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 model comparison with systematic error

Two parameters $(x,y)$ were measured for 3 different objects, wielding the following results: $$\{ (x,y) \}= \{ (1,3), (3,5), (5,9) \}$$ Knowing that the error in the estimation of the values $y$ is ...
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Can somebody help me understand the sentences in more readable expresions?

I was reading a paper about "bayesSimIG" and I have problem in understand the following paragraph.I have read it many times and did a lot of research for it and have understood what each ...
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Is there any Bayesian posterior sampling method where each draw is the solution of a random optimization problem?

Many (maybe all?) sampling methods could be phrased as the solution to a random optimization problem, but are there situations where that's the only way to express the method, or where the method ...
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Conjugate inverseGamma posterior and Multivariate normal?

If I have a multivariate normal distribution for the mean with an InverseGamma for the variance. Lets say $$ p\left(\mu, \sigma^{2}\right) = NIG\left(m_{0}, V_{0}, a_{0}, b_{0}\right) = N\left(\mu|...
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The 'R2jags::autojags()' Function Doesn't Converge

I'm running the following code in R: ...
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Consecutive coin flips, what is the appropriate statistical test for this word problem? [closed]

I was listening to a podcast by NDGT (Neil deGrasse Tyson, a prominent scientist) and he posed a simple thought experiment to illustrate the susceptibilities to cognitive bias. What I've come here to ...
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Calculating Probability Using Bayes? [closed]

A recent survey of residents in Texas concluded that 55% of Austin city residents and 46% of Houston city residents broke a bone at some point during their childhood. Let’s say Austin has 5200 ...
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Bayesian approach to removing outliers from a normal distribution

A lot of what I've seen for Bayesian approaches to removing outliers is for a linear model, not a normal distribution. Is there a way we can take a Bayesian approach to remove outliers from a normal ...
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Trying to replicate figures from Bayesian statistics without tears: A sampling-resampling perspective, but failed [migrated]

I'm trying to replicate the three figures from the paper Bayesian statistics without tears: A sampling-resampling perspective, which can be found here: http://hedibert.org/wp-content/uploads/2013/12/...
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Bayes Factor for two groups comparison with unequal variances from bayes.t.test in bolstad R package [closed]

After asking for a bayesian version of Welch test in a stackoverflow previous thread: https://stackoverflow.com/questions/72171331/bayes-factor-for-two-groups-comparison-with-unequal-variances-is-...
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How can I calculate Posterior Distribution, analytically with given information?

The image below shows that the posterior distribution is as follows with given information: I wonder how the posterior has been calculated, analytically.
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How to forecast sales for entire current month taking into account sales from half of month?

Good afternoon! I want to forecast sales for current month. Since I already know sales for two weeks of current month, I want to incorporate this information into forecast for the whole current month, ...
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Bayesian statistics: what is the variable we are integrating in?

This is a screenshot from Bayesian Data Analysis by Gelman. I am a little bit confused by Equation 1.4 (first and second lines), having read Equation 1.3. In Equation 1.3, the variable of integration ...
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What is Gaussian approximation for the variance of a function?

In Orre 2000, the author provides an asymptotic approach to computing the variance of information component and conditioned posterior distribution. In part 2.2 weights and information components So ...
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Methods for modelling distributions?

As predictor X I have particle size distributions and I would like to run a model y ~ X. I.e. each trial has a response ...
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Conditional probability problem (Bayes Theorem ?) [closed]

Hello, basically, I can't find 1/2 for the very last question. I tried to use the Baye's Theorem, but it wasn't successful Could someone help me ?
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SAS Bayesian 95% credible intervals for proportions or crosstabs [closed]

I am trying to find SAS code for figuring 95% credible intervals as relates to differences two proportions or a contingency table. I see there is proc MCMC but the examples I see are 1 proportion, and ...
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Confidence interval for the parameter of a random variable

I am studying statistics, and I came across a problem that I am not sure if what I am doing is correct or if there is some other way to do this. Any feedback is appreciated. I divided in 2 problems, ...
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Modification of Outliers

I have a practical / applied statistics question. I'm dealing with a specialized dataset with a very small sample (i.e. n < 10). In the sequence of observations, it is possible that a new ...
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1 vote
1 answer
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Are these Bayesian Inference?

