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Bayesian Methods - Science topic
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Questions related to Bayesian Methods
When the research sample consists of individual specific cases, researchers face unique challenges due to the limited size or specific nature of the cases involved. However, several general statistical methods can be applied to ensure the reliability and validity of the research and its results. These methods include descriptive statistics, which help summarize the sample’s characteristics using measures such as the mean and standard deviation; inferential statistics, which are used to draw predictions or inferences about the population based on the sample; regression analysis to understand the relationships between variables; and chi-square tests to examine relationships between categorical variables. Correlation analysis can also be used to measure the strength of relationships between variables. Furthermore, Bayesian methods provide a unique approach by leveraging prior knowledge and updating the analysis with new data. The importance of these methods in ensuring the accuracy of research lies in their ability to interpret data systematically, ensure reliability through hypothesis testing and confidence intervals, reduce bias that could affect the results, and allow researchers to draw valid, evidence-based conclusions. They also ensure the replicability and reproducibility of results, which enhances the credibility of the research. Overall, statistical methods remain essential tools that help researchers understand complex data and draw valid, scientifically supported conclusions.
In the domain of clinical research, where the stakes are as high as the complexities of the data, a new statistical aid emerges: bayer: https://github.com/cccnrc/bayer
This R package is not just an advancement in analytics - it’s a revolution in how researchers can approach data, infer significance, and derive conclusions
What Makes `Bayer` Stand Out?
At its heart, bayer is about making Bayesian analysis robust yet accessible. Born from the powerful synergy with the wonderful brms::brm() function, it simplifies the complex, making the potent Bayesian methods a tool for every researcher’s arsenal.
Streamlined Workflow
bayer offers a seamless experience, from model specification to result interpretation, ensuring that researchers can focus on the science, not the syntax.
Rich Visual Insights
Understanding the impact of variables is no longer a trudge through tables. bayer brings you rich visualizations, like the one above, providing a clear and intuitive understanding of posterior distributions and trace plots.
Big Insights
Clinical trials, especially in rare diseases, often grapple with small sample sizes. `Bayer` rises to the challenge, effectively leveraging prior knowledge to bring out the significance that other methods miss.
Prior Knowledge as a Pillar
Every study builds on the shoulders of giants. `Bayer` respects this, allowing the integration of existing expertise and findings to refine models and enhance the precision of predictions.
From Zero to Bayesian Hero
The bayer package ensures that installation and application are as straightforward as possible. With just a few lines of R code, you’re on your way from data to decision:
# Installation
devtools::install_github(“cccnrc/bayer”)# Example Usage: Bayesian Logistic Regression
library(bayer)
model_logistic <- bayer_logistic( data = mtcars, outcome = ‘am’, covariates = c( ‘mpg’, ‘cyl’, ‘vs’, ‘carb’ ) )
You then have plenty of functions to further analyze you model, take a look at bayer
Analytics with An Edge
bayer isn’t just a tool; it’s your research partner. It opens the door to advanced analyses like IPTW, ensuring that the effects you measure are the effects that matter. With bayer, your insights are no longer just a hypothesis — they’re a narrative grounded in data and powered by Bayesian precision.
Join the Brigade
bayer is open-source and community-driven. Whether you’re contributing code, documentation, or discussions, your insights are invaluable. Together, we can push the boundaries of what’s possible in clinical research.
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Embark on your journey to clearer, more accurate Bayesian analysis. Install `bayer`, explore its capabilities, and join a growing community dedicated to the advancement of clinical research.
bayer is more than a package — it’s a promise that every researcher can harness the full potential of their data.
Explore bayer today and transform your data into decisions that drive the future of clinical research: bayer - https://github.com/cccnrc/bayer

According to Fisher [1], “… probability and likelihood are quantities of an entirely different nature.” Edwards [2] stated, “… this [likelihood] function in no sense gives rise to a statistical distribution.” According to Edwards [2], the likelihood function supplies a nature order of preference among the possibilities under consideration. Consequently, the mode of a likelihood function corresponds to the most preferred parameter value for a given dataset. Therefore, Edwards’ Method of Support or the method of maximum likelihood is a likelihood-based inference procedure that utilizes the mode only for point estimation of unknown parameters; it does not utilize the entire curve of likelihood functions [3]. In contrast, a probability-based inference, whether frequentist or Bayesian, requires using the entire curve of probability density functions for inference [3].
The Bayes Theorem in continuous form combines the likelihood function and the prior distribution (PDF) to form the posterior distribution (PDF). That is,
posterior PDF ~ likelihood function × prior PDF (1)
In the absence of prior information, a flat prior should be used according to Jaynes’ maximum entropy principle. Equation (1) reduces to:
posterior PDF = standardized likelihood function (2)
However, “… probability and likelihood are quantities of an entirely different nature [1]” and “… this [likelihood] function in no sense gives rise to a statistical distribution” [2]. Thus, Eq. (2) is invalid.
