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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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Weibull Distribution with priors on shape and scale diverges

I have a variable that is Weibull Distributed Duration ~ dweib(Shape,Scale) The Shape and Scale parameters are distributed to log-normal and Weibull ...
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“Mean” & “median” comparison and zero variance confusions when making inferences in Bayesian model

Background: In Chapter8 of this great book, the authors build a Bayesian model and use to show the posterior distributions of the latent state $N_{t}$ and its credible intervals. The model is ...
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Models for ranking possible classifications by confidence

What are good means of finding the various highest confidences or likelihoods for a (say) hundred possible outcomes of a classification problem? Inputs belong to only one class, unlike document ...
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precision or variance of a Gamma distribution in a Gibbs Sampler?

I want to confirm my thinking on a quick question I have regarding the Normal-Gamma Gibbs sampler that we see so often, but I am unable to find a satisfactory answer. If we are interested in ...
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Residual Analysis

I have just reproduced an example regarding a regression model for fibre strength data. The data consisted of tensile strengths of silicon carbide fibre at four different lengths. From the data, a ...
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How to Derive SISO Kalman Filter Update Equation Using only Probability Density Functions

I'm trying to prove to myself that a single state/single measurement kalman update can be derived using bayes theorem (as proof of concept for a more complicated task) only using the PDF. I am able ...
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Bayesian estimation from sum of two random variables

Let's say I have a set of observations $Y=\{Y_1,\ldots,Y_N\}$ where each observation is created as the sum of two random variables, i.e. $Y_i=X_{1,i}+X_{2,i}$. Also, I know that $X_1 \sim Dist_1(\...
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Binomial regression check

I have run a simple binomial regression using the rethinking package in R, but I just want to double check that my interpretation is correct. Here is my model: ...
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Why is posterior probability so in BPR paper?

In BPR paper BPR: Bayesian personalized ranking from implicit feedback (Steffen Rendle 2009) $$ \prod_{u \in U} p\left(>_{u} | \Theta\right)=\prod_{(u, i, j) \in U \times I \times I} p\left(i>_{...
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Simulating data in JAGS “ones trick”

I am trying to simulate data to use for posterior predictive checks in JAGS running through R, which is relatively simple for pre-loaded distributions, but I am looking to simulate data when I have ...
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How is the bayesian update (least-squares) derived? [on hold]

I would like to know how the Bayesian update function using least squares is derived
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Custom topic priors in LDA

I've been working with LDA (Latent Dirichlet Allocation topic model) for a while now and I believe I have an intermediate understanding of it. The unsupervised nature of LDA is one of its big ...
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How does variational inference fit in the big picture of inference?

Apologise for the clickbaity title, but it is difficult to frame this question in a single sentence. Also, the practicality of variational inference is very clear: intractable posteriors; intractable ...
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Hierachical Bayesian Linear Regression using PyMC3 is super slow [migrated]

I am trying to write some code for implementing HBM in the case of logistic regression using the adults dataset from the UCI repository. I have already written the code, but sampling is super slow, ...
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Bayesian estimation of weighted proportion

Having bayesian estimates of a proportion is relatively easy. You model that proportion as a binomial variable, you choose a beta-binomial prior and by using the likelihood you obtain a beta-binomial ...
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Regression when dependent and independent variables come from different datasets

I am trying to figure our the most robust way to combine two different sets and run a regression. The first dataset gives me an outcome value for each of several categorical treatment variables, each ...
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Heuristic vs Bayesian [closed]

I'm aware Heuristics and Bayesian methods are two separate things, but I'm attempting to choose between them for a task. As input, I take a sentence of fixed words (so all the words are in a small ...
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Normal-Gamma: Metropolis-Hastings on log-scale, but no Jacobian?

