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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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How to estimate the intriscs probability error of a string of character

So my problem is as follow : I have a given string of characters, and I would like to quantify the uncertainty linked to the probability of each letter types in the string, based on there observed ...
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Is it rational to select a parameter posterior value because it maximizes utility, even if probability is low?

I did Bayesian parameter estimation and I have now an estimate of the posterior distribution for my model parameters (say I have 2000 samples). Now I would like to make the optimal decision under my ...
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Calculating the posterior distribution of linear predictor

I am currently fitting a linear regression model in a bayesian framework in R with the package ngspatial. To investigate the quality of fit, I would like to calculate the bayes R2, as suggested here ...
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Bayesian chi-squared tests

I have a dataset with two groups of participants. Each participant performed a repeated measures task on which three types of errors could be made. I want to measure the difference in distributions of ...
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How can you deal with volatility of a metrics that depends on the count of events?

I am using Herfindahl Index metrics to measure the degree of concentration of posts by email, device_id, IP and other variables to identify potential fraud events. For example, a high degree of ...
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optimization based interpretation of Bayes' theorem

I read about one equivalent interpretation of bayes' theorem as follows: $P(\mathcal{M}|x) = \frac{P(x|\mathcal{M})\cdot\pi(\mathcal{M})}{\int P(x|\mathcal{M})\cdot\pi(\mathcal{M}) d\mathcal{M}}$ is ...
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How do Bayesians verify their methods using Monte Carlo simulation methods?

Background: I have a PhD in social psychology, where theoretical statistics and math were barely covered in my quantitative coursework. Through undergrad and grad school, I was taught (much like many ...
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relation among loss function / MLE / Bayesian estimation

I have read a lot of stuff on the relation between minimizing a loss function / maximizing the likelihood / choose a centrality measure of the posterior (Bayesian estimation); but I cannot see a clear ...
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Non-informative prior for the covariance matrix

I'm currently working on a project around the Bayesian approach to portfolio selection, and I can't manage to wrap my mind around the specification of the non-informative (diffuse) prior. Assuming ...
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Conditional Probability Table in R

I want to perform Bayesian network analysis in R. I have a large network and i am bit confused with defining conditional probability tables! In my network i have a node with in-degree of centrality ...
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Introduction to Variational Bayesian methods?

I am interested in learning about Variational Bayesian methods. I understand the general idea, explained in Wiki, where the aim is to approximate a posterior using a more tractable distribution, in ...
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JAGS: Posterior Predictive Check for a Logistic Regression Model

I want to perform a posterior predictive check on some simple logistic regression models that I fitted in JAGS. I found a function in the R package jagsUI called pp.check (see doc here: (pp.check ...
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help determining ROPE for bayesian multilevel probit model

I am having difficulty determining a justifiable region of practical equivalence (ROPE) for a parameter from a multilevel probit model Below is the posterior distribution for the fixed-effect of ...
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Posterior convergence in expectation vs probability

Let's assume that we are doing approximate Bayesian inference and compute the convergence of our posterior estimate to the true value of the parameter using Wasserstein distance. Why posterior ...
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18 views

Gibbs sampling for drawing samples and estimating parameters

I'm learning Bayesian inference by myself and having a difficulty for understanding Gibbs sampling. From what I understood, Gibbs sampling is to draw samples from a given probability distribution $p(...
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Marginalising over Dependent Random Variables

Suppose I have two RVs, $A$, and $B$. Every place I have looked thus far suggests the following for marginalisation, which for me is fine: $f_A(a) = \int_{-\infty}^{\infty} f_{A,B}(a,b)db $. ...
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Generating data from the posterior distribution

Let $$p(D \mid \mu,\sigma^2) \sim \mathcal{N}(\mu,\sigma^2)$$ where $D=(x_1\ldots x_n)$ is my data. I imposed a normal prior on the mean as $$\pi(\mu) \sim \mathcal{N}(\mu_0,\sigma_0^2)$$ Using Bayes, ...
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Integrals simulation in the program R [closed]

