Questions tagged [bayesian]

Bayesian inference is a method of statistical inference that relies on treating the model parameters as random variables and applying Bayes' theorem to deduce subjective probability statements about the parameters or hypotheses, conditional on the observed dataset.

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12
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5answers
660 views

Do Bayesians ever argue there are cases in which their approach generalizes/overlaps with the frequentist approach?

Do Bayesians ever argue that their approach generalizes the frequentist approach, because one can use non-informative priors and therefore, can recover a typical frequentist model structure? Can ...
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1answer
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How do I complete the square with normal likelihood and normal prior?

How do I complete the square from the point I have left off at, and is this correct so far? I have a normal prior for $\beta$ of the form $p(\beta|\sigma^2)\sim \mathcal{N}(0,\sigma^2V)$, to get: $...
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2answers
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Optimal software package for bayesian analysis

I was wondering which software statistical package do you guys recommend for performing Bayesian Inference. For example, I know that you can run openBUGS or winBUGS as standalones or you can also ...
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2answers
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What is the difference between Informative (IVM) and Relevance (RVM) vector machines

I'm trying to understand if there is any specific difference between Informative IVMs and Relevance RVMs other than the terminology. I've not seen anything explicit. When I'm reading about vector ...
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1answer
4k views

How to write a poker player using Bayes networks

This is my first question on stackexchange and also my first time implementing a Bayesian network so I will apologize ahead of time for any novice mistakes I make. The goal of my project is to ...
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3answers
1k views

Why does this excerpt say that unbiased estimation of standard deviation usually isn't relevant?

I was reading on the computation of the unbiased estimation of standard deviation and the source I read stated (...) except in some important situations, the task has little relevance to ...
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2answers
58k views

Difference between naive Bayes & multinomial naive Bayes

I've dealt with Naive Bayes classifier before. I've been reading about Multinomial Naive Bayes lately. Also Posterior Probability = (Prior * Likelihood)/(Evidence). The only prime difference (while ...
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0answers
107 views

Adaptive stopping rule for spatially autocorrelated Poisson data

I have a problem where I am given an initial prior or proportion for the number of occurrences per some unit with known standard deviation (an example is 3 per mile). I wish to test if this ...
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2answers
6k views

What are R-structure G-structure in a glmm?

I've been using the MCMCglmm package recently. I am confused by what is referred to in the documentation as R-structure and G-structure. These seem to relate to the ...
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3answers
1k views

How to model a biased coin with time varying bias?

Models of biased coins typically have one parameter $\theta = P(\text{Head} | \theta)$. One way to estimate $\theta$ from a series of draws is to use a beta prior and compute posterior distribution ...
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1answer
2k views

Posterior distribution for multinomial parameter

(topic moved from maths.stackexchange.com) I'm currently developing an application integrating a probabilistic inference engine for Bayesian Networks. The Bayesian Network integrates some form of "...
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100 views

How can you convert Bayesian Information Criterion parameters to a probabilistic interpretation?

I'm working with a general bayesian information criteria to determine if this data exhibits a bimodal, trimodal, quadmodal etc. My existing BIC exhibits clear trimodality, but I'd like a hypothesis ...
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1answer
667 views

Gamma-normal distribution as prior

When I study the Bayesian econometrics, the book firstly introduces Gamma-Normal distribution as (conjugate) prior, then the posterior will have the same distribution as the prior. But my question is, ...
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736 views

Generating and analyzing predicted data in JAGS

I am trying to model a logistic regression on data predicted from the results of a previous logistic regression, and am having trouble figuring out how to do it, either in OpenBUGS (BRugs) or JAGS (...
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94 views

Inferring from a combination of uncertain and certain data

I am trying to estimate the surface (isochrone), $z_i(x)$ for which $T(x,z)=0$ from noisy measurements of $T(x,z)$ everywhere and 3 almost noise free control points: Instead of using the $T(x,z)$ ...
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Why is clutter problem intractable for large sample sizes?