I am trying to understand what is and what is not considered Bayesian inference. Let say I am to estimate a parameter or a vector of parameters say $\theta$ and I have data on some features of the ...
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Bayesian Additive Regression Trees: Zero-inflated explanatory variable, will it influence the model and variable selection?

I am currently implementing BART to model the distribution of a marine species (using the embarcadero package). I am using environmental covariates, but also some prey data that are very-much zero-...
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In a mixture model should I update the parameters of variance jointly or one-by-one?

Suppose that I have the following mixture model, where I know the true values of $(\pi_{1},\pi_{2},\pi_{3},\mu_{1},\mu_{2},\mu_{3})$ (I know them for the simulation that I build) $$f(x) = \pi_{1}N(x;\...
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NumPyro: sampling active sites as Bernoulli RVs [closed]

Consider the following Bayesian regression model: $ \begin{align} \begin{split} \alpha&, \beta, p, \sigma \in \mathbb{R}_+ && \text{(known, fixed)}\\ X &\in \mathbb{R}_{+}^{m \times n} ...
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How to use the parameters estimated by MCMC?

Considering this example, taken from the coursera course "Bayesian Statistics: Techniques and Models", Dataset: ...
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Single Sample Probability Inference

I have 144 force activating widgets. Before shipping, the widgets undergo validation that they activate within a prescribed force, lets say the range 170-175lb, at least three times consecutively and ...
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Multiplying (or averaging) effect of independent Bayes Factors

I want to know how to combine the effect of Bayes Factors calculated on subsets of a dataset. Note, this is not the case of replication BF, where I have, say a BF from a previous study (which acts ...
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Forecasting based on few samples

I have to forecast number of enrollments for an international univeristy , challenge is there are only few years of data.So, my data looks somewhat like this: ...
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1 vote
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Bayesian updates for Dirichlet-multinomial with Gamma prior

Let $$ \begin{aligned} X_i &\sim \text{Dir-multinom}(X\mid\lambda)\\ \lambda_{j} &\sim \text{Gamma}(\lambda_j\mid\alpha,\beta)\\ \end{aligned} $$ where $i$ iterates over observations, $j$ ...
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Recovering samples from a density estimation with an additional prior on the samples. Used for Gibbs sampling

Abstract Idea: Given a noisy measured density ($d_j$ at position $p_j$) and a density model, sample from the model parameters under the following stochastic model: Stochastic Model: Prior for model ...
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Application of Bayesian Networks to tabular data

I have been going through some tutorials regarding Bayesian Networks, but i have yet to see them applied to tabular data, i.e. a dataset. I have created this dummy example to experiment, and attempt ...
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5 votes
3 answers
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Why is random sampling good?

First, is there any theory for random sampling being optimal? Second, consider the following example. Suppose there are two balls in an urn. Their colors can be either white or red. So there are three ...
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What is the correct bayesian formulation for the zero-truncated Poisson lognormal model?

In ecology we use compound distributions to describe species-abundance data. One example is the Poisson Lognormal (PLN) distribution which is a Poisson distribution with rate parameter $\lambda$ that ...
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bayesian parameter estimation of hawkes process

I have encountered a problem of modeling event data with hawkes process. I define the intensity function as: $$ \lambda(t) = \lambda_{0} + \alpha\cdot\beta\cdot\Sigma_{i}^{n}exp(-(t-t_{i})) $$ where $...
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Implementation of bayesian optimization

Is there an easy to apply implemented tool in python or R for a bayesian optimization? As I know this topic only superficially, I want to use bayesian optimization to determine the number of ...
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Does it make sense to apply Bayesian formula on top on a classification problem output?

