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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How to analyse data with both GLMM and bayesian GAMM
For my master's dissertation, I am working in R with a dataframe that is: repeated measures, negative binomial and zero-inflated. Variables have been factorised (if categorical), centered (if ...
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Is the conditional probability fallacy exising in the case of an individual with full control [closed]
Hello I had a very interesting discussion and I need your help in clarifying the correct answer.
TLDR: Problem statement for a layman: Given I am a woman and I want to become professor, and given that ...
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How to test whether null effect of condition is due to ceiling effect?
I have data from an intervention study on math learning. Participants were assigned to four treatment conditions in a 2*2 between-participants design. Participants were tested before the intervention (...
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How to Compute Mean Ratios and Their 95% Confidence Intervals in a Bayesian Model
I am working on a Bayesian model using the brm function from the brms package in R, and I am interested in comparing mean responses of different groups. Specifically, I would like to calculate the ...
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Bayesian hierarchical exchangeability assumptions reasonable with a check treatment?
This is information I believe to be true
A practical feature of hierarchical Bayesian models is that partial pooling reduces (eliminates?) the need of adjusting for multiple comparisons when ...
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MCMCglmm package [closed]
the summary() for my ordinal model isn't returning all of my cutpoints. There are four levels in my response variable but I'm only getting two cut points. Does anyone know why?
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where's a good reference and community for help with getting started on Bayesian time series analysis?
I am trying to learn the basics of Bayesian time series analysis, but am having trouble finding some up-to-date basic examples and a discussion forum where I might be able to get some guidance. (...
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Prior probability distribution when we have a single estimate of the mean and no estimate of the variance
Say we have some real parameter $p$ we'd like to determine experimentally. If we have a single estimate of $p$ but no associated uncertainty, what prior probability distribution(s) can/should we use ...
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Bayesian data analysis numerical [closed]
How do I solve the following problem?
Suppose that $x_1,x_2,...,x_n \sim U(0,θ)$ i.i.d. given $θ$ and suppose that $θ$ has the prior pdf:
$$p(θ) = (a/θ_0) * (θ_0/θ)^{a+1} I[θ > θ_0], a > 1$$
a) ...
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SMC sampler weights when $K_n$ leaves $\pi_{n-1}$ invariant
I cannot seem to find this proof anywhere. Suppose I choose $K_n$ to leave $\pi_{n-1}$ invariant, and $L_{n-1}$ to be the reversal kernel. I want to show that the incremental weights
$$
w_n(x_{n-1}, ...
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MCMCglmm package help [closed]
I am trying to run a significance test for a lab experiment and have stumbled upon the MCMCglmm package. My response variable is ordinal with grades "A" "B" "C" "D&...
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Calculation of Posterior distribution numerically
For calculating posterior probabilities numerically, I did not understand that why is in the following codes they have divided by 0.001 in the denominator to calculate ...
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What should be the appropriate choice of prior for a dummy variable in a Bayesian Linear regression?
I have a dataset where the dependent variable is Sales. The independent variables are Media Spends 1, Media Spends 2 and Covid dummy. I am trying to build a Bayesian Linear Regression model. The covid ...
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Choice of Prior
What should be the appropriate prior in case of a dummy variable and an interest rate variable which has values like 4.5, 4.6, 4.9 etc in a Bayesian linear regression?
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Main references for Bayesian Event Tree method?
I am struggling to find the main references for the Bayesian Event Tree method.
At least in my research field, people cite authors that have applied this method to their specific problem, without ...
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The role of variance of the distribution plays in Bayesian inference
Given prior $ \mu \sim \mathcal{N}(\mu_0, \tau^2) $, likelihood $ X_i | \mu \sim \mathcal{N}(\mu, \sigma^2) $, we know the closed-form solution of posterior is $ \mu | X_1, X_2, \ldots, X_n \sim \...
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Convergence of variational posterior
Let $q_\lambda(z)\in\mathcal Q$ be the variational posterior approximation of $p(z|y)$.
