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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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Bayesian hierarchical design

Hope someone can give me a hint!!!! Bayesian hierarchical design Some people think that in the Bayesian statistical model, the design can be distributed to the unknowns in an endless design. For ...
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Difference between objective and subjective Bayesians

What is the difference between objective Bayesians and subjective Bayesians? What objects or procedures do they define or interpret differently? Is there any difference in their choice of methods?
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Bayes estimator with weighted Loss

I have been working through a wide variety of problems involving Bayes risk and loss functions and I couldn't immediately solve the following From "The Bayesian Choice", Consider $x \sim N(\...
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What precisely does it mean to borrow information?

I often people them talk about information borrowing or information sharing in Bayesian hierarchical models. I can't seem to get a straight answer about what this actually means and if it is unique to ...
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Bayesian networks [on hold]

I want to model an biological system with Bayesian network. Almost all biological system has loop or feedback but Bayesian network is a Directed acyclic graph. my question is: What happen to a loop ...
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Calculate the Bayesian Premium and the Credibility Premium (model is inverse Gamma, prior is Gamma) in general form

The question I was given is to calculate the general form (sample size = $n$) of the Bayesian Premium and the Credibility Premium where the losses are distributed as an inverse Gamma distribution with ...
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With two deep learning models, how do I perform Bayesian Model Averaging for better prediction on a test set?

Given two deep learning models that can predict on a test set, what I want to do is use BMA (Bayesian Model Averaging) to average the models to better predict? What exactly is the procedure for this? ...
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1answer
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Ockham's Razor in Bayesian Modelling

This question might be a little philosophical / generate discussion. I hope, there may still be some useful answers. I am currently thinking about how Ockham's Razor relates to Bayesian statistical ...
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Binomial distribution as likelihood in Bayesian modeling. When (not) to use it?

I am currently trying to figure out some strangeness about using the Binomial distribution in Bayesian modeling to define the likelihood. To make an example assume I have two conditions, and in each ...
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Is this a correct use of Bayesian statistics when choosing a box A-E?

Occasionally my friends and I attend a local pub quiz. In the final round of the quiz, the winning team is allowed to select one box from five, labelled: A, B, C, D, E In one of these boxes is a £...
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2answers
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Bayesian approach to report simulation studies?

I am running a simulation study where we want to estimate a proportion $p$. We are reporting the coverage of credible intervals with a uniform prior, and we are doing $500$ Monte Carlo simulations. We ...
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Guidance on time-series change point detection or identification of contributions

Let me preface this by saying that I am not a data scientist. Please excuse any imprecision in my use of subject specific terms or notations. Please feel free to edit my question, to improve any ...
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1answer
31 views

Equivalence of gamma and inverse gamma:Does choosing a prior lead to possibly different evaluations?

Suppose we had an expressions that was proportional to $$\frac{1}{\sigma^{3}}\exp(\frac{-\beta}{\sigma^{2}})$$ My question is, can you choose different possible parametrization for a prior ...
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Some questions about exponential families

Regarding the book The Bayesian Choice I understand most of chapter three on exponential families, but there are two parts I have trouble understanding. The first is Consider$$f(x|\theta)=h(x)\...
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Help modeling rjags 2x2 logistic model with subjects and items as random intercepts (Bayes)? [on hold]

I'm trying to set up a Bayesian 2x2 logistic GLM model in rjags. would like to see if I have set up everything correctly (are the priors reasonable, is the GLM reasonable?). Below is the model in ...
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What is the correct formula for Bayesian update for normal distribution with known variance [duplicate]

As question title states, I'm interesting in Bayesian update of normally distributed data with known variance. I compared three sources and they seems to contradict each other. I use some kind of ...
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unconditional prior distribution of g-prior (Bayesian Linear Regression)

Consider a Gaussian regression model $\boldsymbol{Y} =\boldsymbol{X}\boldsymbol{\beta} + \boldsymbol{\epsilon},\quad \boldsymbol{\epsilon}\sim N( \boldsymbol{0},\sigma^2I)$ I put a Hyper-g Priors (...
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When is it possible to know posterior probabilities in Bayes, without estimation? [on hold]

When is it possible to know posterior probabilities in Bayes, without estimation? Does it mean that one collects data, which is the true response? My notes write (for probabilistic classification ...
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Can the Bayesian but not the frequentist “just add more observations”?