In fact, Eq. (1) is not the original Bayes Theorem in continuous form. It is called the "reformulated" Bayes Theorem by some authors in measurement science. According to Box and Tiao [4], the original Bayes Theorem in continuous form is merely a statement of conditional probability distribution, similar to the Bayes Theorem in discrete form. Furthermore, Eq. (1) violates “the principle of self-consistent operation” [3]. In my opinion, likelihood functions should not be mixed with probability density functions for statistical inference. A likelihood function is a distorted mirror of its probability density function counterpart; its usein Bayes Theorem may be the root cause of biased or incorrect inferences of the traditional Bayesian method [3]. I hope this discussion gets people thinking about this fundamental issue in Bayesian approaches.
References
[1] Edwards A W F 1992 Likelihood (expanded edition) Johns Hopkins University Press Baltimore
[2] Fisher R A 1921 On the ‘Probable Error’ of a coefficient of correlation deduced from a small sample Metron I part 4, 3-32
[3] Huang H 2022 A new modified Bayesian method for measurement uncertainty analysis and the unification of frequentist and Bayesian inference. Journal of Probability and Statistical Science, 20(1), 52-79. https://journals.uregina.ca/jpss/article/view/515
[4] Box G E P and Tiao G C 1992 Bayesian Inference in Statistical Analysis Wiley New York
here is the code:
library(babette)
library(seqinr)
library(BeastJar)
library(beastier)
fasta <- read.fasta("nuc.fasta")
get_default_beast2_bin_path(
beast2_folder = get_default_beast2_folder(),
os = rappdirs::app_dir()$os
)
fasta_filename <- "nuc.fasta"
output <- bbt_run(fasta_filename)
##############after this run it gives following error:
Error in beastier::check_input_filename_validity(beast2_options) :
'input_filename' must be a valid BEAST2 XML file. File 'C:\Users\User\AppData\Local\beastier\beastier\Cache\beast2_9ec3aae162d.xml' is not a valid BEAST2 file. FALSE
I am trying to understand and use the best model selection method for my study. I have inferred models using swarm optimisation methods and used AIC for model selection. On the other hand I am also seeing a lot of references and discussions about BIC as well. Apparently, many papers have tried and concluded to use both AIC and BIC to select the best models. My question here is, What if I use ABC along side with AIC and BIC, how this will effect my study in better way and what would be its pros and corns of using ABC, BIC and AIC as model selection methods ?
Thanks
Hello
I have been in constant discussions with my friends and colleagues in recent years, in my experience I generally use multivariate statistics because most data sets do not have the assumptions for classical frequentist statistics. However, I know some people who use univariate and Bayesian methods to answer the same hypothesis questions. With this, the question would be, what would be the most appropriate way to answer our research questions?
Dear colleagues,
I will appreciate your help in setting the parameters to use two nodes fossil-calibration for a phylogenetic-chronogram reconstruction using BEAST.
I have the divergence time between the outgroup (two species) 43 mya and the crown group of species that I would like to date, and the divergence time of these two species in the outgroup (8.7 mya).
Is there any way to get the a posteriori mutation rate in the way I can use this value later on to estimate populations divergence time using among populations genetic distance?
Many thanks in advance for your help.
Roberto
MCMC sampling is often used to produce samples from Bayesian posterior distributions. However, the MCMC method in general associates with computational difficulty and lack of transparency. Specialized computer programs are needed to implement MCMC sampling and the convergence of MCMC calculations needs to be assessed.
A numerical method known as “probability domain simulation (PDS)” (Huang and Fergen 1997) might be an effective alternative to MCMC sampling. A two-dimensional PDS can be easily implemented with Excel spreadsheets (Huang 2020). It outputs the joint posterior distribution of the two unknown parameters in the form of an m×n matrix, from which the marginal posterior distribution of each parameter can be readily obtained. PDS guarantees that the calculation is convergent. Further study of comparing PDS with MCMC is warranted to evaluate the potential of PDS as a general numerical procedure for Bayesian methods.
Huang H 2020 A new Bayesian method for measurement uncertainty analysis and the unification of frequentist and Bayesian inference, preprint,
Huang H and Fergen R E 1995 Probability-domain simulation - A new probabilistic method for water quality modeling. WEF Specialty Conference "Toxic Substances in Water Environments: Assessment and Control" (Cincinnati, Ohio, May 14-17, 1995),
Conference Paper Probability-domain simulation - A new probabilistic method f...
I want to use BEAST to do EBSP analyses with two loci. I open two "input.nex" files in BEAUti to generate a "output.xml" file (In the Trees panel select Extended Bayesian skyline plot for the tree prior), and then run BEAST. I do not know if this is right and I do not know what to do next. I can not construct the trend of demographic history in Tracer just like BSP. I got one log file but two trees files (for each locus), and I do not know how to import both tree files into Tracer.
I'm trying to establish Bayes factor for the difference between two correlation coefficients (Pearson r). (That is, what evidence is there in favor for the null hypothesis that two correlation coefficients do not differ?)
I have searched extensively online but haven't found an answer. I appreciate any tips, preferably links to online calculators or free software tools that can calculate this.
