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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1answer
265 views

Are Bayesian methods robust to violations of normality?

Consider the simple case $$x|\sigma^2 \sim N(0,\sigma^2)$$ $$\sigma^2\sim IG(\alpha,\beta)$$ Then, marginally, $f(x) \propto (\beta + x^2/2)^{-\alpha}$, is a t-distribution. Does this mean that the ...
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1answer
180 views

Can we always pull a joint posterior apart?

If we have a posterior distribution $p(A,B|\theta)$, is it always true that $p(A,B|\theta) = p(A|\theta)p(B|\theta)?$
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4answers
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Is there a name for the opposite of the gambler's fallacy?

The gambler's fallacy is a fallacy because of the assumed probability and the independence of the events. However, if, after flipping a coin 100 times and obtaining heads each time, I still believe ...
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0answers
9 views

Convert bayesian model to Mixed-Effects Models (lme4)

I am studying some Score in a population of young (Age=1) and old people (Age=2). Each person was studied several times (1-4). ...
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1answer
24 views

High Recall but too low Precision result in imbalanced data

I was training a model using XGBoost Classifier on heavy imbalanced data base with 232:1 of binary class. Because my training data contains 750k rows and 320 features (after doing many feature ...
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2answers
28 views

Where to learn probabilistic deep learning/baysian methods for machine learning

I have completed the machine learning course and deep learning specialization by Andrew Ng on Coursera, and now learning TensorFlow 2 for Deep Learning Specialization by the imperial college of London,...
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0answers
17 views

What is the “empirical distribution” in the context of Bayesian inference?

A colleague of mine was using the functions bayesglm() and sim() from the arm-package in <...
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19 views

Point estimation of parameters

Let $\theta$ be a parameter with values in $\Theta$ that should be estimated by some given data $X$. The corresponding estimate is denoted as $\hat\theta = \hat\theta(X)$. Several times I read that ...
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1answer
36 views

Prior distribution on Bayesian T Test?

I have two subgroups of structure (bone structure) and I want to test if there is any difference of size (area) between them, and if there is, how important this difference is. The first set is a ...
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1answer
62 views

Why was Bayes' Theory not accepted/popular historically until the late 20th century?

I have to write a math history paper. I was going to write it on the rise of Bayes' Theory. I have read around that Bayes' theory was no widely accepted or used until the 20th century. I need to make ...
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0answers
10 views

Separate time-series based data into two trends with known temporal patterns

I am dealing with a problem that need to distangle different patterns of a time series-based data. Specifically, the concentrations of air pollutant for one spo always vary with time due to the ...
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0answers
8 views

Given a target # for the end of year, how can I calculate the probability of reaching the target given my pace at any given moment in time?

Let's say I have a target to reach 100M widgets by the end of the year. I need to monitor in real-time the probability of hitting that target. "What's the probability we'll make it today?" ...
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13 views

Applying Bayesian inference

I want to know if the application of Bayesian inference below is correct and if so, what is the next step. I'm considering buying an old house. Based on its age, I think it has a 75% chance of leaking ...
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2answers
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What is Cromwell's rule and why is it important for Bayesians?

I have just heard of Cromwell's rule, but I'm not sure I understand it very well. What is Cromwell's rule and why is it important for Bayesian statistics?
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0answers
14 views

Clustering with gaussian mixtures: choice of hyperparameters

Question: I am interest in general in understanding how to choose the hyperparameters if we are interested in clustering bivariate vectors assuming a mixture of Gaussian mixture with conjugate Normal-...
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1answer
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+50

Inference in Dirichlet process mixtures via collapsed Gibbs sampling

I need to cluster some data $\{x1, \ldots, x_n\}$ through a Dirichlet process mixture model. Consider the following Dirichlet process mixture model, in which the base measure is a $NIW(\mu_0, \...
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1answer
56 views

Problem with Bayes theorem and bigram probabilities

I'm working with Bayes’ Theorem, but I can't fix the numbers, and I don't know why. I have a very simple set of sequential events, grouping them into bigrams (sequential groups of two events): $$ABBAB ...
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6answers
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How seriously should I think about the different philosophies of statistics?

