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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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Using different models within one bayesian optimization?

I'm using GPyOpt for Bayesian Optimization with Gaussian Proccesses. I have a dataset and want to know which of my models (LSTM, GRU, VANILLA RNN) works best. In Pytorch it is really simple to ...
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BNLearn: How to merge the estimating parameters of a Gaussian Bayesian network with its conditional structure?

I define the structure of a gaussian baesian network usind " iamb" function and then estimated the coeficients of the nodes using "bn.fit". ...
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Bayesian update of a confidence interval

How does one update a confidence interval using Bayes rule? Say, for example, an experiment shows that the mean lies in [A, B] with 95% confidence. Later, a colleague says they ran a similar ...
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Question about using Bayesian rule as a classification for continuous data set

Please note that my question is not about coding. I am now learning Bayesian classification and I think I understand it in a discrete case. I have trouble understanding it for multivariate continuous ...
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Regression via neural network on training data with uncertainties

I have a regression task where all my training data that I want to predict is of the form ($y$, $\sigma$), where $\sigma$ is the Gaussian noise corresponding to $y$, i.e. I want to be able to predict ...
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Independence in this Bayes net

Consider this Bayes net A,B,C forms a v-structure. $B \not\!\perp\!\!\!\perp C | A$, B is not independent with C if A is observed. My question is, if B,A,D are all given, can we write $p(C|B,A,D) = p(...
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Online learning in Bayesian Linear Regression [closed]

Bishop's machine learning textbook describes ways to conduct frequentist Linear Regression, and also examines sequential updating (online learning) in this context. The textbook also covers Bayesian ...
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How does one know when burn-in doesn't need to be discarded from an MCMC simulation?

I'm reading a paper about Bayesian model calibration (https://cfwebprod.sandia.gov/cfdocs/CompResearch/docs/McFCalib0307.pdf). The authors fitted a Bayesian Gaussian process model and sampled from the ...
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Bayesian estimation in 2x2 mixed design study

I'm trying to correctly set up Bayesian parameter estimation for a mixed-design study with one 2-level between-groups independent variable and one 2-level within-subjects independent variable. The ...
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Naive bayes computation of denominator

I'm wondering about the denominator in this computation : ...
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21 views

How to understand bayesian inference in the framework of deeplearning?

It is said that $p \left( \theta | y _ { 1 : N } \right) \propto _ { \theta } p \left( y _ { 1 : N } | \theta \right) p ( \theta )$. And $p \left( \theta | y _ { 1 : N } \right)$ is the posterior, $ ...
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Need help selecting ROPE limits for a Bayesian multilevel model

I am using brms to estimate a Bayesian multilevel (mixed effects) zero-inflated beta regression model and want to use the HDI+ROPE (region of practical equivalence) ...
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credible interval in bayes are higher than the nominal level

When I fitted the nonlinear regression using the openbugs, and calculated the 95% credible interval of the coefficient through the high density interval, I found that the total number of the credible ...
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Bayes vs trial factor (particle physics)

In the statistical inference for particle physics is the trial factor analogous to Bayes factor but for the frequentist analysis?
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Any advantage of Bayesian methods for this data?

I have data of blood sugar level and 8 predictor variables of 15000 subjects. Some of the predictor variables are categorical. I want to determine independent predictors of blood sugar levels. I can ...
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21 views

Setting an upper limit on an estimate

I have used MCMC to estimate the value of a parameter $\theta$ from some data. I have thousands of samples from the (marginal) posterior distribution. The distribution of $\theta$ is roughly Normally ...
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Can Deviance Information Criterion be used for model comparison when the response variable has Poisson distribution?

I just constructed a Bayesian Hierarchical Model for my response variable Y that follows Poisson distribution with the parameter $\lambda$. In my model, I have modelled $log(\lambda)$ as a linear ...
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Estimation of covariance over a range of independent variable

I have a set of data that comprise 2 dependent variables (let's call them $x_1$ and $x_2$) evaluated at different temperatures, T. There is an assumption that for a range of T ($T_0<T<T_1$) ...
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MCMC sampling with a probability density function that have potential negative values

My question might be quite strange, but I will expose you the complete issue in order for you to help me. I am in the context of a parallel randomized clinical trial which aim is to compare two ...
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Bayesian Survival function

I have managed to estimate the posterior of the latent variables of my model which can be stated as follows (adapted from https://docs.pymc.io/notebooks/bayes_param_survival_pymc3.html): \begin{align} ...
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Modeling and testing for trends in hospital-surveillance (count, event) data

Intro Hi all, I'm working with hospital-based surveillance data. My peers and I are trained (loosely speaking) as frequentists. I'm mindful of the aphorism: Statistics: A subject which most ...
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Is it possible to use Bayesian networks to predict numerical values? (non-categorical)

Is it possible to use Bayesian networks to predict numerical values? (non-categorical) For example is it possible to build a Bayesian network in the case of a house price prediction? I found answers ...
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Denominator in Bayes - in the continuous case, why isn't it zero?

For a continuous random variable, the probability of any particular value is zero. Only by integrating over some range is a non-zero probability obtained. The components of the Bayes theorem are ...
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Data generating model

assuming I am to embark on an analysis of a given set of data on length of a movie, but already have a prior belief of 56 minutes on the average for a movie before seeing the data. How do I carry out ...
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Dual Bayesian Interpretation

I am reading a book which says there are two ways of interpreting Bayes. “In the Bayesian approach, parameters can be viewed from two perspectives. Either we view the parameters as truly varying,...
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Am I doing hierarchical bayesian regression?