Thank you!
I am completing a Bayesian Linear Regression in JASP in which I am trying to see whether two key variables (IVs) predict mean accuracy on a task (DV).
When I complete the analysis, for Variable 1 there is a BFinclusion value of 20.802, and for Variable 2 there is a BFinclusion value of 1.271. Given that BFinclusion values quantify the change from prior inclusion odds to posterior inclusion odds and can be interpreted as the evidence in the data for including a predictor in the model, can I directly compare the BFinclusion values for each variable?
For instance, can I say that Variable 1 is approximately 16 times more likely to be included in a model to predict accuracy than Variable 2? (Because 20.802 divided by 1.271 is 16.367 and therefore the inclusion odds for Variable one are approximately 16 times higher).
Thank you in advance for any responses, I really appreciate your time!
My intuition is that Bayesian methods are more commonly being used in ecology, particularly given relatively recent user-friendly tutorials and software packages being published in fields of ecology...
e.g.,:
Kery (2010) Introduction to WinBUGS for Ecologists: A Bayesian approach to regression, ANOVA, mixed models and related analyses
Kery and Schaub (2012) Bayesian Population Analysis using WinBUGS: A hierarchical perspective.
Korner-Nievergelt F, et al. (2015) Bayesian data analysis in ecology using linear models with R, BUGS and Stan.
Kery and Royle (2016) Applied Hierarchical Modeling in Ecology: Analysis of distribution, abundance, and species richness in R and BUGS
etc.,
But, are there any review articles or manuscripts with informal reviews that show the trend of Bayesian analysis implementations in ecology over time?
Thank you!
Dear researchers , i want to ask you how we can use the censored data and bayesian method in insurance, please give me some examples
Thank you in advance .
Would an indirect comparison using frequentist or bayesian methods be the best approach? Are there any other tests to run, and if so, what software would be the best?
Both the formal (MCMC) and informal (Generalized Likelihood Uncertainty Estimation) Bayesian methods are widely used in the quantification of uncertainty. As far as I know, the GLUE method is extremely subjective and the choice of the likelihood function is various. This is confusing. So, what are the advantages of GLUE and is it worthy of being admired? Is it just because it doesn't need to reference the error function? What is the pros and cons between the two methods? What to pay attention to when constructing a new informal likelihood function(like LOA)?
Looking for example data sets and R code for applying Bayesian methods to determine population trends of wildlife using time series abundance or density estimates.
I recently moved from distance-based techniques to model-based techniques and I am trying to analyse a dataset I collected during my PhD using the Bayesian method described in Hui 2016 (boral R package). I collected 50 macroinvertebrate samples in a river stretch (approximatively 10x10 m, so in a very small area) according to a two axes grid (x-axis parallel to the shoreline, y-axis transversal to the river stretch). For each point I have several environmental variables, relative coordinates inside the grid and the community matrix (site x species) with abundance data. With these data I would create a correlated response model (e.i. including both environmental covariates and latent variables) using the boral R package (this will allow me to quantify the effect of environmental variable as well as latent variables for each taxon). According to the boral manual there are two different ways to implement site correlation in the model: via random row-effect or by assuming a non-independence correlation structure for the latent variables across sites (in this case the distance matrix for sites has to be added to the model). As specified at page 6, the latter should be used whether one a-priori believes that the spatial correlation cannot be sufficiently well accounted for by row effect. However, moving away from an independence correlation structure for the latent variables massively increases computation time for MCMC sampling. So, my questions are: which is the best solution accounting for spatial correlation? How can be interpreted the random row-effect? Can it be seen as a proxy for spatial correlation?
Any suggestion would be really appreciated
Thank you
Gemma
I have simulated a data using gama distribution that resulted in normal phenotypic distribution, however non-normal true breeding values (simulated) with a little skewed QQ plot and significant Shapiro Wilks.
Now the question is I want to use GBLUP and not Bayesian approach. However, I am not getting a reference for the same. BLUP is sturdy, however can it be used ignoring bayesian methods? Can I use BLUP for such data/ and if yes, is there a reason to do so?
Dear Researchers/Scholars,
Suppose we have time series variable X1, X2 and Y1. where Y1 is dependent on these two. They are more or less linearly related. Data for all these variables are given from 1970 to 2018. We have to forecast values of Y1 for 2040 or 2060 based on these two variables.
What method would you like to suggest (other than a linear regression)?
We have a fact that these series es have a different pattern since 1990. I want to make this 1990-2018 data as prior information and then to find a posterior for Y1. Now, please let me know how to asses this prior distribution?
or any suggestions?
Best Regards,
Abhay
Bayesian methodologies are oftentimes referred to as being subjective in nature, given the involvement of prior specification, which is usually dependent on researchers' preferences. On the other hand, the frequentists do not require any specification of prior and are said to be objective. However, in the Bayesians paradigm, the process of prior specification has been formalized such that the most appropriate priors suitable for given cases are elicited. Thus, bayesian methods are totally transparent and very much objective as the frequentist methods, if not more.
