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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 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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Find normalization constant from factorized density

Please consider the following Bayes Network: We can express density $p(\mathbf{x}_1 | \mathbf{x}_0, \mathbf{y}_1)$ in terms of measurement and motion models by ignoring normalization constants as: $...
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23 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, ...
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2answers
36 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 ...
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10 views

Bayes Factor for variable importance

Does it make sense to use a Bayes Factor for calculating the effect of a variable on a binary dependent variable? For example, if I have a binary classifier that classifies Y and a predictor variable ...
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3answers
946 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 ...
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1answer
42 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 ...
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22 views

How to compare approximate Bayes Factors (BIC) with glm.nb? (R stats)

I have a situation where I would like to write up an analysis where the statistical significance is non-significant. I wanted to be able to accept the null hypothesis instead of merely 'failing to ...
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21 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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26 views

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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1answer
99 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 ...
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95 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. ...
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1answer
29 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 ...
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2answers
131 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....
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1answer
67 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. ...
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1answer
37 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 ...
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1answer
57 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 ...
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1answer
90 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 ...
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Uniqueness on bayesian factor model's loading matrix

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 ...
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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 ...
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Determining the total amount of evidence for covariates across multiple outcomes

I have a study comparing three different measures of disease severity ($M1$, $M2$, and $M3$) in a disease where there is no gold standard to measure severity. I have six outcomes that are ...
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1answer
137 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 ...
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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 ...
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1answer
181 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 ...
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66 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 ...
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Using Bayes Factor to test geometric vs poissong distribution

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 ...
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287 views

Why is the calculation of Bayes Factors for regression coefficients based on model comparison while delta-R^2 tests are discouraged?

The vast majority of the statistical inference I do is on the basis of multiple regression models (not always OLS, not always single level). Usually the focus is not on the model, but on particular ...
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58 views

Bayes Factor for model and variable selection and type I & II error rate

I am trying to implement Bayes Factor for model and variable selection in Bayesian Linear Regression and finding out corresponding type I and type II error. I need your help regarding this. I will be ...
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1answer
118 views

Choosing a Model Selection Criterion [closed]

I am trying to decide which among for model selection criteria to use for a Bayesian nonparametric model. The candidates are: The L-criterion, as defined by Laud & Ibrahim (1995); Bayes factors; ...
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1answer
177 views

How to account for temporal autocorrelation when computing a Bayes factor between two linear regression models?

I have data of some physiological measure, represented as a vector of 185 measurements taken every 2 seconds. I can model this response in two different ways, and I wish to compare the fit of my two ...
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47 views

Bayes Factor for two exponential samples

I'm trying to solve myself such a problem: calculation of Bayes Factor for two groups from exponential distributions. $$x_1, x_2, \ldots, x_n\sim \exp(\lambda_1)$$ $$y_1, y_2, \ldots, y_m\sim \exp(\...
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138 views

Marginal likelihood (or Bayes factor) when true model *not* in the set

The marginal likelihood (or Bayes factor) method to perform model comparison, based on $\Pr(\text{data}|\text{model})$, assumes that the true model is the model set (closed world assumption). What ...
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478 views

Computing DIC and Bayes factor in R

How can I compute the DIC value and Bayesfactor value for a bayesian glm model? (for both models or even just 1 of the models) I have 2 models I would like to compare. 1. ...
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1answer
354 views

What is the difference between the posterior density, and the posterior “ordinate” in the context of Bayesian modelling

This is the first time I've come across the term posterior "ordinate" and I'm not sure what it means. I understand what the posterior density of some model parameters given some data refers to, but ...
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1answer
167 views

Replication study and Bayes factor

I ran an experiment and got a statistically significant result with an effect size of cohen's d=0.36 (N=20). I decided to run a replication study, this time with 60 participants, and got nothing (d=0....
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560 views

Reporting Bayes factors

I have calculated a Bayes Factor BF10 for the probability of the data under H1 vs. H0. I get very large numbers (the data are very clear, statistics are barely necessary here), in the order of 10^30. ...
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1answer
247 views

Bayes Factor and likelihood for two sample from different distributions?