I'm doing a Bayesian logistic regression to predict the probability of my dependent variable Y with two predictors, one continuous (X) and the other categorical (C). I deal with C by building 3 models ...
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How do I check in practice if a posterior is proper?

I know that improper priors sometimes lead to improper posteriors and that I shouldn't be doing inference with an improper posterior. But short of computing $$ \int \pi(\theta\mid x)\,\text d\theta $$ ...
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Joint “density” of data and indicators in Bayesian mixture model

I'm currently working through the chapter on finite mixture models in BDA3 and came across the following model setup (with the usual slight abuse of notation): Let $\lambda=(\lambda_1,\dots,\lambda_H)...
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Automatic selection of plot bounds for Normal pdfs in a combined chart

Suppose an app's user specifies several Normal priors by setting the mean and variance for each. I'd like to display a combined plot with the prior pdfs, like that on the figure. . Q: What is a good ...
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How to set a Bayesian prior on a set with a large but unknown number of elements?

Let us suppose that we are trying to analyze a given starfish. We would like to know which species does the starfish belong to. We have a list of 1000 starfish species, but we know that there is an ...
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Monte Carlo integration for Bayesian parameter estimation

I want to determine the credible interval of a quantity $\theta_1$. I want to make this estimate using observed data by assuming a certain model which depends on $\theta_1$ as well as about n=15 ...
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Bayesian spatial autoregressive (SAR) model with heteroskedasticity in R

In socio-economic data, I always found heteroskedasticity that can't be solved using transformation.I had read a paper "Spatial autoregressive models with unknown heteroskedasticity:A comparison of ...
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Does specifying normalizing constant significantly improves Hamiltonian Monte Carlo?

From my understanding the energy function needs only be specified such that it is proportional to the log density, and not specifying the normalizing constant should not greatly impact the sampling ...
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Minimizing the expected loss or the mean risk?

Is there a reason why one should choose to pick his Bayesian decision minimizing the expected loss or the mean value of the risk function? The expected loss function \begin{gather} \int \mathscr{L}(\...
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identifying which of $d$ normal distribution generated a given sample

I have $d$ Normal Distributions, $N_1(\mu_1, \sigma_1^2) \cdots N_d(\mu_d, \sigma_d^2)$. We pick one of the $d$ distributions with each distribution having a probability of $\frac{1}{d}$ of being ...
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If I can make up priors, why can't I make up posteriors?

My question is not meant to be a criticism of Bayesian methods; I am simply trying to understand the Bayesian view. Why is it reasonable to believe we know the distribution of our parameters, but not ...
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Model selection with this model of a large number of components

I have a discrete time Markov Chain $\{X_n: n \in \mathbb{N}_0\}$ with unknown transition matrix $P \in \mathbb{R}^{M \times M}$ on the state space $\mathcal{S}_X = \{1,2, \dots, M\}$, with $M \geq 2$....
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Why is the maximum risk of an estimator independent of a prior distribution over the parameter?

One way of choosing an estimator $\delta(x)$ for data $X$ distributed as $P_{\theta}(X)$, where $\theta \in \Theta$ is: $$minimize \sup_{\theta \in \Theta} Risk(\delta(x), \theta)$$ In this case why ...
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Are there useful applications for Bayes Nets (vs. Naive Bayes)?

I am trying to learn about Bayesian networks and try to make them work in the context of a simple prediction problem. But my question is more theoretical: For argument's sake, assume we have a ...
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Inconsistency of Bayesian time varying VAR model

I'm estimating time-varying parameter VAR model of Joushi Nakajima (2011), the model simulates the time-varying parameters using MCMC algorithm and the priors are estimated by implementing standard ...
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Compute conjugate prior from the sample distribution

I feel like this question might be marked as duplicate because I see many similar incurring in that fate but I'll try anyway. I would say I did not find anything similar. I have been thought a ...
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1answer
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Bayesian inference on binarized Poisson distribution

I have a variable that is Poisson distributed. Let's say I have a number of boxes each with a number of balls inside according to a Poisson distribution, with $\lambda=0.4$, (the average number of ...
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What is the posterior distribution of a Bernoulli prior that gets updated with a continuous uniform signal?

I'm trying to figure out what the distribution of the posterior is after I update a Bernoulli prior with a continuous uniform signal, say: P(D=G|u)=x where D{G,I} and u is uniformly distributed on ...
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1answer
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Bayes Factor A/B Testing

I am just starting to look at Bayesian statistics and so far I am aware that Bayes factor summarizes some form of evidence of an alternative hypothesis against the null one. As far as I know we can ...
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Multinomial-dirichlet with fractional counts

Suppose a lepidopterologist wants to estimate the relative proportions of three different species of butterfly. They go out into the field and count $N$ butterflies and record the number of each ...
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Expression for conditional probability with many variables

Say I'm interested in predicting the random variable $Y$, and I have multiple data sets for random variables $A,B,C,D,E,F,G$ that $Y$ may depend on. It seems the correct expression would be $$P(Y|A,...
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1answer
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Posterior predictive: what happens to integral over parameters?

Question I don't understand how when integrating over the parameters in the posterior predictive, the integration "disappears". It's hard for me to ask simply because I am confused, so here is an ...
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Given two related ratios within a population, derive a third ratio (eg. redheads, non-redheads, and skin cancer)

If People X are N times more likely to have attribute A than non-X People X are P percent of the population then What percentage of A's are X? Example (the numbers are just for illustration). If ...
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How to determine p(a) in bayes' formula with this example of symmetric conditional probabilities?

Why is P(A) in this example 1? In class, we were shown an illustrative example of bayes that no one including the professor could understand. P(A|B) = P(A) * P(B|A) / P(B) Question is: Use Bayes ...