Is Bayesian Method the most popular method in reliability prediction and if not why?
When we use the Bayesian method to do prediction of a time series, a typical way is to build the prior and using the time series data to update and predict. This process only uses the current time series data, which could be a kind of the waste if we have a lot of historical time series. I am wondering if there is a way we can take a good use of all the historical time series data library. Let's take an example to make the question clear: we were planning to repeat an experiment for 10 times. We have finished the first 9 times and the acquired 100 data points in each experiment from the begin to the end. When the 10th experiment is half done and we want to predict the next 50 data points. People may do the prediction using the first 50 data points obtained in the 10th experiment, but is there any other way we can employ to use all the data we acquired to do the prediction? Thanks!
Hello!
I am trying to run DAPC analysis in my genome-wide dataset incluiding 188736 genotypes for 188 individuals from 18 different geographic populations. I already know there is some genetic structure in the dataset, at least 2 or 3 groups could be defined. However, when running "find.clusters()" function in order to define the most plausible number of groups that could explain my dataset I obtain strange plots of "Cumulative variance explained by PCA" and "Value of BIC vs number of clusters". The cumulative variance should be higher in the first PCs and decrease as we look at the next ones, showing a curve in the graph up to the 100%. Furthermore, the BIC graph should show an elbow at some point with the smallest level of BIC and do not to represent such a perfect line.
Do you have any idea about why obtaining these results and what do they actually mean? Could it be because the amount of genotypes and samples is such high that the function cannot work with them?
Thank you in advance.
André


Hi all,
I have conducted a mediation analysis using AMOS. The model included 5 predictors, 4 mediators and 1 outcome.
My outcome is binary therefore I conducted Bayesian statistics using the Markov Chain Monte Carlo option. I want to control for multiple comparisons using false rate discovery (FDR) methods. Since there is no p-value with Bayesian, is it correct that the the posterior p-values can be used instead?
If yes, can someone guide me on where to find these posterior p-values for each mediation estimate, as i can only find the posterior predictive p value under "fit measures".
Open to trying multiple comparison correction methods other than FDR.
I have done quiet a bit of reading (the manual, publication, papers that have used the method); however, I still have a question regarding sigma² and obtaining reliable results. The publication states:
"It is important to note that when the method fails to identify the true model, the results obtained give hints that they are not reliable. For instance, the posterior probability of models with either factor is nonnegligible (>15%) and the estimates of sigma² are very high (upper bound of the HPDI well over 1)."
This is one of my latest result:
Highest probability model: 5 (Constant, G3)
mean mode 95% HPDI
a0 -4.80 -4.90 [-7.67 ; -1.81 ] (Constant)
a3 8.32 8.70 [5.02 ; 11.4 ] (G3)
sigma² 37.9 25.6 [11.9 ; 75.9 ]
Am I to conclude that these results are not reliable? What might cause such a large sigma² and unreliable results? I ran the program for a long time so I do not think that's the issue. This problem continues to happen with many other trials that I've done. Does any one have any advice or recommendations? Thanks!
I need the coding or command for estimating the parameters of endogenietic model through Bayesian method of moment or Bayesian two stage least square. If any one have coding or command or package in any software of language to estimating the endogenous predictors of model please mail me I will be very glad.
Hello everyone ,
I have a question about the Bayesian Hierachical model and Simultaneous equations . I want to establish two model, one for the individual tree growth, another for the individual tree mortality. The two models can all build by Bayesian method through the SAS PROC MCMC or R2WinBUGS.
Obviously, there are some relationship between the growth and mortality ,so I want to konw, Can I use the Simultaneous equations or SUR to estimate the two Baysian model together.
Could you give me some advice, Nomatter an essay or code example, thanks a lot.
When doing Bayesian analyses, is there a certain effective sample size that is considered the minimum acceptable sample size, within psychology?
Using R's arms package, I've run two Bayesian analyses, one with "power" as a continuous predictor (the 'null' model) and one with power + condition + condition x power. The WAIC for the two models are nearly identical: -.017 difference. This suggests that there are no condition differences.
But, when I examine the credibility intervals of the condition main effect and the interaction, neither one includes zero: [-0.11, -0.03 ] and [0.05, 0.19]. Further complicating matters, when I use the "hypothesis" command in brms to test if each is zero, the evidence ratios (BFs) are .265 and .798 (indicating evidence in favor of the null, right?) but the test tells me that the expected value of zero is outside the range. I don't understand!
I have the same models tested on a different data set with a different condition manipulation, and again the WAICs are very similar, the CIs don't include zero, but now the evidence ratios are 4.38 and 4.84.
I am very confused. The WAICs for both models indicate no effect of condition but the CIs don't include zero. Furthermore, the BFs indicate a result consistent with (WAIC) no effect in the first experiment but not for the second experiment.
My guess is that this has something to do with my specification of the prior, but I would have thought that all three metrics would be affected similarly by my specification of the prior. Any ideas?
