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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Bayesian update vs optimization in multivariate case

Say I have a multivariate normal vector $r$~$N(\mu , \Sigma )$ and I observe that $y \equiv Pr + \epsilon = Q$ where $P$ is a matrix and $Q$ a vector and $\epsilon$~$N(0 , \Omega )$. Now I ...
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Conditional probability table from deterministic relationships of two discetizied distributions - for Bayesian Networks

Consider a simple Bayesian Network of three variables A, B, and C. All of the variables are discrete variables between (0,1] that are discretized as below: ...
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Estimate distribution of aleatoric variable using Bayesian inference

Given a model as follows: $$y = cx + e$$ where y is the model output, x is the model input, c is an unknown variable and e is a Gaussian model error with zero mean: $$e \sim N(0,\sigma)$$ Data is ...
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Why does the likelihood function of a binomial distribution not include the combinatorics term? [duplicate]

So the likelihood function for a binomial distribution is: Why is the likelihood function above not multiplied by a combinatorics term: n! / (x! * (n - x)!) If the likelihood function is ...
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How do I approach this Bayesian question?

I am auditing a Bayesian Statistics course and I am facing problem in understanding the following question. Suppose you are given a coin and told that the coin is either biased towards heads (p = 0.6)...
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Marginal In Bayesian Optimization Expression

I am reading a paper and presentation on batch Bayesian optimization and came across the following formula. Question 1: Does the expression inside the redbox evaluate to $p(\mathcal I_{t,0})$? ...
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Probability that a set of values came from a distribution

I have a probability distribution. And I have a set of values. I need to figure out how to calculate the probability that these values were generated by the same model as the distribution. I found ...
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In the example of guess a specified number between 1 and 20 (both inclusive), what is the sample space?

This post is discussing Bayesian reasoning in the context of guess a specified number between 1 and 20 (both inclusive). Consider the following example: I’m thinking of a number between 1 and 20 (...
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Covariance Matrix of Bayesian Network [on hold]

I have a bayesian network that the edges are likelihood estimations from features {x1,...,xn}. how can to estimate a covariance matrix from bayesian net between x? Normally, we use from a correlation ...
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How do we determine marginal Pr(Data) in Bayesian Analysis?

I am trying to learn Bayesian Analysis and I am really confused as to how to calculate the required equations/values. From a very high level standpoint, I understand the concept. We basically use ...
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Conditional expectation of hierarchical model parameters via marginalisation

Firstly apologies, I have fairly limited mathematical skills so there is a good chance that my question is simple or obvious. I have a model in which I want to calculate the conditional expectation ...
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Bayesian Optimization does not improve RMSE of XGBoost

I have some serious problems with Bayesian optimization of an XGBoost model. The optimal hyperparameters resulting from Bayesian Optimization lead to an RMSE that is higher than through ...
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Making inference about correlated values after some observations

I'm working on making an inference out of some observations of correlated values. Suppose there are two values $x_1$ and $x_2$ which are independently drawn according to a CDF $F$. There also are ...
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Bayesian case control binary regression

tl;dr I would like to evaluate the posterior distribution for the parameters $\theta$ of a binary regression model $P(y_i=1|x_i, \theta)=\rho(x_i, \theta)$ given the features $x_A$ of all positive ...
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Why does the marginal likelihood integral have no closed-form solution?

In Bayesian inference we end up with the formula: $$P(\mathbf{w|t,X)}= \frac{P(\mathbf{t|w,X)}P(\mathbf{w)}}{\int P(\mathbf{t|w,X}) P(\mathbf{w}) d\mathbf{w}}$$ Assume the prior $P(w)$ is a ...
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Are the **likelihood** in Bayes Rule the same to the one in [Maximum likelihood estimation]?

"Think Bayes by Allen B. Downey" calls the P(X | A) part likelihood in Bayes Rule \begin{align} P( A | X ) = & \frac{ P(X | A) P(A) } {P(X) } \\\\[5pt] \end{...
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Can I use a Bayesian method to test for enrichment instead of the hypergeometric test?

When I test for enrichment with the hypergeometric test, I determine the probability of having obtained a number of successes in a sample given the total number of possible successes/failures in the ...
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Understanding priors and full conditional posteriors

I have a question regarding this problem that we are discussing in one of my classes. a) I understand that the prior is a beta distribution with the given parameters below, and that if I have a ...
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Interpretation of tauBs in output of jointModelBayes [closed]

I am using the JMbayes package for R to fit joint models between a longitudinal and time-to-event outcome. The model output lists a variable for "tauBs" however I am uncertain as to what this refers. ...
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Bayesian hierarchical model with varying scales [on hold]

I would like to have a bayesian hierarchical regression model. Suppose that we have multiple data sets, which adhere to a hierarchy. Let us call the response variable in dataset 1 and 2 as $Y_1, Y_2$. ...
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Between Subject Design with multiple Trials per participant

Between the subject experiment with two groups: Each group has a pair of 10 participants. (Player 1 and Player 2) Pairs in both groups play a game where one factor is manipulated. Hypothesis: The ...
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What is the conceptual difference between posterior and likelihood? [duplicate]

I have trouble discerning conceptually between these two notions. I am aware of their formal relations, proprieties and what not, but I just can't wrap my head around what they "mean", if that even ...
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bayesian estimation of difference between 2 non-normal groups

Lets say we have 2 sets of groups with random variable X as shown. Features of X based on real dataset: They are all positive numbers have really long right tail and almost no left tail Cant share ...
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The significance of 'significant'

I am writing up a paper where I report the results of a set of analyses using Bayesian parameter estimating but am really struggling to come up with synonyms for significant. Take this sentence. "...
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Samples from distributions that change slowly in time [closed]

Suppose I receive a sequence of random samples $\{(t_i,x_i)\}_{i=1}^\ell$, where $x_i\sim\rho_{t_i}(x)$. That is, $\rho_t$ is a time-varying distribution over $x$, and occasionally I receive a single ...
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Dirichlet Process Concentration Parameter - collapse at zero

Background I've implemented the blocked gibbs sampler for sampling from the posterior of a dirichlet process mixture model as described on p.552 of Bayesian Data Analysis, placing a Gamma prior on the ...
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How is that likelihood is fixed by the model

When talking about conjugate distributions on a online video, it applies the Bayes theorem as: $$Pr(\theta|X) = \frac{Pr(X|\theta) Pr(\theta)}{Pr(X)}$$ and says that $Pr(X|\theta)$ is fixed by our ...
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“Adaptation incomplete” in rjags. How bad is it?

I'm new to jags and Bayesian inference, but I've run a fairly complex model in jags via rjags. However, I get the warning "adaptation incomplete". As far as I understand it, this means that the ...
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Bayesian model when the raw data isn't available? [closed]

I have data of the form $X = (X_0, X_1, ..., X_T)$ where $X$ is a sequence of categorical variables ($k$-dimensional) captured over time $t = 0,...,T$. The variables are fully observed. I am trying to ...