries, and treeing the resulting alignment. Depending on how you define the term "family" you would also want to include known negatives in the analysis as well. I.e. a closely related families that are not part of the one you are examining. This will allow you to see the boundaries of yours and not misidentify divergent genes as new versions in the family. 

In contrast to Ariel Chipman, I favour ML and Bayesian methods. NJ and other less computationally intensive tree-building tend to fall victim to artefacts in complex data more easily than ML and Bayes, such as long branch attraction (although they have their failings, too). I would interpret polytomies as he suggests, but would conclude that NJ is falling prey to the data rather than answering a different question. But I do not aim to start a fight. Really, we would hope that each method would yield similar or identical results. That is how you can be most confident. ML will work best if you use an appropriate model. Programs like jModelTest (DNA) and ProtTest (protein) can give you an estimate of the best model. I prefer the AICc criterion for my DNA sequences, but ideally AICc, BIC and DT will all agree on the same model. Bayesian programs, such as MrBayes can either be instructed to use this model or you can skip the model testing and instruct the program to select the best model as part of its run using the "mixed" parameter.

If you do not normalize data and extract components from covariance instead of correlation matrix you keep alive the initial standard deviation of variables.

A likelihood function equal to a Dirac delta is a degenerate case, as the Dirac delta is not a function. It would mean that, after the observations, you are completely sure about the value of the parameter and all possible uncertainty is removed. In theory you can deal with such cases, but in practice, they are imposible. If your question arise from a practical situation, the observation model should be reviewed.

For such likelihood functions, discrepancy analysis is also degenerate, as the final (posterior) distribution of the parameter/s is concentrated in a single value of the parameter/s.

After your run finishes a file is generated called pstat. There are statistics for all of your parameters in there. The manual for v3.2 suggests That minESS for each variable should be 200 or greater and that PSRF should be 1. If memory serves, ESS is effective sample size (you have enough samples from the run to make a judgement) and PSRF is an estimate of how similar the two chains are (converged).

Tell us what you are computing.    The answer to a Bayesian question is usually a posterior probability density, which is always normalized so that the INTEGRAL over all parameter space is equal to one, but the density values are dependent on the scaling (units) and can take on any (positive) values.

Thanks everybody! LogCombiner seems to work when I use an old version (1.7).

Hey,

so as far as I can tell the derivation in Xuan agrees with my point - that you can't integrate over an inverse gamma prior on the variance unless the prior on sigma2 is linked to the prior on the mean (beta in this case). The horizontal arrow in Figure 2.1 of Xuan is crucial! It is this assumption that makes 2.22 still come out as Gaussian with variance proportional to sigma2, and not some horrible combination of parameters.

The fact that the priors are linked is very important, and often under-appreciated. To understand this, imagine a slider that allows you to change the value of sigma2 in the Xuan model. As you move this slider you change the variance of your likelihood AND the variance of your prior on beta. This is not the same as a model with independent priors on beta and sigma2, in which moving the slider would have no effect on the prior on beta.

Connecting the priors up in this way is exactly equivalent to assuming a joint normal-inverse-gamma prior on both parameters - in other words the results of Xuan and Greenberg that you found are identical (notice that Xuan 2.25 is the same as Greenberg's final answer, aside from a change of variables).

As for what you want to do, I am slightly confused. You want to assume a Gaussian likelihood and integrate over a normal-inverse-gamma prior on means and variances? If so then isn't the result in Greenberg already exactly what you want?

I'm interested to hear where this goes!

Bob

BUGS seems easier and here is a free version: http://www.openbugs.net/w/FrontPage

Since it is a bayesian method, anything related to the data influence the output. Excluding some taxa should not influence so much the estimate, but the distribution of them across the years may do. If you have more taxa from a specific range of time, this may drive the estimate towards one direction rather than another. The punctual estimate may not change, but then you can have a broader 95% HPD.

To expand a little bit on what Thomas said: 

1. Check the box for "Node Labels" to display values at the nodes

2. At the drop-down menu for "Display:" choose "height_95%_HPD"

The numbers given here will be the upper and lower values within the 95% highest probability density recovered from your (assuming) BEAST run. So, [10, 24.58] means that the 95% HPD for that node is between an age of 10 (assuming millions of years, but depends on what you put in here) and 24.58 (Mya). This range is exactly what is shown by the bars that are given when you select "Node bars" and choose Display -> "height_95%_HPD".

Generally, I think the node label output from FigTree can be a little messy when you are dealing with ranges - you might want to go and edit these in Illustrator. 

As mentioned you can recourse to DIC, Posterior Predictive checks. Have a look at the Bugs book and Gelman's book "Bayesian Data Analysis"

There are lots of papers on this which will be a better way to inform your opinion than a small number of brief responses. Maybe if we list examples of these. I'll start with Efron at http://statweb.stanford.edu/~ckirby/brad/papers/2005BayesFreqSci.pdf which I think provides a fairly direct answer to your question from someone whose opinions about statistics are much better to listen to than mine!

Dear Prakash;

i agree with you; i was just hoping that such comparison does exist; it seems that i should do it myself to find out;

kind regards;

Amer.

I'm sorry Mr, i don't know mure about you.... 

But i really thanks to you for your attention to me so far...

I'll send you my script and data...

Thanks before for your help

Melissa, it seems that MrBayes can do what you ask. I have never tried that, but at least there is an option for specifying continuous characters in the input nexus file ("Datatype = Continuous"):

Hi Amol,

If you have a whole genome, are you sure MrBayes is the best approach to use? It can take quite a long time for the runs to converge and provide reliable results with a whole genome dataset. Any other Bayesian approach (e.g. BEAST) will have more or less the same problem. You might want to try running a ML analysis using RAxML for example if your aim is to generate a phylogenetic hypothesis.

Anyway, if you want to proceed with MrBayes, you have to arbitrary choose how to divide the data, like by loci, or by loci and codons within each loci. Here's an example using two concatenated loci (A and B), the first with 1000bp and second with 500bp.

By loci only:

charset lociA = 1-1000;

charset lociB = 1001-1500;

By loci and codons:

charset lociA1 = 1-1000\3;

charset lociA2 = 2-1000\3;

charset lociA3 = 3-1000\3;

charset lociB1 = 1001-1500\3;

charset lociB2 = 1002-1500\3;

charset lociB3 = 1003-1500\3;

Now for deciding what's the best partition strategy for your data (instead of an arbitrary choice), the best option will be using PartitionFinder: http://www.robertlanfear.com/partitionfinder/

That's a really nice software, and it's definitely better than "guessing" the best partitions strategy.

I hope that helps!

Cheers,

   Fabricius

http://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation can help you 

Jan,

I'm not an expert on this but the answer seems to me to be that you should go with the model with the simplest parametrization because as you say "data I have to compare these different mechanisms is a special case for the common part of all models (not related to the mechanism I'm interested in): both rate parameters have to be equal and the third parameter has to be zero."

Other than that, in the future I guess you may want to apply a full parametrization to new data that do not fall in the special case you describe.

Hth,

cheers,

SCM