Hello,
I'm using dominant genetic markers to measure genetic differentiation among populations and genetic diversity within populations. Since I'm using dominant markers, I had to calculate allelic frequencies using a bayesian method (Zhivotovsky 1999). There are a lot of measures In the literature (eg. FST; F'ST; GST; G'ST; PhiST; Phi'ST; D) and I want to know which must I choose. I want compare my results with published works with similar species too.
Thank you
P.S. Sorry for my bad english
I have both the Reaction Time (RT) and Accuracy Rate (ACC,range from 0 to 1) data for my 2*2 designed experiment. I want to know whether there is an interaction between the two factors. Two-way ANOVA could be used easily for my purpose. But I would like to calculate the bayes factor (BF) to further confirm the result. I use the same R code with MCMCregress function to do this. The RT variale seems to get compatible BF results as compared to the ANOVA. However, the BFs of ACC are pretty small (less than 1) for all my data, even when the interaction effects are very significant based on the ANOVA.The code goes as follows:
model1.ACC <- MCMCregress(ACC~cond+precond+cond*precond,
data=matrix.bayes,
b0=0,
B0=0.001,c0=0.001, d0=0.001, delta0=0, Delta0=0.001,
marginal.likelihood="Chib95", mcmc=50000)
model2.ACC <- MCMCregress(ACC~cond+precond,
data=matrix.bayes,
b0=0,
B0=0.001,c0=0.001, d0=0.001, delta0=0, Delta0=0.001,
marginal.likelihood="Chib95", mcmc=50000)
BF.ACC <- BayesFactor(model1.ACC, model2.ACC)
mod.probs.ACC <- PostProbMod(BF.ACC)
print (BF.ACC)
print(mod.probs.ACC)
Is there anything wrong in my code? Any guidance will be appreciated.
To see complete details, please find the attached file. Thanks.
I have prepared some sets of climatic data such as temperature and precipitation and have found a strong correlation between these climatic data and my disease incidence data. There are some ways to demonstrate this correlation such as following methods. Which one is more academic and appropriate in this case to publish? And also please let me know if there is any other academic and reliable method in this case.
These are some methods that I know up to now:
-Linear Regression
-Pearson, Kendall and Spearman coefficients
-ANOVA
-Bayesian Interactive Model
-Principal Component Analysis
Can we use Bayesian processing methods to achieve the reconstruction of linear scrambler? What should be focused on when using an optimization algorithm to solve the problem?
When using Bayesian methods to estimate mixture models, such as latent class analysis (LCA) and growth mixture models (GMMs), researchers seem to use common priors for class-specific parameters. Of course, this makes sense when using so-called "noninformative" priors, yet Monte carlo studies often indicate that such priors provide biased and variable estimates, even with relatively large samples.
Confirmatory approaches to mixture modeling, using (weakly) informative priors, performs much better than "noninformative" priors. However, care must be taken when selecting prior distributions (e.g., through careful elicitation from experts or previous research findings).
But consider a scenario in which latent classes are unbalanced (e.g., a two-class model with .80/.20 class proportions). To my knowledge, most researchers use the same priors for parameters in each class, regardless of differences in relative class size. Does anybody know of research in which priors for class-specific parameters have been adjusted to equate their informativeness, dependent on the number of observations in each class? I would be happy to hear of any research where such an approach has been used.
I'm using a Bayesian Network for reliability analysis of a structures. The network is quite big and result in NaN after inference. Different algorithms for inference have been tried but I always obtained the same NaN results. I found the only way to avoid this problems it to reduce the BN size, does any one know another solutions to avoid this ? Thank a lot
I´d like to use approximate bayesian computation to compare three different demographic scenarios (bottleneck vs. constant population vs. population decline) for several species with microsatellites. Is there any tutorial or paper that gives an outline over the whole process (from simulation to parameter estimation and model selection) on how to do this in R or with the command line (not in a point-and-klick way)?
Are there any recent recommendation for measures of convergence and diagnostics criterion in a mixed treatment comparison. Moreover, apart from the standard ranking, OR / mean treatment effects, probability of being the best, Any there any other output which can be interesting to report ?
Dear all,
I recently started my PhD and the main topic of my project is Bayesian estimation with small samples. To get a clear overview of the field, I am conducting a comprehensive literature review on the topic and am trying to ensure that I have found all the relevant work in this area. I'm wondering if you know about any papers in which simulation studies are used to study the performance of Bayesian estimation (in all kind of models), when the sample size is small.
If you know about a paper in which these three topics (simulation study, Bayesian estimation and small samples) are discussed, or if you are working on such a paper right now (especially in press or recently accepted papers that would not appear in databases that I am using for my search), could you please let me know?
I would appreciate any help!
Kind regards,
Sanne Smid
The usual Bayesian analysis takes a prior and updates it to a posterior, using some given data (and a probability model -> likelihood). The prior represents what we already know (believe) about the model. There is nothing like an absolutely uninformative prior, but there can be priors with very high information content (like sharp peaks at a particular hypothesis).
