# 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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### MMSE estimator with dirac delta prior pdf

The question is as follows, it's mainly part 3 that I was having problem with. A discrete-valued parameter with the prior pdf $$p(x) = > \sum_{i=1}^2p_i\delta(x-i)$$ is measured with the additive ...
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### Bayesian analysis used merely as a computational tool?

I have sometimes seen some statisticians used bayesian analysis and related techniques such as MCMC simply as a tool when a frequentist approach is not satisfying, typically for example when the ...
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### Beginner: Understanding difference between pmf, conditional pmf and likelihood

I have a point of confusion regarding the three types functions. I have looked at some other posts here and blogs and scripts and YouTube videos. But I still don't get it. Let's look at the coin toss ...
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### What can I do to make Student-T priors in a brm Bayes model less tall? [closed]

What can I do to make Student-T priors in a brm Bayes model less tall? Particularly this is a linear model: $a+bx$ And my current priors are: ...
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### How to select a variance for student-t, when it approximates coefficient of linear model?

How to select a variance for student-t, when it approximates coefficient of linear model? Especially in context of Bayesian priors. Or as in: https://github.com/stan-dev/stan/wiki/Prior-Choice-...
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### Is there any relationship between confidence ratio in association rule and Bayesian rule?

I am currently studying Association Rule and somehow I thought about if there is any relationship between confidence ratio in Association Rule and Bayesian Rule. My knowledge in Bayesian Rule is not ...
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### If one fits a linear model with just one $x_i$ then does this mean df=1-2=-1?

If one fits a linear model with just one $x_i$ then does this mean that the number of degrees of freedom $=1-2=-1$? For a linear model the degrees of freedom is: $${\rm df}=n-k$$ where $k$ is number ...
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### Find marginal distribution of X (Bayesian setting)

$X|\theta$ follows $N(\theta,w)$ and $\theta$ follows $N(\mu,\sigma^2)$ Both follow a normal distribution but with different mean and variance. I assume it is a Bayesian setting. How to find the ...
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### What methods exist to identify the optimal splits in some exogenous variable, such that a dependent variable is maximized?

I've come across an interesting problem recently, and I'm wondering if I'm missing some obvious approach here. The problem statement is thus: Imagine I run an online business, and I'm interested in ...
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### Running Regression estimation using rstan [migrated]

I am using stan through rstan package in R. Below is my model. This model has an interaction term as ...
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### Regarding Gibbs sampling and HMC in fitting Bayesian model, their differences and advantages

I have a question regarding the two MCMC algorithms, Gibbs sampling and Hamiltonian Monte Carlo (HMC) for performing the Bayesian analysis. If using Gibbs sampling, my understanding is that we need to ...
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### Why do we need the concept of Risk in Bayesian Decision theory?

I'm studying Bayesian decision theory as introduction to machine learning and I see the concept of Risk in a lot of places. In the course I read, they define risk as: Risk is the expected error ...
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### Statistical conclusions from incompatible measurement results

I assume that the following situation is not uncommon in scientific practice: Two research groups analyse two samples. The reported results concern the same physical quantity at the same location ...
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### Bayesian multivariate regression with common coefficients

In a hierarchical model I'm working on, I have $K$ different $N\times P$ predictor matrices, each denoted $X_k$ and $K$ length $N$ outcome vectors each denoted $y_k$. Essentially, I have a ...
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### Can stochastic gradient descent for Bayesian Inference? [duplicate]

I was looking at the Bayesian MAP estimate formula which is the "argmax(likelihood * prior)". Can this be calculated using stochastic gradient descent? Gradient descent requires knowing the ...
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### Coherence of conditional probabilities

Dennis Lindley's paper The Philosophy of Statistics in 2001 includes the following 'simple' example of statistical coherence: "A set of uncertainty statements is said to be coherent if they ...
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### How to measure the strength of association between two variables where majority of pair are assosiated?

I am quite new to the stat so facing a huge problem in result extraction, I have a large dataset running ~19000 (genes) x1500 (patients). I would like to see the dependence between two variables (one ...
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### Why is naive Bayes overconfident?

In the fourth edition of "Artificial Intelligence: a modern approach" by Russel and Norvig, they write in section 12.6, regarding the Naive Bayes Model for text classification, the following:...
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### Estimating the population distribution of a quantity from multiple finite-error experiments

I'm trying to understand how one can estimate the "true variability" of a quantity, given a finite number of experiments, where each experiment collects a finite number of data points. ...
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### How to create bayesian test for ROI/ROAS metric

I am interested in using A/B Bayesian testing to compare ROAS for marketing scenarios. I've seen references dealing with cases such as: Using a beta distribution prior to model a binomial-distributed ...
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### Abuse of notation : same function name for different distributions

Is this too much of an abuse of notation to use the same letter, e.g. $f$, to designate the joint - $f(x,y)$, marginal - $f(x), f(y)$, and conditional - $f(x|y), f(y|x)$ - probability/cumulative ...
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### Making sure that the design matrix is positive (-semi) definite

In bayesian linear regression, how to make sure that the design matrix produced by a neural network $\Phi$ is positive definite? Because to computing the covariance matrix on the weight requires ...
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### Reducing Size of Credible Interval Bayesian Regression Pymc3

I am interested in ways to reduce the width/size of a credible interval in a Bayesian regression. Suppose you have a simple Bayesian linear regression $y \sim \mathcal{N}(\mu, \sigma)$, formulated ...
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### Bayesian updating of a constant probability using one data point

A reformulation of a question that came up in a model: Imagine a toy store that sells $K$ toys, where our prior is that each toy has equal probability $1/K$ of being purchased by a customer. Then you ...
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### Modelling time both as a fixed effect and as part of an autocorrelation structure?

I want to build a model to assess whether a species is declining in three different national parks. My dependent variable is count data of the species and I have date, park, season and food as ...
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### Compute likelihood of state given multiple observations?

I am trying to use Bayes formula to compute the likelihood of a given state given a collection of independent but not sequenced observations - knowing the priors and knowing the probabilities of being ...
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### Rate of convergence for Beta posterior

Recently I started studying posterior distribution rates of convergence. In order to check what I understand I tried to formulate an example. Let $X_{1}, X_{2},..., X_{n}\sim Bin(N,p)$, we then ...
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### Summarization and resources for Bayesian decision theory

Looking for textbooks and/or resources to get familiar with Bayesian decision making. I have the book, Statistical Rethinking, by Richard McElreath and I've found this to be a really great resource ...
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### Help in understanding zero inflated neg binomial model summary

I'm writing this topic because I would need to get some more information about model conversion in brms (zero-inflated_negbinomial) model. Let's say I have this model result : Where I want to model ...
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### Help with rstan models [closed]

I would need help in order to write a specific Stan model. The biological question The idea of the model is modeling the number of Bones (NbBones : discret ...
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### Centre-scaled data and Approximate Bayesian Computation (ABC)

I have 200000 simulations and I want to use Approximate Bayesian Computation (ABC) to determine the best 1000, based on specific targets. These simulations have 12 parameters (my priors, dependent ...
I'd like to try and understand how one can prove that a particular strategy for assessing correctness of computational methods for Bayesian inference is sound. For a number $M$ of simulations, ...