Since the frequentist's p-values are uniformly distributed under the null hypothesis, it is a highly problematic practice to add more and more data to your sample until you find a significant result. ...
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About PAC-Bayesian bounds in learning theory

Consider PAC-Bayesian bounds used in learning theory (as defined in say section $1.2$, page $3$ of this paper, https://arxiv.org/pdf/1707.09564.pdf). I want to know what is the precise mathematical ...
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Beta prior for zero events

Good day, What are the best recommendations for beta priors for zero events in a binomial model? I have read that neutral prior (0.33, 0.33) and Bayes uniform prior (1, 1) are appropriate per Kerman ...
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0answers
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variational inference derivation

According to this lecture note, Eq. 25 gives the coordinate ascent update for latent variable $z_k$ as follows $$q^*(z_k)\propto\exp(E_{-k}[\log{p(z_k,Z_{-k},x)}])$$ and I understand the derivation ...
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How to derive the noninformative prior for location parameters and scale parameter?

I am reading this paper, in it: I have a lot of confusion reading it, I will list it one by one: Let $X$ be distributed as $f(x-\theta)$, which is a location invariant density. Q1: The sentence <...
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How does Bayesianism deal with made up / post hoc explanations?

Consider the example of an object spontaneously going up in flames. Now one hypothesis may be that it was (A) some chemical reaction, but another could be (B) an invisible man with a lighter. This ...
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How are bayesian networks created from an attribute matrix and target vector?

I'm very familiar with correlation networks but I can't seem to grasp my head around how Bayesian Networks are constructed. How are the "edges" determined? How is the structure determined? I was ...
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Clarification: Are Generative Adversarial Networks an alternative to MCMC sampling?

I have been reading the original Goodfellow, et. al. paper on Generative Adversarial Networks and the way that they can obtain estimates of the posterior distribution of a discriminative network or ...
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Sigma interpretation in Bayesian Linear Model?

I have two question concerning my output of my bayesian linear regression. 1) I have all beta posterior and obviously, having used a prior for Sigma, i have a posterior for Sigma too, but what can i ...
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1answer
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Basic probability theory

I was recently given the following statistics: On a particular highway, 18% of drivers are black, 63% of drivers searched by the police are black. So, a black driver is 7.7 times more likely to be ...
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Std dev should be less than 0.289 (help in understanding)

In Kruschke’s book (Doing Bayesian Analysis), he talks about using mean and standard deviation as one way to establish the beta priors for Binomial Bayesian model. He advises that the std dev should ...
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Large discrepancy between MorePower and G*Power

I am planning the required number of subjects for a 2x2 analysis (one within-subject and one between-subject) to detect a medium-sized interaction effect ($\eta_p^2$ = 0.0588). As a first estimate, I ...
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1answer
41 views

Which kernel is this

If $x \sim N(0,\sigma^{2})$ and $\pi(\sigma)=\frac{1}{\sigma}exp(\frac{-a}{\sigma^{2}})$ then the posterior would be proportional to As, $f(x|\sigma)$ proportional to $\frac{1}{\sigma}exp(\frac{-...
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Moments of the Generalized Dirichlet distribution

I have been trying to solve the following integral. $ \int\theta_j \sum_{k=1}^K \theta_k \beta_{k,w} \prod_{k=1}^K \frac{\Gamma(\alpha_k + \beta_k)}{\Gamma(\alpha_k)\Gamma(\beta_k)} \theta_k^{\...
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Examples of state space models where the filtering problem can be solved analytically

Background A discrete-time, Markovian state space model takes the form \begin{align} \mathbf{y}_t&\sim p(\mathbf{y}_t\,|\,\mathbf{s}_t,\,\boldsymbol{\theta})\\ \mathbf{s}_t&\sim p(\mathbf{s}...
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Validating the target value [closed]

I have metric which has never met target, and it seems that the target is too high so how can I prove statistically the target is Unachievable
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3answers
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Averaging Bayesian posteriors [duplicate]