I am reading the paper by Griffin and Brown (2010) where at one step in their MCMC procedure they need to sample from the following conditional posterior: $$ p(\lambda|\gamma, \Psi)\propto \pi(\...
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meaning of posterior distribution and credible internal

In Bayesian method, we can get a posterior distribution of a parameter. Now I want to do some simulation to know if the posterior distribution is the same as the true distribution. For example, mean ...
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Rigorous Bayesian Model Selection

I am learning Bayesian Model Selection. I want to understand the rigorous mathematics behind the idea of encompassing model. To be more specific, suppose we want to compare M models: Model $\mathcal{...
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Treating Word Embeddings as Samples From Random Variables

Suppose I want to specify some probabilistic clustering model (such as a mixture model or lda) over words, and instead of using the traditional method of representing words as an indicator vector $z$, ...
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In the fully supervised case, provided we have contingency matrices, is Bayesian inference the optimal method?

BACKGROUND Imagine that we have contingency matrices, i.e., counts or frequencies, linking the features (say, columns) and targets (rows). One could then compute the posterior probabilities, i.e., ...
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The posterior distribution of Bt is Bernoulli

I'm trying to follow the math of Estimating Heston's and Bates’ models parameters using Markov chain Monte Carlo simulation in Journal of Statistical Computation and Simulation, but I'm having trouble ...
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Estimating state covariance with the Unscented Transform and diffuse prior

I have a set of measurements (assume additive Gaussian noise on each), a non-linear measurement model, and a diffuse prior. The state covariance estimate: $P = (H^T R^{-1} H)^{-1}$ where $H$ is the ...
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Time series forecast with probability

I have historical data for a particular metric for each month for the last 3 years for different categories. The metric is a percentage and its heavily skewed towards 1 with more than 75% of values ...
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1answer
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Another round of some simple Bayesian probability questions

Following questions like this one, I have some very simple probability questions for which I guess that Bayes theorem is the tool to answer. I think that Bayes theorem is the tool because each ...
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Binary logistic regression with brms

I've run a binary logistic regression in R, using brms. I have one independent variable (Age) and 3 dependent variables, Y1, Y2, and Y3. These dependent variables are all pass/fail tasks. For each ...
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Determining the optimal number of clusters using plots of Bayesian Information Criterion

I am having trouble interpreting the results from an Expectation Maximization clustering using mclust and the Iris flower data, Using R. Reproducible example If ...
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How to choose the parameters of a prior distribution based on a range for the variance?

How can I use R to calculate the parameters of a prior distribution if I want the variance to fall within a specific range? For instance, I have a variable that follows the inverse gamma distribution ...
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Uniform prior 3 sided dice marginal probability equation [duplicate]

Given a 3 sided dice with a uniform prior. What is the probability of observing ordered data $D = \{n_1, n_2, n_3\}$. Where $n_1$ is the number of observed 1s. Denoting the bias on the dice by $\...
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Computing marginal probability and Bayes factor of structural model

I have a Bayesian structural model of the following format: $Y1 = X \alpha +\epsilon$ $Y2 = S \beta + \eta $ $\epsilon = \gamma \eta + \chi $ where Y1 and Y2 are linked by the error terms. I ...
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Bayes factors in R for correlated proportions (such as a “Bayesian McNemar's test”)

Is there any way to get Bayes factors in R for correlated proportions (i.e., paired sample)? For example, the same group of 90 people is measured with one technique, then with another; once there are ...
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DIC to compare models with different numbers of parameter?

I am interested in comparing hierarchical Bayesian models based on the same dataset but differing in their spatial and temporal resolution. In short, I am looking at animal population changes over ...
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What is the difference between Naive Bayes & AODE (Average One Dependent Estimator)? [closed]

I am trying to increase my knowledge about kinds of algorithms and am stuck at this point as I can't find much useful information about AODE.
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Understanding of conjugation relationship in Bishop book

Referring to Pattern Recognition and Machine Learning by Bishop(Page 367, Section 8.1): Such models have particularly nice properties if we choose the relationship between each parent-child pair in ...
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'Randomizing' Gradient method for the proposal of Metro-Hastings step

In my problem, I've used a gradient method for the mean of the proposal. Let my proposal be $q(\mu_n,\Sigma)$, where $\mu_n = \mu_{n-1}+s\frac{\partial}{\partial \theta}\log(f(y,\theta))$ and $s$ is ...
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Why is the bayesian information criterion called that way?