Now consider the experiments to measure the speed of light from Michelson and Morley. The data shows systematic differences between runs and experiments. Given we knew this variability and performed only a single experiment, how could we include the knowledge about the variabilty between experiments? I suspect that this should give wider credible intervals.
As I understand do "non-informative priors" like Jeffreys prior still assume that the data is "globally representative", so the posterior tells me what to expect given my particular experiment, but it ignored that I know that a further experiment would likely give me a different estimate.
I know that a possible solution was to actually perform several Experiments, but here I want to consider the case that I have some konwledge about the variability between experiments but that I can not actually perform several experiments [due to contraints on availability, money].
Another example: a hospital investigates the effect of a particular treatment of its patients. The data is representative for this hospital, but it is well known that the effects will vary between hospitals. If this information is available (at least approximately), is it possible to consider this in the analysis of the data that was obtained only from a single hospital?
In Bayesian approach, the prior probability is often computed by the ratio of sample in training set. Is it really suitable? Is there any method to calculate the prior probability without considering training data?
In Crystal Structure Prediction of organic molecular crystals, almost no prior information is used. Usually, only a rough accounting of space group prior probability is included by preferentially sampling the most common space groups, but even this is done to save computer time, not because it is considered a scientifically sound thing to do!
Sometimes CSD database frequencies of nearest neighbor interactions or hydrogen bonding motifs are used to score crystal structures, but this seems to be applied in an ad hoc manner, without mathematical rigor. In the latest blind test only scoring functions based on energy was used.
Why don't we consider prior probabilities of crystal structure properties, and perform the CSP as a Bayesian update? The scoring function would then be a probability evaluated by Bayes' theorem, the probability of observing a predicted structure is the prior probability times the evidence provided by the crystal structure prediction. An obvious advantage of this method is that it captures kinetic effects during nucleation and growth.
Attached are details of a new framework for meta-analysis that we created that is easy for the main-stream researcher to implement. In addition, it avoids many assumptions involved with the Bayesian method and thus may actually be the more accurate framework. Does anyone with Bayesian interests have any thoughts vis a vis using this as a replacement to the Bayesian framework in network meta-analysis?
See this paper:
In Bayesian networks continuous data is often made discrete, for example:
< 21.5 becomes 0
21.5 > .. < 43 becomes 1
> 43 becomes 2
If you run an optimisation script to find the best thresholds, and not define them using equal count/width, will that lead to overfitting? I personally would expect that it will not lead to overfitting.
Dear colleagues,
for my last manuscript I calculated the outliers from Fst values using Mcheza (basically LOSITAN for dominant markers, using DFDIST). The reviewers asked to verify the outliers using Bayesian methods. I did the re-calculation with BayeScan as it was mentioned by the reviewers. The total amount of detected outliers was slightly less using BayeScan (24 vs. 28, out of 284 loci). But, while almost all outliers apparently under positive selection were identified with both approaches (14 out of 17), none of the outliers under apparent balancing selection identified in Mcheza (11) were identified in BayeScan (7) and vice versa. I assumed, that the Bayesian approach should be more conservative and identify less outlying loci. I did not expect a completely different set for loci under balancing selection. Especially, when the set of loci under positive selection is almost identical. Any idea about how that might have happened or how to interpret it?
Thanks in advance!!!
Regards,
Klaus
I'm very new in SEM and I'm concerned about the reliability of Bayesian estimation of categorical variable in AMOS; then, if it is reliable, how can I interpret those results? How can I know which category is associated with the outcome in the latent variable? It is assumed that only that categorical variable measures the latent construct.
in Bayesian inference we can model prior knowledge using prior distribution. There is a lot of information available on how to construct flat or weakly informative priors, but I cannot find good examples of how to construct a prior from historical data.
How, would I, for example, deal with the following situations:
1) A manager has to decide on whether to stop or pursuit the redesign of a website. A pilot study is inconclusive about the expected revenue. But, the manager has had five projects in the past, with a recorded revenue increase of factor 1.1, 1.2, 1.1, 1.3, 1. How can one add the managers optimism as a prior to the data from the pilot study.
2) An experiment (N = 20) is conducted where response time is measured in two conditions, A and B. The same experiment has been done in dozens of studies before, and all studies have reported their sample size, the average response time and standard deviation of A and B. Again: How to put that into priors?
I would be very thankful for any pointers to accessible material on the issue.
--Martin
Is it possible to use both kinds (nominal, numerical) of features in designing training set for Naive byes machine learning algorithm. Can we mention feature frequencies for designing feature vectors in Naive Byes machine learning algorithm. when Features are represented in Byes algorithm, which out of binary(term x and y are represented by 0,1) and TF (term geography and chemistry are represented by 10,20) approach is better for classifying large size documents.
Please see my question that is attached about prior distribution.

As the models used in Kalman filtering are also Gaussian processes, one would expect that there would be a connection between GP regression and Kalman filtering. If so, could one claim that GP regression is more general than Kalman filtering? In that case, aside from computational efficiency, what would be the other advantages of using Kalman filtering?