Note that the optimal $\lambda^*$ is approximated by the following recursive sequence
$$
\lambda^{(k+1)}=\lambda^...
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Is bayesian updating framework a valid concept?
When I google search for the term, only 6 pages showed up. There is no authoritative paper on this, except https://arxiv.org/abs/1306.6430 which argues for using informatics concepts to generalize a ...
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Why do T prior and likelihood make a bimodal posterior?
In this post, the author shows that when a likelihood and prior are both T-distributed with $2$ degrees of freedom, the posterior is bimodal. The given reason is that
The two modes persist - the ...
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How can I restrict the predicted values of a bayesian linear regression?
Is there a way to restrict the predicted values, say, to only positive values or an interval of values? Let's say I want to estimate a linear model, y = a + Xb, using Bayesian techniques. I specify ...
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Please help me evaluate these results if a Bayesian Mixture Model is better than K-Means Clustering
Dataset
I am performing Clustering in this dataset which some samples are:
Now, I am comparing the results of:
K-Means Clustering
Bayesian Mixture Model (BMM)
I set $K=6$ clusters for both of them ...
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Normalizing constant calculation of Strauss Process
Suppose that I have the following Strauss Process up to a proportionality constant
$$p(\mu_{1}, \mu_{2},..., \mu_{K},K)\propto \xi^{K}\prod_{i=1}^{K} I(\mu_{i}\in R) *a^{\sum_{i,j}|\mu_{i}-\mu_{j}|<...
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Getting negative predictions while fitting a Bayesian linear regression model
I am trying to fit a Bayesian linear regression model on a data set of $3$ years. I have used both pymc and pytorch libraries and the NUTS sampler for sampling.
The dependent variable is Sales, and ...
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Gaussian linear regression with no noise
In short: is there an alternative expression for posterior on weights in a linear model, that works with no observation noise?
In Rasmussen & Williams "Gaussian Processes" they consider ...
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Bayesian imputation model for day of month when the year, month, and day of week are available
I'm considering including vehicle incident data paired to date, however the most extensive data for the region I am interested in does not have dates. I would like to include it in a multivariable ...
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Bayesian Analysis of Coin Toss with Three Outcomes: Incorporating a Fixed Probability of a 'Side flip' event
I'm working on a Bayesian analysis of a coin-toss scenario and have a conceptual question to clarify my understanding.
Background
Given a uniform prior on the probability that a coin lands tails over $...
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Process Modelling with LSTMs vs Probabilistic Programming
I am trying to model an aircraft’s turnaround process from the beginning (in-block) to the end (off-block). The goal is
to gain transparency about the progress of the process / subprocesses and
to ...
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How to check assumptions for Bayesian Linear Mixed Models in R?
I'm trying to create a Bayesian mixed linear model for my master thesis but having trouble to check all assumptions (especially normality of errors)/ I'm not sure if I'm doing it right, because I'm an ...
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How can I fuse data from multiple sensors with non-Gaussian error distributions by multiplying their distributions?
I am working on a project that involves multiple sensors for measuring the one-dimensional position of a small car. Each sensor has its own error distribution, which is not necessarily Gaussian.
To be ...
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Bayesian model with maybe-missing data
Suppose we have data that come from a normal distribution with unknown $\mu$ and $\sigma$ parameters. The twist is that each value is missing with the given probability $p$, i.e. we observe a vector ...
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What to attribute the difference of observed probabilty in a bayesian model to simply sampling from data?
Comparing the probability from data that a zombie has iq > 18 the bayesian approach
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Predictive Diagnostic, Comparison of simulated data with observed data
The question is quite abstract, so I display it with only the essential information.
Suppose that we have three models $B_{1}, B_{2}$ and $F_{3}$. The $B_{1}, B_{2}$ are Bayesian models and the $F_{3}$...
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Conditional structure with 4 conditionals in JAGS
I'm using JAGS for Bayesian estimation.
Ideally, I would like to define 4 different scenarios (x=a, x=b, x=c, x=d). Depending on the scenario, some different actions should be done.
My problem is that ...
