# 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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### estimating preference rate

I'm offering an online service and want to determine how often people choose my service compared to my competitors. To estimate this, I have some data that tracks when users are presented with a list ...
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### Bayesian: Formally comparing prior and posterior distributions

Consider Bayesian inference in the regression model: \begin{align*} y &= \beta_0+\beta_1x_1+\beta_2x_2 + \varepsilon \\ \varepsilon &\sim \mathcal{N}(0,\sigma^2) \end{align*} Suppose we ...
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### Bayesian hierarchical model for comparing reviewers

I am working on a research paper about reviewing people's expertise. I have 21 respondents, each answered 10 questions. Now I have asked 4 groups of reviewers (each group consists of 3 people) to ...
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### Is TTA (test-time augmentation) somehow related to Bayesian DL?

I'm trying to make up a taxonomy of UQ methods for deep learning models, if possible (this paper provides a nice overview imo, albeit in a specific field). Currently there's cluster of UQ approaches I'...
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### This is on linear regression [closed]

If I calculate my yt and I get a negative answer for my predicted value (-1.23) and the observed value is (2.34) using polinomial regression to transform my x. Can I just assumed it's zero since it is ...
1 vote
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### Use importance sampling to post processing the posterior result of the MCMC chains

In one of the studies, I once found the following heuristics to perform the calibration, Step 1: Running MCMC to get model parameters, with K chains Step 2: Compute weight for these K chains, the ...
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### Sum to zero contrast that makes it easy to express equal uncertainty about each factor level

How do I need to set-up a sum-to-zero contrast so that it is easy to express equal uncertainty about each factor level? E.g. when I go with the default offered by R such as: ...
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### Recycling MCMC samples for another data set from the same distribution

Suppose I'm given $\theta_0$ and I want to sample data from a density $f(Y|\theta_0)$ and then sample from the posterior of $\theta|Y$ (given, obviously, some prior). I want to do this lots of times, ...
1 vote
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### how can predictive distributions be considered as expectations?

I guess that the prior and posterior predictive distributions can be considered expectation of $p(y|\theta )$ (in case of prior predictive distribution) and $p(\widetilde{y}|\theta )$ (in case of ...
1 vote
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### What does sample space look like for 3 dice?

Learning Bayes statistics from Allen Downey's Think Bayes There are three dice, 6-sided, 8-sided and 12-sided. A randomly chosen dice is rolled and the outcome is "1". What's the probability ...
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### two-step gibbs sampling vs block gibbs sampling

While reading Bayesian-related technical articles, I can see algorithms such as two-step Gibbs sampling and block gibbs sampling ...
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### Applying Bayesian probability to a generalized Monty Hall problem

I posted this question about the Monty Hall problem and Monty's knowledge of the probability distribution several months ago. I got some good answers and this one in particular helped me gain some ...
1 vote
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### known variance in conjugate normal

$Posterior\ mean=\frac{1}{\frac{1}{\sigma_{0}^{2}} + \frac{n}{\sigma^{2}}}\left( \frac{\mu_{0}}{\sigma_{0}^{2}} + \frac{\sum_{i=1}^{n} x_i}{\sigma^2} \right)$ Using this updating equation with known ...
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### Experimental Design: Selecting value of $n$ given desired width of credible interval

Note that this is a cross post from here. I realize this is probably a better space Suppose I have $n$ IID Bernoulli trials with $k$ successes. Assume that as a prior we are assuming that $P(\theta)$ ...
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### Measured value represents range in timeseries

I have datasets that consist of measured points (measuring m), across a landscape/area (x and y) and time (t). The issue comes in that the measurements are actually made over a period of time, a month ...
1 vote
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### When running a Bayesian mixed effects regression, if a random effect estimate has 95% CIs that include zero, should it be disregarded?

Consider a Bayesian mixed effects regression. I am interested in the correlation between two of the random slopes. However, the 95% CIs for the correlation value include 0. Should I disregard the ...
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### Error in Bayesian Derivation of Covariance Matrix in Least Squares

I know variants of this question have been asked a million times, but rather than just asking "how do I derive the covariance matrix" I ask you to check the error in my calculations, because ...
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### Bayesian updating with affine transformation of random variable

I want to estimate a parameter $\theta$, and I have a prior $\pi(\theta)$. I receive the realization of a random variable $Y$, which has some likelihood $f_Y (y \mid \theta)$. My posterior then ...
Consider the following problem of estimating an unknown parameter from normal samples: Suppose that $\theta \sim N(0, \tau_\theta^{-1})$, where $\tau_\theta \ge 0$ is the prior precision. Consider two ...