I'd like to calculate Bayes Factor for two-sample t-test $H_0: \mu_1=\mu_2$ (model $M_0$) against $H_1: \mu_1\not=\mu_2$ (model $M_1$) My data are: $x_1,x_2,\ldots, x_{n_1}\sim N(\mu_1, \sigma)$ ...
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1answer
412 views

Discrepancy in the results of LMER and BayesFactor (R)

I have a within-subject dataset with 3 two-level factors and 1 numeric predictor. I was using LMER with a random-intercept model (a full random-effect model yield the same results though throws ...
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275 views

Different Bayes Factor values for correlation with the same JZS approach

Trying to get the Bayes Factor for a correlation between two variables in my data, I tried three different functions. All implement the Jeffreys–Zellner–Siow (JZS) prior, but I get quite different ...
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2answers
1k views

Mixed bayesian ANOVA using BayesFactor package in R

According to a recent paper (open pdf here), one can specify both within- and between-subjects effects in a Bayes factor ANOVA. In the example they give (p. 28), this is specified in the following way:...
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182 views

Directional vs Non-Directional Alternative Hypothesis in Bayesian Model Comparison?

I have recently completed a study where I hypothesised a significant difference between two groups. I hypothesised that Group B would be report a significantly lower score on the outcome variable on ...
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2answers
552 views

Bayesian Model Comparison - Neutral Prior Information

Let's say I estimate two models, $M_{0}$ and $M_{1}$. The posterior odds ratio for for model $M_{0}$ against $M_{1}$ given the data, $y$, is, $\frac{Pr\left(M_{0}\mid y\right)}{Pr\left(M_{1}\mid y\...
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81 views

Bayes factor and hypothesis test in Bayesian inference

Let $$\pi_0=P(\theta\in\Theta_0)=\int_{\Theta_0}\pi(\theta)d\theta$$ $$\pi_1=P(\theta\in\Theta_1)=\int_{\Theta_1}\pi(\theta)d\theta$$ $$a_0=P(\theta\in \Theta_0|x)$$ $$a_1=P(\theta\in \Theta_1|x)$$ ...
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1answer
114 views

Bayesian model comparison in high school

I teach physics to high-school students, and I would like my students to conduct a rudimentary Bayesian model comparison for data from their experiments. I figured out a way for them to do so (see ...
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2answers
336 views

Bayes Factor approximation

A brute force method to approximate the Bayes Factor (the ratio of the denominators (normalizing constants) in the Bayes formula) is to do the following for the two models of interest: repeat ...
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1answer
354 views

Can I make a decision using a Bayes factor?

Bayes factors denote how well a certain model is supported. Say that I am running a controlled experiment and I have two models: the null model and the alternative model. If I have a high Bayes ...
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108 views

Comparing the rates of Poisson distribution using Bayesian inference

In the 'Theory of Probability' book by Sir Harold Jeffreys, (5.15), the form of the Bayes Factors that he derives for the comparison of Poisson rates is the same as that of Binomial rates. But I did ...
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250 views

Bayes factor for effect size

I need to construct Bayes Factor for testing: $$ H_0: \quad 0 = \mu_t - \mu_c $$ $$ H_1: \quad 0 \neq \mu_t - \mu_c $$ and my prior knowledge is modeled by distribution of effect size: $ \delta = \...
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1answer
177 views

Bayes factor (B) vs p-values: sensitive (H0/H1) vs insensitive data

The question of a beginner in Bayesian stats. As far as I understand, it is claimed (e.g. Dienes 2014) that B-based inference allows us to either confidently reject/accept the null, OR declare the ...
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1answer
377 views

Bayes Factors for more than 2 hypotheses

Naïve question: I would like to use Bayesian framework for model selection. I have more than 10 models with the same number of parameters (just different assumptions on underlying parameters of the ...