# 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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### Baysian probability of false positive COVID-19 test

I am wondering what the probability of a false positive COVID-19 test would be in my city. I'm attempting to use Bayes Theorem to calculate this, however I'm getting very different results based on ...
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### Chernoff bound for bayes classifier

It's mentioned in many pattern recognition textbooks (Duda, Theodoridis,etc) that Chernoff distance is: but I couldn't find the proof and I wasn't able to derive it myself. Some insight on the ...
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### How to prepare a dichotomous predictor for the same prior as continuous predictors?

I would like to use a standard weakly informative prior in my model (i.e., normal(0, 1)). I believe that I would scale this to the mean and sd of my dependent variable. For example, if my DV is ...
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### What is an appropriate model for K continuous parameters on [0, 1]?

Question Summary What kind of model is appropriate for estimating K parameters on [0, 1]? In particular, what kind of joint posterior should a model put on K parameters with support [0, 1]^K? ...
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### Bayesian: Exponential Prior and Poisson Likelihood: Posterior Calculation

I am needing assistance in a particular question and need confirmation of my understanding. The belief is that absences in a company follow a Poisson(λ) distribution. It is believed additionally that ...
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### Can a Bayesian estimator perform better than an MVUE?

According to wikipedia: In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any ...
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### Does a conjugate prior always exists? [duplicate]

Are there distributions where no conjugate prior exists? Is there a necessary and/or sufficient condition which guarantees the existence of a conjugate prior? Edit: Why has this question been closed? ...
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### Can the posterior mean always be expressed as a weighted sum of the maximum likelihood estimate and the prior mean?

See this question. Is this always true? Can the posterior mean always be expressed as a weighted sum of the maximum likelihood estimate and the prior mean (after choosing some appropriate prior)?
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### How to check the robustness of a null result of an lmer() model using a Bayesian analysis?

I have an lmer() model that has a theoretically important null result. I would like to use a Bayesian analysis to check the robustness of this null result. What is the best way to do this? I had ...
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### $P(w, v \mid x, y)$ is proportional to $P(x \mid w, v) P(x, y \mid v) P(w) P(v)$?

I am currently studying Transfer Learning by Qiang Yang, Yu Zhang, Wenyuan Dai, and Sinno Jialin Pan. Chapter 2.2.1 Discriminatively Distinguish Source and Target Data says the following: One simple ...
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### Properties of estimators for a Normal Normal distribution under Bayesian view

Suppose that we have a model that $y_1,...y_2$ ~$N(\mu,\sigma^2)$ and we do not know the value of $\sigma^2$. Let us specify the conjugate prior of $\mu$~$N(\mu_o,\frac{\sigma^2}{k_0})$. If we assume ...
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### Under what circumstances can an improper prior be used in bayesian analysis?

I am attempting to gain some intuition about the use of priors in bayesian analysis. I have read in some instances that an improper prior can be used when no information is known. However here is my ...
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### Should prior distribution reflect stationarity assumptions?

In the paper Dynamic Hierarchical Factor Models they present a four-level dynamic factor model and estimate it using a Gibbs sampler. One interesting feature of the model is that the error terms are ...
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### Does the Bernstein–von Mises theorem imply convergence in distribution between a Bayesian estimator and the MLE analogue?

Does the Bernstein–von Mises theorem imply convergence in distribution between a Bayesian estimator and its MLE analogue? Say I have \begin{equation*} \begin{aligned} & \mu \sim N(m, s^2) \\ & ...
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### Using Theils' Mixed Estimation (Dummy observations) to handle zero counts

Consider a binary response $Y$ and two binary predictors $X_1$ and $X_2$. Here is some synthetic data to illustrate the problem. ...
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### Bayesian factor BF10 and normal distribution

I´m trying to understand whether it is possible to use Bayesian Factors for contrasting data whose distribution is not normal. Should I apply any correction, or BF10 does not care about the ...
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### How to create a generalized linear model of choice using time as the measure of preference?

Supposed you run an experiment in which there are four choice options. In each trial, two of the four options will appear, one on the left side of the room and another on the right side. A participant ...
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### How do I estimate survival probabilities using datasets that cover different amounts of time?

I'm looking for help classifying a problem that I don't yet have the statistical terminology for, and for help thinking about possible approaches to work on the problem. Below, I give an analogous ...
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### Uncertainty and distribution of a percentile

In a Bayesian analysis (Normal case), it is possible to obtain a posterior distribution of the mean and variance. We can also obtain quantiles, median,... of these distributions. My question now is: ...
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### What is the correct procedure for posterior inference about the cumulative distribution $F(y|\theta)$?

Let $y$ follow $f(y|\theta,x)$ with $\theta$ parameters with prior $\pi(\theta)$ and $x$ covariates with distribution $p(x)$. Let $p(\theta| D)$ be the posterior distribution of the parameters, where ...
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### How to define informative priors from previous studies using stan_glm?

I am trying to develop a linear regression model for estimating stature from handprint measurements. I would like to employ the Bayesian approach and define informative priors from the previous ...
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### Implicit for loops in PyMC3 using likelihood of matrices?

I'm confused about (for lack of a better word) "implicit for loops" in PyMC3. You'll note below that I define a 5x5 matrix, k. This matrix represents whether a specific child answers a ...
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### Which statistical model is being used in the Pfizer study design for vaccine efficacy?

I know there's a similar question here: How to calculate 95% CI of vaccine with 90% efficacy? but it doesn't have an answer, at the moment. Also, my question is different: the other question asks how ...
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### How to calculate the winning probability for Tottenham vs LiverPool? [closed]

I wonder how frequentist and bayesian calculate the winning probability for Tottenham versus Arsnel, Saturday. For frequentists, the following is how I understand: Imagine a population made of all ...
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### Why is autocorrelation bad for MCMC samplers?

I've read a number of times that autocorrelation is highly undesirable in any MCMC samplers and, when it is high, your number of effective samples will be reduced, which in turn means that the ...
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### Bayesian Latent Factor Analysis - Difficulty with Sampler in PyMC3

I have the simplest possible latent factor model, simulated as follows: ...
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### Understanding the Bayesian a posteriori criterion with a simple classification problem

Let's say I want to predict gender ($m$, $f$) from body height ($x$) using the following dataset ...
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### Weibull with known shape parameter

I am new to Bayesian robustness. If I have Weibull likelihood $X$~ Weibull($\lambda$, $\beta$)$= \lambda \beta x^{-\beta} \exp(-\lambda x^\beta)$ with $\lambda$ unknown and $\beta$ known. we know that ...
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### Sampling model / likelihood using Poisson distribution in Bayesian inference?

I'm trying to solve a problem/question from my professor. The problem/question is we want to know the proportion of the population in city A who is infected with COVID-19. For that, an examination was ...
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### What does Certainty Factors mean in Artificial Intelligence?

I am wondering what Certainty Factors could mean in Artificial Intelligence. I just got the term while googling for the meaning of uncertainty related to Bayesian Statistics. I also wonder if there is ...
### How does the author get ${P(T_{\text{new}}\leq 6|y_N) = \int P(Y_{new}\leq 6|r)p(r|y_N)dr}$
So this is probably a really stupid question, but I don't get where this particular formula comes from. I'm reading a Machine Learning book, and at one point the author states the following formula: ...