Given the simulation with the R program, show that the integral is below $\int_0^{\sigma^\pi (x)} x^2 \lambda e^{-\lambda x} d x =1/2$ . Assumptions of the problem let $x|\lambda \sim exp (\lambda) \...
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Bayesian Linear Regression to Gaussian Process

I'm trying to understand how a Gaussian Process with a squared exponential covariance function can be obtained from Bayesian Linear Regression with a Gaussian prior $N(0,\sigma_p^2 I)$ on the ...
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1answer
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MCMC - how to compute prior(𝜃)

Question How to compute the prior $P(𝜃)$ and $P(𝜃')$ in MCMC when calculating the posteriors? Prior I thought prior keeps updated with the accepted θ'. However, the way it is computed in the ...
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Can I use Poisson regression to model prevalence ratios if I only have information on events?

I often used Poisson regression models to estimate prevalence ratios. However, in these cases my data contained information on the whole population, including events (1) and non events (0). ...
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How can I determine what values of alpha and kappa to use for Bayesian Optimization?

I'm using the pretty great Bayesian Optimization package for python. I have a very noisy function I'd like to optimize for a given hyperparameter. I've read a little on this, and it seems like if ...
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Using information about optimising function in bayesian optimisation

I know that bayesian optimisation is a strategy for optimising black-box functions. But if i have some information about type of function or it's specific behaviour at some interval what methods of ...
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Bayesian A/B test for LogNormal data

I'm currently working on a (manual) calculation for a bayesian A/B test on logNormal data. I'm currently working with simulated data to increase my understanding. It's giving me some problems, so I ...
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How to calculate Kernel Density for Bootstrap Likelihood

I am attempting to write R code to generate bootstrap likelihood as described in section 3 of this paper https://arxiv.org/pdf/1510.07287.pdf. I am confident that I performed the bootstraps correct, ...
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Can you calculate Bayes Factors for effects in a non-significant regression model

I ran a linear regression model and want to calculate Bayes Factors (BF) for any non-significant effects that are generated by the model. However, the regression model itself is not significant (p = 0....
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dirichlet distribution and excessively large numerator

what I am trying to do is calculating posterior probability using dirichlet distribution as my prior. the situation is like this. a web log have three variables A, B, C, and each variable's value is ...
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ZINB error code in winbugs: order of negative binomial y[1] must be an integer [migrated]

I have a problem while running ZINB regression using Winbugs, it keeps showing "order of negative binomial y[1] must be an integer" when I click "gen inits" in the Specification Tool tab. This is my ...
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Building a psychometric function for tasks using adaptivity paradigm [closed]

I'm trying to build a psychometric function via the Bayesian Estimate approach developed by Treutwein and Strasburger in Fitting the Psychometric Function: https://link.springer.com/article/10.3758/...
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Is assigning an inverse-Wishart distribution to a diagonal matrix problematic?

I'm reading the paper Bayesian Vector Autoregressions by Thomas Wozniak. He considers the model $$y_t = \mu + A_1 y_{t-1} + \cdots A_k y_{t-k} + u_t$$ where each $y_i$ is a $N$-vector, each $A_j$ is a ...
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How to visualise uncertainty on error plots summarising multiple mcmc simulations [closed]

I am plotting the non-integer outputs of parameters x, y and z computed across 100 simulations for subjects A to E (via mcmc). My plot shows error on the y-axis, and subjects A - E on the x axis. ...
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Find normalization constant from factorized density

Please consider the following Bayes Network: We can express density $p(\mathbf{x}_1 | \mathbf{x}_0, \mathbf{y}_1)$ in terms of measurement and motion models by ignoring normalization constants as: $...
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Calibrating LASSO prior (how to select the scale hyperparameter)?

I want to use a LASSO prior (Laplace prior) for a location parameter $\mu$ $$\pi(\mu \mid s) = \dfrac{1}{2s}\exp\left(-\frac{\vert \mu \vert}{s}\right).$$ However, I do not know to calibrate this ...
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2answers
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Simple up/down vote rating but weighted by number of responses

I am trying to analyse the ratings for restaurants from a website. The rating system on the website is pretty simple: people can up-vote or down-vote. The restaurant is then presented to website ...
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How to calculate mean and variance from very small function proportional to the density?