Does it make sense to use different uninformative priors and then take the mean of all the posteriors? For example, use (0,0), (0.5, 0.5), (1, 1) and calculate three posteriors and then take the mean. ...
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Non-deterministic MCMC model with updates

0 down vote favorite I have historical data for three variables : Y, X1, X2, for example 1000 points. The distribution of future values of Y depends from X1 and X2 and can't be expressed in ...
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Formulating likelihood for MCMC with observations (data) being randomly sampled

My problem is the following: I want to get a distribution of cumulative damage to a structure over its service life (say, 50 years) given observed extreme events. I have a function for cumulative ...
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Failing to implement Bayesian Chi2 goodness of fit test

I am trying to implement one of the methods described in Valen Johnson's A Bayesian Chi-Squared Test for Goodness of Fit. It presents a couple of variants depending on whether the random variable of ...
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1answer
61 views

Check if log-likelihood function is correctly derived

This question is a continuation of this one. By guesswork, I found out that $\vec{\theta}=(5.2,5.3,1.0)=$ $(A,B,C)$ was a good guess that made my model $$y_i=A\sin\left(\frac{x_i}{B}\right)+C\...
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2answers
44 views

Probability that a sample came from a known distribution

I'm looking for a general solution to what I assume must be a common problem because it comes up in every Bayesian calculation, but doesn't seem to be directly answered anywhere. I have an extremely ...
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1answer
85 views

How to find the likelihood given data?

I have a textfile with the two columns $$\mathbf{x}=(x_1,...,x_i)$$ $$\mathbf{y}=(y_1,...,y_i)$$ I want to use the following model for the data $$y_i=A\sin\left(\frac{x_i}{B}\right)+C\epsilon_i,$$...
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1answer
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Interpretation of a classic multinomial logit vs. BMA of multinomial logit

EDIT #1 Most likely I have set up the function bic.mlogit in a wrong way. @Jesper Hybel, hopefully, directed me in the right way. With the new setup I get two sets ...
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Is propensity score analysis with a bayesian weighted outcome regression model conceivable?

I want to implement a Bayesian Model Averaging for Propensity Score Analysis as discussed here and here. Chen and Kaplan 2014 argue that a "benefit of conducting Bayesian propensity score analysis is ...
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Bayesian hypothesis testing with multiple beta-binomials

I want to test questions relating to whether individual ants of a certain species have personal food preferences, using a Bayesian model built up of multiple beta-binomial distributions. My problems ...
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2answers
161 views

Posterior of $\text{Normal}(\theta,1)$ with a Cauchy prior distribution

If $X \sim N(\theta,1)$ with Cauchy as robust prior $$\pi(\theta) = \frac{1}{\pi(1+\theta^2)} \qquad -\infty < \theta < \infty$$ What will be the posterior distribution when Cauchy is $(-2 <...
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Posterior predictive for the beta distribution? [duplicate]

I'm looking to do Bayesian inference using the beta distribution. Are there any sources for a derivation of the posterior predictive? It's an exponential family, so it should have a conjugate prior, ...
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1answer
330 views

Proof of Approximate / Exact Bayesian Computation

the ABC algorithm is given as Draw $\theta \sim \pi(\theta)$ Simulate data $X \sim \pi(x | \theta)$ Accept $\theta$ if $\rho(X, D) < \varepsilon$ where $\pi(\theta)$ is the prior, $\pi(x | \...
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1answer
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Basic question on proportionality in Bayesian Inference for Normal distribution

I have a nagging question regarding the Normal distribution and maintaining proportionality in Bayesian Inference. Say for example that: $\pi(\theta|Y) \propto L(Y|\theta)\pi(\theta)$ $Y | \theta \...
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2answers
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How does one usually compute the gradient and the Hessian of a proposal in a MCMC algorithm?

In some proposals of a MCMC, the mean/location vector and the covariance/scale matrix are functions of the gradient/jacobian and hessian of the log-likelihood. I'm wondering how does one usually find ...
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Hamiltonian MCMC information gathering [duplicate]

I started gathering information about Hamiltonian MCMC and I would like to ask if someone knows some good papers or books.If it possible notes that give a detailed explanation of Hamiltonian MCMC. ...