Please, I will like to know if the Bayesian approach to research has been successfully employed in studies in forest ecology and conservation. Relevant literature will be appreciated. Thanks.
We have a poolof hairs (around 10 for each reference sample coming from one individual) representing 15 individuals (e.g.).
We can characterize each of them by microscopy for several morphological characters, and by microspectrophotometry for colours informations.
These methods results for each hair in one set of discontinuous/qualitative data (morphological characters) and for the same hair in one set of continuous/quantitative data (colours informations). We can analyze them separately. That is not a problem.
But how can we analyse the two sets in a pooled matrix (combining qualitative and quantitative data) following a standardized protocol (that could be reused latter, like that)?
The questions we need to answer are :
- to test if all hairs coming from the same people cluster in the same group;
- for an unknown sample (of one hair at minimum), to search the group from which is the closest;
- and of course, to have a statistical estimation of the validity of the clusters or the similarity between unknown hairs and the closest clusters.
What is the best way to do that and the best software easy to use? (like XlStat?)
Thank you for your suggestions and ideas.
I am curious about what people think of the approach, from: great idea, bad form mixing two different paradigms, to not ready to use it yet as it hasn't been applied very often etc
I am looking for a good introduction (book/article/chapter) to using Bayesian methods/stats for the design and analysis of psychology experiments. Any suggestions are much appreciated.
hello, I am doing a model based population structure analysis following Bayesian method in R. I have SNP data from 100 diploid individual. I am using K=1,2,3,4,5,6 and 7. Now the problem is when I use k values up to 3 I see only one color in the figure generated in R. But when I use values like 4,5,6 and 7 I see minor color change in the tip of 5-6 vertical line. I thought that there is only one population as majority are showing only one color, but then I checked the lnProb values for each k and it was showing that the highest lnProb value is for k=7. please share your thoughts and suggest me. I have attached 2 figures. Give me some idea.


Hello anyone
I'm trying to perform an analysis of BSSVS (a Bayesian Stochastic Search Variable Selection), but when I run BEAST (including Version 1.75, 1.8.0, 1.8.1 and 1.8.2) under Windows 7(64bit), using BEAGLE 2.1, the program displays the error message:
"Underflow calculating likelihood. Attempting a rescaling...
Underflow calculating likelihood. Attempting a rescaling...
State 1000467: State was not correctly restored after reject step.
Likelihood before: -9781.963977882762 Likelihood after: -9022.104627201184
Operator: bitFlip(Locations.indicators) bitFlip(Locations.indicators)"
Alternatively, I tried to run it under iMAC (yosemite) ,but it can work only for 1 millions generations. And after that the same problems stilly occured.
Does anyone know how I can solve this problem?
The details of the BEAGLE as follows.
Thanks.
Best regards,
Raindy
BEAGLE resources available:
0 : CPU
Flags: PRECISION_SINGLE PRECISION_DOUBLE COMPUTATION_SYNCH EIGEN_REAL EIGEN_COMPLEX SCALING_MANUAL SCALING_AUTO SCALING_ALWAYS SCALERS_RAW SCALERS_LOG VECTOR_SSE VECTOR_NONE THREADING_NONE PROCESSOR_CPU FRAMEWORK_CPU
1 : Intel(R) HD Graphics 4600 (OpenCL 1.2 )
Global memory (MB): 1624
Clock speed (Ghz): 0.40
Number of multiprocessors: 20
Flags: PRECISION_SINGLE COMPUTATION_SYNCH EIGEN_REAL EIGEN_COMPLEX SCALING_MANUAL SCALING_AUTO SCALING_ALWAYS SCALERS_RAW SCALERS_LOG VECTOR_NONE THREADING_NONE PROCESSOR_GPU FRAMEWORK_OPENCL
I have a Hierarchical Bayes probit model, but I'm seeking answers in general for any random coefficients model. Depending on what level I calculate DIC (sum the DICs per unit a vs. DIC for the average respondant), I get different answers in model comparison to a regular probit model. The by unit way is worse than the regular probit, the other is better. The hit rate for the HB model is superior the regular probit, so I don't why the sum of the by unit DICs is worse than regular probit.
I have panel data of 200 regions over 20 years. My goal is to estimate a dynamic spatial (space-time) panel model. I would like to employ an extension of model used in Debarsy/Ertur/LeSage (2009): “Interpreting dynamic space-time panel data models” and in Parent/LeSage: “Spatial dynamic panel data models with random effects,” Regional Science & Urban Economics. 2012, Volume 42, Issue 4, pp. 727-738. See the attached word-file for more information (formulas).
I got three questions:
1.) Is it possible to add lagged exogenous covariates?
Referring to Anselin (2008) in “The Econometric of Panel Data (page: 647)” this would result in an identification problem, since Y_t-1 already includes X_t-1.
2.) I want to use a “twoways” (region and year) fixed effects specification instead of a random effects. Does that lead to any complications?
In my view, it should be possible to de-mean the data first and then apply the MCMC sampler in usual fashion. Is that correct?