In classification tasks we normally get a set of numbers that represent a probability distribution - they sum to 1. For further discussion, suppose we only have two classes: ...
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Developing a predictive model using only cross-sectional data

Let us assume I am trying to develop a predictive model that will give an indication of the progression of the percentage crack area on bridge decks. Engineering knowledge indicates that the crack ...
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2 answers
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Posterior distribution is impossible depending on which prior hyperparameters are used?

Suppose we randomly select one of two coins and flip it. In that situation we have random variables $\alpha$ and $\delta$, where $\alpha$ tells us which coin we select, and $\delta$ tells us whether ...
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Monte Carlo Gradient Estimation in Auto-encoding Variational Bayes

I am currently reading paper Auto-encoding Variational Bayes and I am not being able to understand the highlighted part in the screenshot below: I am not understanding why there is f(z) and what is ...
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Compounding Gamma with Gamma to yield F-distribution?

I am working through some problems from my Bayesian Statistics course and am having trouble understanding a step in the solution to a question. For reference this is the question: And here is the ...
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True and Estimated Posterior of a Mixture of Gaussians in Bayesian Learning via SGLD

I am trying to recreate one of the experiments in this paper, (Bayesian Learning via Stochastic Gradient Langevin Dynamics). To be exact experiment 5.1. I am pretty sure, I am missing something here ...
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How to determine uncertainty of data from a bayesian posterior distribution

I am a bit confused as to how we determine the uncertainty of a set of data from Bayesian Analysis. In my specific case, I am asked the following: Assume $f(x,x_0)$ as the correct model for the ...
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Bayesian update with the shifted and scaled data

Suppose I have data $y$ (N observations) which follows a normal distribution: $y \sim N(\alpha+\beta*\mu,\sigma^2)$ while $\alpha$ and $\beta$ are known parameters. I want to update $\mu$ and the ...
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Why are Gaussian Processes used in Bayesian Optimization? [duplicate]

In Bayesian Optimization, the function (i.e. objective function) that we are trying to optimize is modelled using some surrogate function - this surrogate function usually turns out to be a Gaussian ...
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How to combine priors for empirical bayes

I am trying to estimate $Z_{i} = P(Y=1 | A=a_{i}, B = b_{i}, C =c_{i})$ using something like empirical Bayes as in http://varianceexplained.org/r/empirical_bayes_baseball/ aggregating a massive amount ...
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3 votes
2 answers
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Bayesian Poisson Regression with Gamma Prior Formulas

Are there closed form formulas for the posterior and evidence of a Poisson-Gamma Bayesian regression model? I was not able to find anything that is accessible online. I am not sure for which model can ...
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1 vote
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MCMC "for dummies" || how to estimate parameters and what limitations should I consider?

I'm interested in parameter estimation. In a nutshell, I have an expression, e.g., $$f(x,y,w,z; t) = \frac{x\cdot\,y}{w\cdot\,z} \, \frac{k_1}{k_2}\,\frac{j_1}{j_2}\,t$$ in which I know variables $x,y,...
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How is the q(z) function added at the end of this Bayesian formula?

At the bottom of this Bayesian formula why is a q(z) is brought into numerator and denominator positions? Is this within the rules of Algebra? Could anything be placed in the numerator and denominator?...
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What is a good introductory guide to Bayesian MCMC Analysis in R?

I am trying to perform Bayesian Analysis in R, using of Monte Carlo Markov Chains to calculate the probability of, in a set of data, there being a gaussian peak at a certain location $x_0$ (my 'target'...
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Does approximating the likelihood function violate the likelihood principle in Bayesian Inference?

Suppose we have a prior $p(\theta)$ and a likelihood function $L(\theta|x)$, and that the likelihood $L(\theta|x)$ is intractable somehow (difficult or impossible to compute) and we instead replace it ...
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Identify name of sampling / simulation strategy

From what I've learned, it seems like in order to simulate draws from a distribution $X \sim p(X)$ one can take advantage of the fact that $p(X) = \int p(X, z)p(z)dz$ and use the following strategy: ...
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