I've just finished a module where we covered the different approaches to statistical problems – mainly Bayesian vs frequentist. The lecturer also announced that she is a frequentist. We covered some ...
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0answers
13 views

Determing a change in relationship between features and outcome (Bayesian approach)

I have a datasets A and B (A is before some date and B is after). I did a change on the date and I want to check whether it affected the outcome (= the relationship between features and outcome). ...
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3answers
116 views

What does it mean that a Gaussian process is 'infinite dimensional?'

I have glossed over this phrase many times without really understanding what it means. According to Wikipedia - Gaussian process Gaussian processes can be seen as an infinite-dimensional ...
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0answers
15 views

Sequential Bayesian Linear Regression with Diagonal Covariance

The standard update rules for a sequential Bayesian linear regression are well-known (heck, they're even on wikipedia: https://en.wikipedia.org/wiki/Bayesian_linear_regression). However, in large ...
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2answers
84 views

Beginner Bayesian question - which statement is false?

I'm working my way through Statistical Rethinking as a beginner Bayesian and am struggling with one of the concept-check questions. Book is here but is paywalled, so I'll also link to the solutions ...
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0answers
14 views

Using MCMC to find mean of each group by R [closed]

I have a data file that has one column of data to record y, and another column to record its corresponding group number. For example: | y | x | |---|---| |123|1| |456|2| Let's say there is 4 level in ...
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0answers
55 views

Modelling a multivariate changepoint analysis

I'm trying to model a multivariate multiple change point analysis. The data I have is as follows: Multiple sensors, positive count data, multiple change points and a time series. For example, imagine ...
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0answers
68 views

How do I compare two count data and show that there is true difference between them through Bayesian statistics?

I have two categories : Protein and Carbohydrate denoting two type of food available in a setup. From Protein, 335 food pieces has been eaten from a total of 1095 pieces and from Carbohydrate, 70 food ...
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28 views

What is the parameter of this Gamma posterior distribution with Poisson likelihood and constant prior?

I am trying to figure out the parameter for this driven posterior distribution. I have searched online and found that the constant prior distribution with the Poisson likelihood function should give a ...
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1answer
33 views

Bayes by Backprop applied to Regression

I have been reading the Bayes by Backprop paper "Weight Uncertainty in Neural Networks" from 2015 (https://arxiv.org/pdf/1505.05424.pdf). I think I have a decent understanding of the content ...
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1answer
33 views

Does marginal likelihood have closed-form solution for hyperparameters in Bayesian linear regression?

We know that marginal likelihood has the following form in Bayesian linear regression, $$ \mathbf{K} = \sigma_w^2XX^T + \sigma_n^2I\\ p(\mathbf{y}|X) \sim \mathcal{N}(0, K)\\ \log p(\mathbf{y}|X) = -...
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0answers
48 views

Bayesian inference - Pi notation

I often see people use $\pi(\theta|y)$ and $\pi(\theta)$ for posterior distribution and prior, respectively. e.g. $\pi(\theta|y) \propto f(y|\theta)*\pi(\theta)$ sometime, the notation is simply ...
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1answer
35 views

Seeking clarity regarding kernels

With regards to Bayesian statistics, I understand the kernel of a probability density function (pdf) or probability mass function (pmf) to be the form of the pdf or pmf in which any factors that are ...
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0answers
11 views

Defining an LKJ prior not centered at zero

I am working with a Hierarchical Bayesian Model. In each of its units, I need to define a covariance matrix between 2 variables. I am planning to sample the covariance matrix from the LKJ prior. ...
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1answer
30 views

Deriving bayes formulas from “Overcoming catastrophic forgetting in neural networks”

I am trying to understand the formulas from the paper "Overcoming catastrophic forgetting in neural networks" and am wondering if someone could help explain how they derive these formulas. ...
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1answer
39 views

What is the advantage of using Bayesian (especially Gaussian Process methods) over 'traditional' methods of classification?

What are the advantages of using a Bayesian (especially a Gaussian Process method) over 'traditional' methods of classification? I understand that Gaussian process regression might be easier and more ...
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0answers
63 views
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Best way to combine MCMC inference with multiple imputation?