3.) As a last step, I try to add a non-dynamic spatial error term (SAR). Note that the spatial weights (row-stand.) are different for the spatial lag (durbin-part) and spatial error. Is that possible?
I have a question concerning the time scale (x-axis) of Bayesian Skyline Plot (BSP) analysis as implemented in BEAST. I am not very familiar with the model underlying this analysis.
I run BSP analyses on three different dataset (one each population) for the mitochondrial COI (537bp). The first population included 97 sequences, the second population 167 sequences, and the third population 48 sequences. The programs (Beauti + BEAST + Tracer) produced 3 BSPs with different time scales: the first population, 0 to 450 Kya; second population, 0 to 1800 Kya; and third population 0 to 350 Kya. My question is “how the more ancient value of x-axis is obtained? It seems related to the number of sequences in the original dataset, does it? If so, which is the relation between the number of sequences and the length of x-axis (time) of the BSP?
Any suggestion will be greatly appreciated.
Ciao
Ferruccio
I'm working on a method to determine the prior-predictive value (PPV, also known as evidence or normalization) in Bayes formula which, in the case of a multi-modal posterior, should work significantly better than common thermodynamic integration methods.
I would like to test my method on a real example.
Does someone know an application of Bayes formula where a high-dimensional, multi-modal posterior hinders an accurate calculation of the PPV? With the data and the explicit form of the likelihood available?
I would like to receive suggestions on applied research if possible. Individually there are plenty of work, but I haven't found much research using the combination of both areas. Thanks in advance for your contribution.
I get error message, "Fatal exception during plot;Illegal range values, can't calibrate" when I try Bayesian skyline reconstruction in "Tracer" program. I would like to know what is wrong. Is MCMC not enough?
I am searching different methods in "blind image restoration" and "blind PSF estimation". What are the advantages of non-Bayesian methods and how can one improve these methods in order to obtain a more precise PSF and image? In Bayesian methods how can we assign probabilities to f, h, and n, and obtain the original image from these probabilities? where can I find the codes for simulating these methods? I want to simulate a method for standard images and then improve it to get better results. which method do you think is better to start with?
I have selected representative strains from each cluster in my Maximum Likelihood tree for divergence dates estimation but I made sure I covered the entire time period of detection of these strains (1975-2012). Will my exclusion of some of the strains affect my estimated evolutionary rate and times of divergence at the nodes after BEAST analysis?
Is HPD Interval is the best interval that we could use as interval estimator?
From posterior distribution, we could form many Bayesian Credible Interval/Region. HPD interval is the shortest interval among all of the Bayesian Credible Intervals. Many literature said that we could use HPD interval as the interval estimator.
What is the requirement for any interval so it could be use as a good interval estimator?
I'm not a statistician. Just an interested MD. So, please, suggest somethitng relatively understandable. WinBUGS, e.g., is out of question. It has to have GUI, not only a command line. I have some expirience in Object Pascal and Java but not much. I'd appreciate any advise for beginner. I'm planning to start with observational longitudinal data (register and survey) and, maybe later, move towards network meta-analysis.
As my question may sound a bit bulky, please consider the following example:
You want to estimate the latent abilities of p participants who have answered i items in a questionnaire. The individual answers to the different items can be ascribed with the following model:
Answer_i,p = u_i + u_p; u_i ~ Normal(0, sd) and u_p ~ Normal(0, sd)
where u_i and u_p are randomly varying parameter manifestations of item difficulty and participant ability, respectively.
Suppose you expect (from previous studies) that participant ability is driven by some covariate C that you can assess and/or experimentally manipulate. A regression of u_p on C does not suggest any significant association between participant ability and this covariate, although the effect (beta) points numerically to the expected direction.
Therefore you try to inform your psychometric model by including a (fully standardized) covariate C as a second level predictor of participant ability:
Answer_i,p = u_i + u_p; u_i ~ Normal(0, sd), u_p ~ Normal(beta*C, sd)
Surprisingly, the beta of C now differs significantly from zero, as the estimates of participant ability have changed. Thus the estimates of participant ability become informed by a covariate, which did not have any predictive value before.
I repeatedly encountered this phenomenon. Nonetheless I must admit, that it remains quite elusive to me. Moreover this seems to introduce some kind of arbitrariness in the interpretation of predictors for latent abilities. Is the covariate indeed informative with regard to participant ability or is it not?
Does anyone have a solution to this issue? Proably such situations should be dealt with by appropriate model comparision strategies (i.e., one should refrain from interpreting estimates of such nested effects in isolation)?
Which method is more efficient (fast and reliable) for a corpus covering not more than 20 categories?
Can anyone compare Particle Filter and Gibbs Sampling methods for approximate inference (filtering) and learning (parameter estimation) tasks in general DBNs containing both discrete and continues hidden random variables? Are both methods applicable? Which one is more computationally efficient? Which one is suitable for which task?
I am asking for estimating the location parameter of logistic distribution by Bayesian methods. I am in need of a proper prior distribution for µ , and how to know the prior is Normal ? or logistic ? Or how to know what is the result for posterior distribution for µ.