Tagged Questions

Bayesian inference is a method of statistical inference which uses Bayes' theorem to find probability estimates of parameters or hypotheses.

learn more… | top users | synonyms

0
votes
0answers
5 views

Marginal Likelihoods for Bayes Factors with Multiple Discrete Hypothesis

If I have some data that I believe is Normally distributed and I just want to test the hypotheses that the mean is equal to 1 of 3 values, my understanding is that the Bayes Factor is the ratio of ...
5
votes
1answer
117 views

Probability of getting the correct direction, given you get the same answer

A town is composed of $2/5$ out of town couples and $3/5$ in town couples. If a couple is from out of town, the probability that the husband and wife will give you the correct directions ...
-1
votes
0answers
21 views

My naive bayes classifier doesn't show probabilities [duplicate]

I'm trying to predict the probability between 1-0 and have found that naive bayes is supposed to show this, however when I use it I only have ...
0
votes
1answer
13 views

bayesglm (arm) versus MCMCpack

Both bayesglm() (in the arm R package) and various functions in the MCMCpack package are aimed at doing Bayesian estimation of generalized linear models, but I'm not sure they're actually computing ...
4
votes
1answer
62 views

What is meant by this formulation of Bayes' Rule?

From the Wikipedia article on Bayesian inference, we get the following formulation of Bayes' Rule: $$p(\theta \mid \mathbf{X},\alpha) = \frac{p(\mathbf{X} \mid \theta) p(\theta \mid ...
0
votes
1answer
43 views

Gaussian is conjugate of Gaussian?

Someone told me that, Gaussian distribution is conjugate to distribution because a Gaussian times a Gaussian would still be Gaussian distribution ? Why is that ? Say the following situation: $X\sim ...
2
votes
2answers
82 views

Bounds on correlation to ensure covariance matrix is positive definite

UPDATED: I am constructing a correlation matrix for an MA(1) process, which would look something like... $$ C = \left( \begin{array}{cccccccccccccccccc} 1 & \rho & 0 & 0 & 0 & 0 ...
2
votes
1answer
34 views

Posterior predictive check following ABC inference for multiple parameters

I am relatively new to Bayesian statistics so please be gentle. I have just performed Approximate Bayesian Computation (ABC) for the inference of a multi-parameter model. Now I am looking to perform ...
0
votes
0answers
12 views

game scoring marginal probability estimation

I have a game scoring time series data, where X[i] shows the score of player 1 minus player 2 after the ith turn. The game is played in turns, meaning if player 1 plays at ith turn, player 2 plays at ...
0
votes
0answers
15 views

multiple ROC curves in one image (Bayes predictor) [on hold]

I have several Bayes models made in KNIME and I need to plot their ROC curves in one image. In KNIME there is ROC curve node, but it can't plot more than one ROC curves at one time (or I don't know ...
1
vote
1answer
28 views

Distinguishing diffusion from white noise

I have a time series that looks like this: This comes from an experiment, and I know the following: Originally, for $t < s$ the time series is $x_t = vt + e_i$, where $v$ for this particular ...
2
votes
1answer
27 views

Choosing Variance for Gaussian Prior

I'm relatively new to bayesian inference, and was trying to apply a bayesian model in a real-world scenario. Let me describe the model in brief: We have $N$ i.i.d. random variables $D =(X_1, X_2, ...
2
votes
0answers
25 views

Multivariate survival with recurrent events and spikes back to 100% alive

I am trying to solve for what seems to be a multivariate survival model, but am getting stuck as there are both recurrent events and also jumps back to 100% alive. Rephrasing the larger project in ...
0
votes
0answers
23 views

Greedy subtree selection in Nested Hierarchical Dirichlet Processes

I'm implementing the Nested Hierarchical Dirichlet Process as described in this paper by Paisly et. al, 2014: http://arxiv.org/abs/1210.6738 My question is about the variational objective in Equation ...
0
votes
0answers
20 views

Identifiability issues for linear mixed models with cross-classified data

I have a dataset that could be easily simulated like this: ...
0
votes
1answer
45 views

Need help calculating poisson posterior distribution given prior

I have been attempting to figure this out for hours, but gamma distribution is somehow beyond me. I have a question where we are given α=5 and ...
1
vote
1answer
45 views

Fitting a Gaussian to a histogram when the bin size is significant

I'd like to fit a Gaussian to some experimental data that is binned (the binning is a result of the physical limits of the device). Importantly, the bin size is significant enough that the gaussian ...
2
votes
0answers
22 views

Conjugate Prior for correlation matrix

Suppose x is normally distributed with unknown mean and covariance matrix. Is there a set of conjugate priors for the mean and correlation matrix. I know that for covariance matrices one can use ...
0
votes
0answers
17 views

Latent Class Analysis — 0.632+ Bootstrap vs. Bayesian LCA and Empirical Bootstrapping?

