Questions tagged [bayes-factors]
Given some data and two competing models, Bayes factor is the ratio of probabilities to observe these data under one and under another model.
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strong evidence for H1 with Bayes factor but very weak with Bayesian regression estimation
I performed a Bayesian hierarchal regression with the brm package. Looking at the parameter estimation and confidence interval, I found no support for one of the parameters. However, when I computed ...
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Why can a likelihood ratio not give evidence for the null since it is a model comparison?
I am curious as to why a likelihood ratio cannot give positive evidence for the null, since it is a model comparison.
Indeed, this is more confusing given the fact that Bayes Factors are similar ...
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Similarities between Bayes Factor and WAIC formulas?
It looks for me that WAIC and Bayes Factor are very similar in some circumstances. If we assume an equal prior for each parameter set Q (p(Q)), the Bayes Factor ...
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Compare two proportions with a Bayesian analysis
I'm conducting an experiment in which participants receive either an object A or an object B. Next, we ask participants if they want to trade their objects with the alternative object (i.e., object B ...
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Specifying Model of Alternative Hypothesis for Calculating Bayes Factors
I'm new to Bayesian statistics. I'm running a linear mixed effects model in R (using lmer), and I want to report Bayes Factors using these results, as demonstrated ...
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Using BayesFactor R Package Instead of P-Values in Mixed Modelling
I have been using lme4 in R to run a linear mixed effects model.
...
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Detection limit for a drop in speed, due to stopping between measurements
Assume that a device is traveling at a constant expected speed $\mu$, subject to random variation with standard deviation $\sigma$, for a measurement period of duration $t$. Then the expected travel ...
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ABC model selection from posterior samples
I would like to know if there is a general scheme to do model selection based on the posterior samples from a set of ABC (Approximate Bayesian Computation) runs for a given set of models.
Particularly ...
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Bayes factor for testing fit of different spatial models in Stan
I have a question about testing of different spatial specifications of a polynomial regression. I am using Stan for Bayesian inference, but I did some initial exploration using the R packages ...
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Bayes factor for one-tailed correlation (differences between results from Bayesfactor package in R vs JASP)
I want to compute a Bayes factor for one-tailed correlation (n~600).
Using NHS, Pearson's r = 0.01 and p-value =0.42
With JASP, I get a one-tailed BF of 0.059, so strongly in favour of the null ...
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Asymptotical convergence of the Likelihood ratio test in general hypotheses testing
I'm aware that the 2-loglikelihood ratio is asymptotically distributed as a Chi-squared distribution under the Null hypotheses for nested hypotheses. My question is, there is any generalized formula ...
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Multiple testing adjustments for Bayes Factors
I manage an platform that has succesfully gotten a Bayesian approach to experimentation in production.
One new feature we want to implement is to do inference for multiple metrics (e.g. conversion ...
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Bayesian test if two discrete random variables are independent
I want to test whether two discrete random variables $X_1$ and $X_2$ are independent. Given $N$ observations, I read this can be done in a non-Bayesian way by calculating the "deviance":
$$\...
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Do I need to renormalize my prior when computing the marginal likelihood for a subset of my parameter space?
I'm trying to generate Bayes-Factors from sequential t-tests. Based on this paper, I'm interested in using a Cauchy prior on the effect-size parameter $\delta$.
At first I was calculating the Bayes ...
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Single sample classification between 2 Normal distributions using Bayes factor
I need to validate my approach, since I keep getting more and more confused the more I read into this.
Situation: I am measuring some feature on two groups of people. I have two samples, representing ...
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How calculate the conditional probabilities for Bayesian hypothesis test?
Suppose that I obtain a sample $S=(S_1,\dots,S_n)$ from my research. The null hypothesis $H_0$ says that all $S_i$ are drawn from a normal distribution with mean 0 and standard deviation 1. The ...
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Bayesian model averaging
In which situation would you refrain from using BMA. It seems to me it is always a good idea to use the posterior probabilities when infering/predicting.
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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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Hypothesis testing: Should it be done on the transformed parameter or the non-transformed?
I want to compare two proportions, for example:
succN <- 2
d <- data.frame(pledge = c("yes", "no"),
s = c(succN, succN),n = c(100, 100))
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How to fix hypothesis testing: MBF versus "directional correctness"
A common misinterpretation of a p-value is that it represents the probability of a false positive in the context of hypothesis testing. Here a "positive" means rejecting the null.
There are ...
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Savage-Dickey density ratio under horseshoe prior
Suppose one has a linear regression with Gaussian noise. The regression coefficients have a horseshoe prior. To test that some regression coefficients equal 0, one applies the Savage-Dickey density ...
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Why does the contigency table Bayes Factor test does not behave like an omnibus test?
I have a contigency table and want to know whether the distributions differ between columns. For example, let's say I want to know whether the distribution of children with academic vs. non-academic ...
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Marginal likelihood for linear model with random effects to do Bayesian model comparison
Suppose I have behavioral data from multiple participants to four different conditions (four observations per participant per condition). The conditions can be characterized in terms of two fixed ...
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Bayesian A/B testing and decision metrics
Say I need to test two different product features ({existing/control: blue} vs {new/treatment: red} font on webpage, for example), and need to boil my analysis down a to a single go/don't go criteria ...
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Comparing posterior predicted probabilities with "known" to be true probabilities
Following this description I have implemented a Bayesian logistic regression (BLR) model on some data.
Lets say I have this kind of data:
...
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(Why) is the Bayes factor not sensitive to the choice of prior distribution on hypotheses?
I learned that the posterior odds is the ratio of the two posterior probabilities of hypothesis:
\begin{align}
PO[H_1:H_2] &= \frac{P(H_1|\text{data})}{P(H_2|\text{data})} \\
&= \frac{P(\text{...