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What is the advantage of running generalized mixed effect linear regression model with bayesian with non-informative prior vs frequentist approach?
I am curious as to whether the bayesian approach with non-informative prior (flat prior) is more suitable for generalized mixed effects linear model than frequentist approach and what the reasons may ...
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Why is the statement "the bayes estimator is bayes optimal" profound?
I'm trying to understand why people make a big deal about the optimality of a Bayes estimator. Certainly, if I have a Bayes estimator, then my expected loss is minimized, almost by definition. So,
$$
\...
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Do we need stationarity for Bayesian network modelling?
Most of the Bayesian network packages in R dealing with continuous data require data to be Gaussian. Does this necessitate the data should also be stationary in order to run the model?
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Two different methods to plot residuals with rstan but two different distributions [closed]
The following is the first exercice of chapter 5 from the Book 'Bayesian Statistical Modeling with Stan, R and Python' of Kentaro Matsuura, 2023.
I am fitting a bayesian linear model in rstan and I ...
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Using mcmc to estimate parameters of Dirichlet distribution
We have a probabilistic model with two parameters, $\theta$ and $\eta$, both of which are uniformly distributed between 0 and 1. The model has five possible outcomes, and the probability of each ...
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Calculate acceptance ratio of Jacobian of split-merge RJMCMC
I am keep studying the RJMCMC and want to ask question regarding the acceptance ratio of split/merge step of RJMCMC
The split/merge step, suggested by Richardson and Green (1997) is following for w_j, ...
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How to obtain marginal density [x], given [y|x] and [y]
I came across a problem knowing density of Y, conditional density of Y given X, how would I obtain density of X? Or would this even unique?
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Scoring races + ranking index, with Bayesian approach
Challenge: Is this the best approach for scoring multicompetitor races? How do I account for both uncertain prior & uncertain evidence when scoring?
Case: athletes getting scores in each race, ...
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What is Bayesian PCA and its cousin?
When I think of the phrase "Bayesian PCA" I think of two things, but these two things are what I have contrived rather than conventional notions. I would appreciate guidance on what these ...
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How to take a negative ranged prior using pymc package?
I was trying to fit bayesian linear regression using pymc package. But for certain model coefficients I need to choose the prior as a negative ranged distribution (for example negative halfnormal) so ...
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Do Bernardo Priors still Encounter Paradoxes?
I heard that Bernardo Priors are better versions of Jeffrey's prior that work in multi-dimensions & match frequentist confidence intervals.
Apparently they also dodge many paradoxes of other ...
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For mixed effects model with multiple random intercepts, are bayesian approaches (with MCMC) more robust than frequentist?
I stumbled upon this particular webpage from UCLA containing the following text:
[...]
Inference from GLMMs is complicated. Except for cases where there are many observations at each level (...
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Definition of priors for GLM
I am building a generalized linear model using the logit function in R using JAGS. Whenever I saw code people only define priors for the parameters of the model, but never for parameters of the ...
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Terms and assumptions in trans-dimensional MCMC (RJ-MCMC) for Green 1995 paper
I want to use Trans-dimensional MCMC in my research and for fundamental understanding, I am trying to learn from Green (1995) paper, which is foundation of RJ-MCMC.
In part of 3.3 'switching between ...
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In the Monty Hall problem, does it matter that the host knows which door the car is behind? If so, why?
If I'm thinking about this correctly, regardless of how the host chooses which door to open, there's a 1/3 chance the player initially picks the door with the car behind it, in which case they shouldn'...
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How to calculate the log marginal distribution in Tweedie's formula?
2018 Bayes, oracle Bayes, and empirical Bayes
2021 Empirical Bayes: Concepts and methods
Two modeling strategies for empirical Bayes estimation
2013 Empirical Bayes modeling, computation, and ...
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Doing empirical Bayes with improper prior - marginals that do not exist?
I am considering a Bayesian linear model for which the prior is not proper.
The model is as usual $y = X \theta + w$ where $w \sim N(0, \sigma^2)$, and $\theta, \sigma^2$ are unknown.
The distribution ...