Suppose we have a set of points $\mathbf{y} = \{y_1, y_2, \ldots, y_N \}$. Each point $y_i$ is generated using distribution $$ p(y_i| x) = \frac12 \mathcal{N}(x, 1) + \frac12 \mathcal{N}(0, 10). $$ ...
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2answers
182 views

How to go about selecting an algorithm for approximate Bayesian inference

I am wondering if there are any good rules of thumb for how to go about selecting an approximate inference algorithm for a problem/model (specifically when exact inference is intractable)? When you ...
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0answers
675 views

How to sample from the prior predictive distribution in jags? [closed]

Is there an example available of how I can sample from the prior predictive distribution (without data) in jags? I would like to get a better sense for the contribution of the prior in a multilevel ...
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“Fully Bayesian” vs “Bayesian”

I have been learning about Bayesian statistics, and I often have read in articles "we adopt a Bayesian approach" or something similar. I also noticed, less often: "we adopt a fully Bayesian ...
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6answers
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Bayesian vs frequentist Interpretations of Probability

Can someone give a good rundown of the differences between the Bayesian and the frequentist approach to probability? From what I understand: The frequentists view is that the data is a repeatable ...
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6answers
3k views

What is the connection between credible regions and Bayesian hypothesis tests?

In frequentist statistics, there is a close connection between confidence intervals and tests. Using inference about $\mu$ in the $\rm N(\mu,\sigma^2)$ distribution as an example, the $1-\alpha$ ...
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1answer
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How to get prediction for a specific variable in WinBUGS?

I am a new user of WinBUGS and have one question for your help. After running the following code, I got parameters of beta0 through ...
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1answer
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Help me understand $p$-values in Bayesian glm

I am trying to run a Bayesian logit on the data here. I am using bayesglm() in the arm package in R. The coding is ...
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2answers
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Linear discriminant analysis and Bayes rule: classification

What is the relation between Linear discriminant analysis and Bayes rule? I understand that LDA is used in classification by trying to minimize the ratio of within group variance and between group ...
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1answer
571 views

Using Bayesian model diagrams to present both model description and results (posteriors)?

The model diagrams in "Doing Bayesian Data Analysis", John Kruschke creates diagrams like this: To represent The following BUGS/JAGS code: He discusses this representation in his related blog post, ...
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2answers
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Hierarchical multinomial logit with R/JAGS

I am working on a small project where I have to do a Choice Based Conjoint (CBC) analysis. In order to get the part-worths for the different consumers I need to estimate a hierarchical multinomial ...
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2answers
565 views

Absolute error loss minimization

From Robert (The Bayesian Choice, 2001), it is proposed that the Bayes Estimator associated with the prior distribution $\pi$ and the multilinear loss is a $(k_2/(k_1+k_2))$ fractile of $\pi(\theta|x)$...
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0answers
58 views

Analysing choices pattern

we have a process in which, at each step, a set of elements are presented to user, the user choses one, his choice is recorded and next round starts with a new set of elements. For example: 1. {20,50,...
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1answer
6k views

Estimation of parameters as a mode of posterior distribution

I was referring to this http://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation. Here it is mentioned that estimating the parameters $\theta$ is actually finding the mode of the posterior ...
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6answers
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If you use a point estimate that maximizes $P(x | \theta)$, what does that say about your philosophy? (frequentist or Bayesian or something else?)

If somebody said "That method uses the MLE the point estimate for the parameter which maximizes $\mathrm{P}(x|\theta)$, therefore it is frequentist; and further it is not Bayesian." would you agree?...
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2answers
226 views

Inducing sparsity in a Bayesian model

Can someone explain or point me to an introductory reference that deals with the notion of sparsity in Bayesian modeling? What does the idea of sparsity really mean? What does it mean to 'induce ...
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0answers
181 views

Popularity of Bayesian methods in statistics and machine learning

I know I have seen some research, perhaps in the contexts of time-varying topic models, on the popularity of Bayesian methods in statistics and machine learning over the last 20 years. Unfortunately ...
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3answers
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What are some illustrative applications of empirical likelihood?