Problem Say I have the following function $g(x)$, which is proportional to the density function $f_\theta(\theta)$ of random variable $\theta$, i.e. $g(\theta) \propto f(\theta)$, such that $$ \...
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Posterior using Numerical integration - why divided by (sum of posterior / number of samples)

Background Reading Markov Chain Monte Carlo (MCMC) and the numerical integration method to get the posterior. Question The implementation code divides the posterior with (post.sum() / len(thetas)). ...
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Bayesian methods are about averaging over uncertainty rather than optimization. Explain?

I came across the statement "The key ingredient in Bayesian methods is to average over your uncertain variables and parameters, rather than to optimize". Can someone explain why this is? ...
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Is expectation maximization an example of empirical Bayes?

I don't think I truly understand what methods are classified as "empirical Bayes". Is expectation maximization considered an example of this?
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Can you find the posterior mode of an unknown distribution without MCMC?

I was wondering if you wanted to compute the MAP estimate of an unknown posterior distribution, is there a non-sampling based method that would suffice? As in, if you don’t need to know anything more ...
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Computationally verifying the equivalence of ridge regression estimates and Bayesian regression estimates

I'm trying to show that the numerical estimates of ridge regression's parameter estimates are the same as the MAP parameter estimates of a Bayesian regression model with normal prior distributions. So ...
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55 views

Label Switching and Pivot method

I am working on the so called label switching problem in Bayesian inference with Gaussian Mixture Models. To put in a nutshell, when your favourite MCMC samplers estimates the parameters of your GMM,...
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2answers
43 views

Finding the posterior distribution of a Bayesian analysis prior

I have a prior distribution $f(x)=\pi cos(\pi x) $ where $x$ is the probability of getting tails in a coin toss. Should a coin toss result in tails, how would this be reflected in the posterior ...
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2answers
104 views

MCMC algorithm going wrong [closed]

Given this integral \begin{equation} \int_0^\infty \chi_{[1,2]}(x)\Gamma(C,x)\left|\cos(R x)\right| \, dx \end{equation} where $\chi_{[1,2]}=\begin{cases}1, & x \in [1,2] \\ 0, & x\not \in [...
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How to choose estimates after Bayesian regression?

In a Bayesian logistic regression with two predictor variables $x_{1}$ and $x_{2}$, I did MCMC (2000 samples) to estimate posterior distribution. Now it's done, how can I choose the final estimates ...
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Finding the posterior distribution for Beta likelihood with unknown alpha [duplicate]

If $(y_i|\theta)$ is distributed as $Beta(y_i,\theta,\beta)$ then what prior distribution do I use? My initial thought was to use a Beta prior. Is this right? I found the likelihood but I'm not sure ...
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EDIT) Bayesian prediction using regression

I have a very basic, introductory statistical background but learning Bayesian analysis with Bayesian Data Analysis(A.Gelman) and I desperately need any hint to help me grasp a concept. As long as I ...
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Posterior as prior for correlated parameters [closed]

I want to use the posterior distribution of the model parameters $\theta$ given data in the time frame $[0,t]$ days, $P(\theta|y_{0:t})$; as a prior for the parameters in the time frame $[t+1, t+n]$ ...
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SD of a likelihood function: can it replace the Standard error of a sampling distribution

I was wondering if "standard deviation" of a "likelihood function" could ever represent the "Standard error" of a "sampling distribution"? I ask this, because when one follows a Bayesian approach ...
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Admissible and Inadmissible actions

Consider the following loss matrix. $\begin{array}{|c|c|c|c|} \hline & \alpha_1 & \alpha_2 & \alpha_3 \\ \hline \theta_1 & 1000& -300& 4000\\ \hline \theta_2 & -1000&...
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How to infer the distribution of a statistic (Bayesian inference?)

I have a list of approximately 30,000 venues in a major US city. These venues hold all kinds of events, sports, conferences, concerts etc. I want to know the distribution of the 'capacity' of these ...