# 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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### 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-...
21 views

### 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 ...
35 views

### 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)) ...
109 views

### 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 ...
24 views

### 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 ...
40 views

### 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 ...
60 views

### 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 ...
1 vote
142 views

### 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 ...
71 views

### How to perform a directional hypothesis using Bayes Factors?

I would like to test a directional hypothesis using bayes factors, but I don't know how to do it. Given this data I perform a "bayesian anova" using the ...
39 views

### 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: ...
119 views

### (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{...
1 vote
38 views

### 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 ...
119 views

### 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 ...
78 views

### 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 (...
31 views

### 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 ...
1 vote
433 views

### 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) ...
194 views

### 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 ...
1 vote
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1 vote
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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 ...
347 views

### How to compute contrats 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 ...
238 views

### 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 ...
110 views

### 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 ...
1 vote
46 views

### 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 ...
1 vote
167 views

### 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 ...
822 views

### 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 ... 1k views

### 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,... 101 views

### 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 ...
35 views

### 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, ...
525 views

### 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 ...
2k views

### 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 ...
273 views

### 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 ...
291 views

### 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 $f(\mathcal{M}_1), \dots, f(\mathcal{M}_k).$ ...
737 views

### 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 ...
233 views

### How are Bayes factors actually Bayesian?

I have been doing some linear model analyses involving Bayes factors lately and I have two probably very basic questions: 1) As far as I understand, a Bayes factor is simply a likelihood ratio, i.e. ...
44 views

### How to interpret a statistically signficant finding that becomes unsignificant after bonferroni correlation

I hypothesised I would find a main effect of X which I did (p=0.028), however, upon using the bonferroni correction my alpha dropped to 0.0125, making this result no longer significant. I found a ...
282 views

### Bayes Factor Poisson-Hidden Markov Model

I am following the Hidden Markov Models guide text for Time Series An Introduction Using R (Walter Zucchini). Chapter 7. Bayesian inference for Poisson-hidden Markov models. Specifically in section 7....
211 views

### ABC, compute Bayes factor from posteriors

I am pretty new to ABC stuff so I may be saying dumb things. My question is: I ran an ABC with two models $M_1$ and $M_2$ and now I have an approximation of the posterior distribution for both model. ...
361 views

### Calculating Bayes Factor from Z score, n, and No

I'm completely stuck on how to get this answer from a course below. I guessed the answer, but I'm lost on how they get to it. I did the following in R ...
276 views

### Computation within log space

What is the conversion of the following equation into log space? $bf2 = 1 + (p * (bf1 - 1))$ Given log.bf1 (log Bayes factor), how do I get to log.bf2 without having to compute bf1, but instead ...
274 views

### Diffuse priors Bayes Factor

In textbooks I always read that it is necessary to have a proper prior on the parameter that we want to test with Bayes factor, otherwise we would always posteriori favor the model with less ...
1 vote
26 views

I'm doing uniqueness on factor loading matrix in a factor model. $y = \Lambda f + \epsilon$ where $f \sim N(0,\Sigma)$ , $\epsilon \sim N(0,\Omega)$ and $\epsilon \perp f$. It's well known that ...
38 views

### How does Lindley compare a Bayes factor and a p-value?

I was reading this paper by Dennis Lindley ("Analysis of a Wine Tasting", J. Wine Econ. 2006). Statistically, the paper is a straightforward analysis of a $10\times 11$ two-way table. To test whether ...
185 views

### Bayesian models: Bayesian t-test on effect posterior against 0 as index of effect existence

I am fitting Bayesian models (using R and rstanarm). Beyond estimating the effect of each predictor (and extracting pointwise indices such as median, MAD and 90% CI), I am also interested in having a ...
1 vote
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### How do I prepare data for Rouder & Morey (2012) default prior?

I am going to run an analysis using the default prior outlined by Rouder and Morey (2012); however, I am unclear how exactly to prepare the data. As a quick overview, I have a continuous DV and a ...
465 views

### How would I use the largest expected effect size to determine a prior?

I have a simple experiment in which ~30 people responded to 100 words, half of which were of Type A and half of which were of Type B. I am using a mixed effects linear regression to predict reaction ...
169 views

### Calculating Bayes' factor for 2 Gamma distributions

I have 2 model $M_1$ and $M_2$ which both have a gamma distribution and the same priors $H_0 : \quad x_i \sim M_1 \\ H_a: \quad x_i \sim M_2$ Both $M_1$ and $M_2$ have prior $\sim Ga(7,3000)$ but my ...
1 vote
I have a sample of 200 observations and need to test $H_0: X \sim Geom(p)$ vs. $H_1: X \sim Pois(\lambda)$. Prior distributions are $U[0, 1]$ and $U[0, 20]$. I need to construct a bayes test to ...