I have heard of Owen's empirical likelihood, but until recently paid it no heed until I came across it in a paper of interest (Mengersen et al. 2012). In my efforts to understand it, I have gleaned ...
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1answer
729 views

Posterior simulations of the variances with the mcmcsamp function

I would like to get the posterior simulations of the variance components of a lmer() model with the mcmcsamp() function. How to do ? For instance, below is the result of a lmer() fitting : ...
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0answers
120 views

bayesian test of linear regression hypothesis

write program bayesian test of linear regression hypothesis In R or winbugs : ...
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0answers
4k views

Posterior derivation with prior as Normal-Gamma distribution [duplicate]

I am studying Gary Koop's Bayesian Econometrics , it is bit confusing in the beginning. I will reproduce some results from the textbook here in order to smoothly move to my question. For a simple ...
3
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1answer
374 views

False discovery rate of a Bayesian classifier: scaling based on prior odds?

I am trying to assess the performance of my Bayesian classifier. One measure that I calculate is the false discovery rate (FDR): FP / (FP + TP), where FP = False Positive and TP = True Positive. ...
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3answers
1k views

A question about parameters of Gamma distribution in Bayesian econometrics

The Wikipedia article on the Gamma distribution, lists two different parameterisation methods, one of them frequently used in Bayesian econometrics with $\alpha>0$ and $\beta>0$, $\alpha$ is ...
2
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1answer
169 views

How to calculate a posterior for the given model?

Suppose we have a joint distribution on vector $[\mathbf{x}, y]$: $$ p([y, \mathbf{x}] ) = \mathcal{N}\left(\begin{pmatrix} y \\ \mathbf{x}\end{pmatrix}| 0, \begin{pmatrix} k& \mathbf{v} \\ \...
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2answers
4k views

What is the relationship between sample size and the influence of prior on posterior?

If we have a small sample size, will the prior distribution influence the posterior distribution a lot?
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1answer
277 views

Bayesian, MDL or ML interpretation of cross-validation?

Is there any known Bayesian, ML or MDL interpretation of cross-validation? Can I interpret cross validation as performing the right update on a specifically crafted prior?
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1answer
3k views

Calculate R-squared with JAGS and R

I have the following model that I am running in JAGS from R: ...
7
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3answers
6k views

Priors for log-normal models

I am trying to determine what the most appropriate non-informative priors are for the two parameters of a log-normal distribution (for an accelerated failure time model). I had been working with a ...
21
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1answer
4k views

Residual diagnostics in MCMC -based regression models

I've recently embarked on fitting regression mixed models in the Bayesian framework, using a MCMC algorithm (function MCMCglmm in R actually). I believe I have understood how to diagnose convergence ...
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2answers
267 views

How to move from some arbitrary “distance” to a probability distribution?

I'm doing some object recognition, and when I compare two images, I get some unbounded "distance" between the two images, representing how similar they are. This is somewhat useful, but it seems like ...
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2answers
105 views

How to calculate the probability that an algorithm classifies seven wines out of ten correctly when the true error is 0.23?

I am considering the following problem. Calculate the exact probability that an algorithm classifies seven wines out of ten correctly when the true error is 0.23. Should I solve this with Bayes' ...
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2answers
555 views

Frequentism and priors

Robby McKilliam says in a comment to this post: It should be pointed out that, from the frequentists point of view, there is no reason that you can't incorporate the prior knowledge into the model. ...
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2answers
103 views

Inference on random graph, with an application to mobile sensors

I've attended a course on Machine Learning and another one in Network Analysis, and I wonder if this two topics already intersect, in particular I'm interested in the following model: we have a ...
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1answer
396 views

Multinomial Naive Bayes

I'm looking for an article, program, algorithm that can clearly explain whats going on inside a Multinomial Naive Bayes classifier compared to a Gaussian Naive Bayes Classifier.
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2answers
317 views

What is the appropriate machine learning algorithm for this problem?

I am working on a problem which looks like this: Input Variables Categorical a b c d Continuous e Output Variables Discrete(Integers) v x y Continuous z The major issue that I am facing is ...