# 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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### Hypothesis testing via separate inference for each group and then combining

Suppose there are two groups, A and B, and we are interested in inferring a certain parameter for each one and also the difference between the two parameters. Here we can take a Bayesian perspective ...
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### Calculate Conversion "Weight" based on Multiple Conversions

I'd like to estimate the value of each "conversion" starting from a free trial signup all the way to that user becoming a paid user. Let's say I have an online coding course website that ...
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### Interpreting non linear brms output - estimates of posterior cooefficient and user supplied formula

I am a bit confused about how to approximate the equation from a nonlinear model constructed in brms, and was hoping someone could explain it to me. Say I have the below model: ...
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### Is it practical to distinguish aleatoric uncertainty from epistemic uncertainty?

I know the difference between the two, but don't know if it is practical to tell them apart technically. Say, I have trained a deep neural network and I use some techniques to get the posterior ...
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### Comparing two groups with measurements over multiple time points with Bayesian analysis

I have data from a surgical drug study with multiple measurements over time. In both groups A (treatment) and B (control), a biomarker indicating inflammatory response is measured at the following ...
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### How to compute the mean of two conjugate distributions in an analytic posterior distribution?

I do not know why in the following picture the mean of this posterior is $\mu_n= (X^TX+\Lambda_0)^{-1}(X^TX\hat{\beta}+\Lambda_0\mu_0)$
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### Frequentist vs bayesian and P(data | H0) vs P(H0 | data) giving same result

In hypothesis testing using a frequentist approach, we usually compute a p-value = $P(data\ or\ more\ extreme | H0)$. Moving to a bayesian approach, we are then able to compute different things, such ...
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### dlmForecast error : "dlmForecast only works with constant models"

I have a dataset with intervention dummy variable to be incorporated inside the measurement equation (let's call Lambda) I picture my measurement and state are as below : measurement : Lambda + Et ...
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### Likelihood in Bayesian inference: p(x|theta, I) = p(x| I)?

In page 164 of the book “Probability theory: the logic of science” the author says that: $$p(D|\theta I) = \prod_{i=1}^{n} p(x_i|\theta I) = \theta^r(1-\theta)^{n-r}$$ $\theta$, in this equation, ...
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### Bayesian combination of expert opinion

In a population of $N$, $K$ experts pick $M_{k\in\{1, ..., K\}}$ individuals that will have a certain attribute. Note that $M$ can be different across experts (e.g., one expert can pick 5 individuals, ...
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### Finding a,b parameters if Highest Posterior Density is known

I know that a beta distribution with unknown parameters a,b has a 95% HPD of [0.25, 0.75]. What is the correct approach to solve for a,b?
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### Logit-link logistic regression: Calculating effect size between a continuous predictor's max and min value

Let's assume I have a logistic regression logit-link model as follows. binary_y ~ year I mostly work with bayesian regression models. Calculating the effect size ...
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### Prior knowledge in context of nullhypothesis testing

I am currently working through the book Doing Bayesian Data Analysis - John Kruschke and have trouble to reason about a text paragraph [Page 315] Suppose that we are not flipping a coin, but we are ...
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### How to understand maximum likelihood estimation from an objective Bayesian paradigm?

I am trying to understand maximum likelihood estimation from an objective Bayesian/Jaynesian paradigm. My current understanding is that: There is a parametric family of functions f(x; theta) indexed ...
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### Interpreting false positives of Placebo group with full information

I'd like to make sure that I am interpreting a study correctly; I'm getting tripped up by Bayes Rule. Formulas and data are listed below my question. Here's the background: There is a study where ...
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### why Gamma inverse is the conjugate prior of normal distribution?

I am trying to understand Bayesian regression. Then in Wikipedia enter link description here, it is written that by using the following relation we get the Gamma inverse as follow for the conjugate ...
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### Binomial distribution - estimating confidence interval without mean?

This question is probably easy but I couldn't find the answer, nor remember my lectures in statistic. I have an (infinite) bag of red (A) and blue (B) chips, i.e. $P(A) = p = 1 - P(B)$ I want to ...
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### Which kinds of priors could be applied in Bayesian linear regression?

I would like to know can we use any kind of prior distribution in Bayesian linear regression and still convergent to a close mean solution to the Least square solution? Or it should be just a ...
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### Trying to find a distribution for time dependent drought

I would like to seek your support on a modelling issue for which I could not find relevant past postings or published literature resolve it. I am running a cost benefit model to assess the impact of ...
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### Bayes theorem with multiple draws

Setting I have a question on the "Cookie Problem Revisited" exercise from Allen Downey's Think Bayes 2e. The Bayes theorem is defined as: $$P(H | E) = \frac{P(H) \ P(E | H)}{P(E)}$$ where ...
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### How to calculate alpha and beta parameters from an known mean and variance in normal-inverse gamma distribution

How can I calculate the $\alpha$ and $\beta$ parameters for a normal-inverse gamma distribution if I know the mean and variance?
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### What is the importance of non-informative prior in Bayesian Inference? [duplicate]

By the name, noninformative prior, the prior distribution doesn't contain any information about the parameter. Then why we use this thing to estimate the parameter by the Bayesian approach?
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### Bayesian update for a Gaussian distribution with unknown mean and variance

I am trying to implement the Bayesian Online Changepoint: https://arxiv.org/pdf/0710.3742.pdf in python. And I also have the step to update the sufficient statistics (variance and mean). I have a ...
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### Variable selection in Bayesian hierarchical models with R-INLA

I'm working with Bayesian hierarchichal regressions fitted with R-INLA. I would like to simplify my model by reducing the number of covariates. According to my understanding, Bayesian variable ...
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### Bayesian linear regression with given distributions X, y instead of pairs {(X1, y1),..(X100, y100)}

I'm wondering if is it possible to model data by knowing only distribution of features (X) and targets (y). Thus, instead of paired variables {(X1, y1), (X2, y2), .., (Xn, yn)} I know only mean value ...
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### How to apply MCMC to bayes when likelihood is not easy to compute

Let $z$ be observations and $w$ be the parameter that we want to infer. Assuming that we know the prior $p(x)$, by using Bayes law, we have $p(x|z) = p(z|x)p(x)/p(z)$ where $Z$ is the marginal ...
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### Why is the beta distribution so flat when a, b=1?

If the beta distribution is a prior of a Bernoulli distribution (i.e. a rate of success for a binary outcome), then it is completely counterintuitive to me that the beta distribution should be ...
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### Predictive posterior update for unknown mean and variance

I am trying to implement the Bayesian Online Changepoint: https://arxiv.org/pdf/0710.3742.pdf in python. And I also have the step to update the sufficient statistics (variance and mean). The work is ...