The word "Bayes" suggests that we are updating a distribution using data, to get a posterior distribution. The fact that the Bayesian information criterion (BIC) is used to select a model from a set ...
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Distribution to model Binomial distribution with parameter p in trial n dependent on result from trial n-1?

I'm wondering how one can model a Binomial distribution as described in question. E.g., p = 0.5 for trial n = 0; p(n+1) = p(n) + 0.01 if for trial n Bernoulli(p(n)) samples to 1, else p(n+1) = p(n) - ...
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Bayesian Estimation of a Mean and Standard Deviation (2D)

(Originally Posted at: https://stackoverflow.com/questions/56399700/bayesian-estimation-of-a-mean-and-standard-deviation-2d) I'm currently following Think Bayes, an introductory text to Bayesian ...
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Value of using a better normal distribution

I tried to derive this on my own, but my stats education proved too far back… (This is a problem in Bayesian decision theory – if that makes you uncomfortable, feel free to reformulate it) Let's say ...
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Bayesian A/B testing with parameters other than success rate

If I have certain number of clicks and conversions for a group of ads, I can do Bayesian A/B testing following this method http://ucanalytics.com/blogs/bayesian-statistics-to-improve-ab-testing-...
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Bayesian updating - update probability that measurement is real

I have a sequence of observations, which are either a measurement of 'active' or 'inactive'. These measurements are not necessarily accurate, with false negatives being more unlikely than false ...
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Is Variational Bayes (VB) and Mean-Field Approximation Useful In practice

I have just had a course in Bayesian Inference, and I am left puzzled about what method should I actually use in practice. Assume I have a multivariate model with multiple parameters $\theta$, where ...
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Gaussian process regression model for comparing two groups

I have a data set consisting of functional observations, where $Y_{mi}$ is the response of the $m^{th}$ functional observation from the $i^{th}$ group, $m=1,...,M$ and $i=1,2,$. The observations are ...
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What is the correct way to write the elastic net?

I am confused about the correct way to write the elastic net. After reading some research papers there seems to be three forms 1) $\exp\{-\lambda_1|\beta_k|-\lambda_2\beta_k^2\}$ 2) $\exp\{-\frac{(\...
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Difference between two dimensions sampled from Dirichlet distribution

Say I'm doing Bayesian inference on a Dirichlet-Multinomial model: $$ x \in [1,2,3]; \\ x \sim Multinomial(p_1, p_2, p_3); \\ p_1, p_2, p_3 \sim Dirichlet(\alpha_1, \alpha_2, \alpha_3); \\ \alpha_n =...
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Using marginal likelihood for weighting in bayesian hierarchical model?

I have data from a series of experiments. I have a simple model for generating the data these experiments which allows me to estimate a parameter. Some experiments do not conform to my model and ...
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Modelling dynamic price elasticity with bsts [closed]

I have approximately 2000 daily data which contains total daily sales and median price of sales for a particular product. I read the paper but the level of bayseian math is too high for me but from ...
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Generalizing Bayesian methods by assuming a “distribution of distributions” instead of a prior

Bayesian methods assume a prior distribution with several hyperparameters. Unfortunately, this is asymptotically incorrect, because distributions in the real world are never exact. For example, the ...
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Is a Bayesian posterior kind of like the marginal distribution of a frequentist estimator?

I've been thinking a lot about the relationships between various concepts like hypothesis testing, posterior distributions, and estimators. If I understand correctly, a frequentist estimator $\hat\...