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Bayes Factor Analysis
I am new to Bayesian statistics.
I have one group (n=10) with two measurements per subject (before/after a treatment manipulation, i.e., Phase "2" and "3" below).
I originally used ...
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Checking my understanding of Bayes factor hypothesis testing
I am new to Bayesian statistics. I am trying to understand my course notes on this topic. Here are the notes:
I will try to explain what these notes are saying and hopefully someone can correct my ...
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The ratio of two Bayes factors for two opposite one-tailed hypotheses
I am trying to understand how Bayesian inference works, so this might be a very simple question. I have an experiment where I test two hypotheses predicting opposite results. Let’s say, hypothesis 1 (...
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Significant p-value and anecdotical BF
I'm conducting frequentist as well as Bayesian analyses. However, I have difficulties to interpret data.
Indeed, results showed significant p-value, but anecdotal BF10 (< 3). Likewise, there are ...
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Compare two models of binomial distributions via Bayes Factor
(This question is similar to How to compare two models of binomial distributions?, except that I would like to use a Bayes Factor for model selection)
I have a bunch of binary (Bernoulli distributed) ...
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AIC model selection for group studies
In some areas, it is common to fit a model separately to multiple clusters in a data set, for instance fitting a cognitive model separately to data from each participant in an experiment.
Model ...
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Asymptotics of Marginal Likelihood
I'm working with Bayes factors, and I want to develop some intuition for the result
$$
\frac{m_1(\mathbf{X})}{p_n(\mathbf{X}|\hat\theta_n)}\xrightarrow{p}\frac{\pi_1(\theta_0)\sqrt{2\pi}}{\sqrt{\...
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Relatively fast approximations to the marginal likelihood?
Let $\theta\in{\mathbb R}^d$ be a multidimensional parameters, where $d$ can be large (e.g. $d=100$ or more). What approximations can I use for the marginal likelihood:
$$\int f(x\mid \theta)\pi(\...
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Bayes Factor, Likelihood Ratio, and p-values
I am interested in "simple" changepoint detection algorithms.
I originally was using very simples approaches that consist of making t-test calculations and calculate a p-value (similar to what is ...
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How to compute contrasts between levels of a parameter in bayesian mixed-effects models and produce bayes factors in R?
I would like to compute contrasts between different levels of a parameter from my Bayesian mixed-effects models in R, and produce bayes factors. My outcome (Jud) is binary (1=Yes/In synch, 0=No/Out ...
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Why does Bayes Factor go to infinity as $n$ goes to infinity?
Why does Bayes Factor go to infinity as $n$ goes to infinity when considering a bilateral alternative hypothesis?
The Bayes factor is $BF=\frac{postodds}{prior odds}$, and since the prior odds are ...
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How to calculate Bayes factor for conditional probability?
I have a data set of 1000 drug-effect pairs. I am trying to identify which drug is most likely given the observed effect.
My original approach was to calculate $P\left(d_j | e_i\right)$ for each ...
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Can I exponentiate the log-Bayes factor to get the Bayes factor?
Simple question here. I'm using Bayesian Confirmatory Factor Analysis and I can get a log-Bayes Factor with the Laplace approximation. However, I'm wondering whether I can just exponentiate this value ...
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Expressing one-sided p values of directional hypothesis tests as Bayes factors
Assume we want to test the directional hypothesis that $µ<0$. From a frequentist angle we use a one-tailed $t$-test and imagine we obtain a 1-sided $p$ value of say 0.07, which then would imply ...
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Bayes-Poincaré solution to the Behrens-Fisher problem 2: calculations for Jeffreys’ priors [closed]
In a previous post Bayes-Poincaré solution to k-sample tests for comparison and the Behrens-Fisher problem?, the classical Bayesian and likelihoodist solutions to 2-sample tests for comparison and the ...
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Bayes-Poincaré solution to k-sample tests for comparison and the Behrens-Fisher problem?
I’d like to share and submit for (dis)approval and discussion yet another, simple but original (to the best of my knowledge) Bayesian solution to the classical problem of comparing k samples or groups,...
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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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Likelihood ratio to quantify the similarity between one sample with two other matched samples
I conducted a study with 3 conditions and N subjects. All subjects
performed all conditions once. I would like to know if the first condition
is similar to the second or third condition.
Formally, ...
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Bayes factors and predictive accuracy in model comparison in rstan / brms
Despite reading up on the subject, I can't wrap my head round it, so the question remains on shaky grounds, and responses along the lines of "read chapter x" are very welcome.
What I'm doing is I'm ...
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Why are the cut-offs used for Bayes factors and p-values so different?
I am trying to understand Bayes Factor (BF). I believe they are like likelihood ratio of 2 hypotheses. So if BF is 5, it means H1 is 5 times more likely than H0. And value of 3-10 indicates moderate ...
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Bayes Factor A/B Testing
I am just starting to look at Bayesian statistics and so far I am aware that Bayes factor summarizes some form of evidence of an alternative hypothesis against the null one.
As far as I know we can ...
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Random effects in a linear model using BayesFactor package: why do bayes factors vary?
I'm using the BayesFactor package with the lmBF and generalTestBF functions to compare different linear models that include participant as a random effect. Below is an example of one of these model ...
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Model selection for this model with one observation
I would like to perform model selection given a range of $k$ models $\mathcal{M}_1, \mathcal{M}_2, ..., \mathcal{M}_k$, each with some prior probability $f(\mathcal{M}_1), \dots, f(\mathcal{M}_k).$
...
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Bayes factors from MCMC samples
I'm working to implement Bayesian model selection among models whose posteriors have already been sampled via MCMC. After reviewing some discussions of Bayes factors, I understand that they are ...