I can derive an MCMC algorithm for sampling from the posterior distribution of a parameter vector of interest, but only starting with a dataset that has no missing values. The actual dataset that I ...
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0answers
11 views

Predict probability of association using Bayesian logistic model in R

I am developing a ordered logistic regression model from a survey conducted where y variable takes on 5 ordinate values: ‘very good’, ‘good’, ‘neutral’, ‘bad’ and ‘very bad’. I have one x predictor ...
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1answer
57 views

Unintuitive result involving Bayes' Law

I just watched a video claiming that for a test for property X that has a 99% success rate, candidate A tests positive, but the probability of candidate A having property X is NOT 99%. Instead I am ...
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4answers
207 views

Better understanding what is the model in Bayesian approach

I was trying to understand model likelihood and now with great confidence I can also call it: integrative likelihood marginal likelihood predictive likelihood the evidence since I read the paper: ...
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1answer
26 views

Getting started with Bayesian Dynamic Networks?

Dagum developed DBNs to unify and extend traditional linear state-space models such as Kalman filters, linear and normal forecasting models such as ARMA and simple dependency models such as hidden ...
4
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1answer
81 views

Bayesian inference—interpretation of P(X)

Let's assume we have a simple neural network model for which we want to use Bayesian inference. $X$ - is the data we have seen so far $W$ - is the weights space of our neural network. In order to ...
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0answers
25 views

Convergence of credible regions on simple Bayesian model

Consider a basic Bayesian model : $$ \begin{array}{rcl} \theta &\sim &\pi(\theta)\\ X_1, \cdots, X_n&\overset{IID}{\sim} &\mathcal{N}(\theta, I_d)\\ \end{array} $$ where $d$ is the (...
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1answer
102 views

What is the role of model likelihood?

$$ p(\theta \mid X, M)=\frac{p(X \mid \theta, M) p(\theta \mid M)}{p(X \mid M)} $$ Just proved this is upper probability equation is correct. It differs a bit from the ordinary Bayesian rule: $$ p(\...
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0answers
26 views

Estimate joint probability [duplicate]

I have N random variables, which are not independent form each other. I can reasonably estimate the probabilities p(x|y) and p(x) and p(y) for all x, y among these N variables. Therefore, I can also ...
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0answers
29 views

Bayesian sequential updating with current Bayesian sampling software?

I'm having a hard time implementing sequential updating with current software, I don't even know how to start. Basically, I'm having to refit the whole model by simply appending the new data to the ...
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1answer
34 views

How to eliminate graph cycles?

I checked Why do Bayesian Networks use acyclicity assumption and read two books on Bayesian probability but I haven't found why DAGs (Direct Acyclic Graphs) are must and what would possible be wrong ...
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0answers
17 views

Can you use information criterion to decide if random effects are important in your model?

I want to know if adding random effects in a model improves its predictive performance. I have a model with fixed effects below: m1<- stan_glmer(a~b+c) Which I want to compare with a mixed effects ...
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0answers
14 views

Can I use posterior beta parameters from a previous experiment to use as priors for my current experiment?

I am doing a Bayesian comparison between two proportions, H0 being Proportion(Protein)> Proportion(Mixed). Here the Proportion is of no. of times a free-ranging dog(s) ate from a box(Protein, Mixed)...
9
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2answers
288 views

What is the “effective sample size” of the prior in Bayesian statistics?

In Bayesian statistic, what is the mathematical definition of "effective sample size" of the prior? Could you provide what the "effective sample size" is for the well known classes ...
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2answers
30 views

How does one compute the posterior in a two-stage Bayesian model?

Given a random variable $X$ depending on a parameter $\theta$ which itself depends on a parameter $\psi$, how do I compute $p(\theta|X,\psi)$? A website I have found$^1$ claims that $p(\theta|X,\psi)=...
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0answers
26 views

Should Likelihood add to 1 in frequentist case? [duplicate]

I know maximum likelihood and Bayes formula works for both frequentist and Bayesian approach. We know there are two approaches to statistics, and likelihood is a term that is used in both frequentest ...
1
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1answer
19 views

Bayes continuous case and a uniform marginal density

Assume I have a population $A$ distrubuted Uniform $U(a, b)$ and now assume I have a Conditional probability distribution conditioned on $S$ given $A$ i.e. $f(S | A)$ where $S$ is a binary variable ...

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