I am working on a project that involves the use of latent class analysis (LCA) and have been thinking about how best to perform variable selection (with relatively high-dimensional data [approximately ...
2
votes
1answer
50 views

Difference in 2 groups when group assignment is not certain

Suppose you have two groups and you want to see whether these two groups differ in regards to some variable. This sounds like a basic t-test or perhaps non-parametric Wilcoxon rank sum test. Suppose ...
1
vote
1answer
34 views

Help setting up a Bayes rule problem

I am relatively new to using Bayes rules for continuous variables and am having trouble setting up part of the formula and am looking for help. The example I am trying to work through is the ...
0
votes
1answer
32 views

Likely mean of a multinomial distribution with dirichlet prior

I am working to create a Bayesian non-parametric estimate of the mean of a distribution given a distribution of observations. Ultimately I'd like to get to a credibility interval of the likely mean of ...
2
votes
1answer
25 views

What does “CRP is a marginalized version of PYP” mean?

I've been reading this phrase and I don't know what it means "CRP is a marginalized version of PYP". What are the parameters/latent-variables we are marginalizing out to drive CRP from PYP?
0
votes
0answers
3 views

Gibbs sampling scheme on Ozone35 data set [migrated]

I'm attempting to run a Gibbs sampling scheme on the data set Ozone35 from the BayesVarSel package in R. Here is the info on the data set Ozone35: ...
0
votes
2answers
70 views

Predict interesting articles: increase accuracy

I'm trying to write a gui to display articles, and predict which articles I could like, based on the articles I previously liked. This post is the continuation of this one: ...
2
votes
1answer
39 views

Probability of being each demographic

Relatively simple problem, but can't see how to solve it. Rephrasing in terms of everyday events. Assume there is a fair in town for three days. Each day the total visitors are known, and so are ...
1
vote
1answer
44 views

Good venue to find online tutor in mathematical statistics?

I've been having trouble finding a qualified online tutor to work with me on NHST vs. Bayesian concepts and experimental design. I'm sure there must be people around & available with real chops in ...
3
votes
2answers
103 views

Can $p(Y|a,b)$ ever be equal to $p(Y|a) \cdot p(Y|b)$?

This strikes me as a simple question, but in re-visiting how the Naive Classifier works I started wondering if there is any probabilistic model that under certain independency assumptions obtains: ...
0
votes
1answer
22 views

Inverse Gamma Prior with Scale Parameter set to 1

\begin{align*} X_{ij} \mid \mu_i , \sigma^2 & \sim N(\mu_i, \sigma^2) \nonumber \\ \mu_i & \sim N(\mu_0, \tau^2) \nonumber\\ % S_i^2 \mid \sigma^2 & \iid \chi_{n-1}^2/(n-1) \nonumber \\ ...
1
vote
1answer
26 views

How can regression trees be fit in WinBUGS/OpenBUGS/JAGS?

There is an R package called BayesTree which can fit regression trees in Bayesian environment. However, this way only simple regression is possible. I would like to use regression trees as a part of a ...
0
votes
1answer
30 views

Backward message passing in variational Bayesian inference

I have come across in a research paper that, I do understand the logic. But the paper has't mentioned about the way of updating $\eta_{t}$. When I asked from the authors they said when we equate ...
2
votes
1answer
39 views

Bayesian inference

Assume two demographics $[F,M]$ and each person has a choice of attending only one of four different lectures $[A,B,C,D]$ all occurring at the same time so they can only attend one. The following ...
0
votes
0answers
20 views

Conjugate prior equivalent prior sample size with respect to the mean

In Cowles's book ([Applied Bayesian Statistics - With R and OpenBUGS Examples–(http://www.springer.com/statistics/statistical+theory+and+methods/book/978-1-4614-5695-7)), page 108, there is a ...
1
vote
1answer
37 views

Am I choosing correct likelihood?

I am using Bayes theorem to solve links upvoting problem for reddit/hacker new style website. Every link has a probability $P(Q)$, that the link is a high quality one. And every user has probability ...
0
votes
1answer
20 views

Posterior mode estimator unchanged under coordinate transformation?

I'm looking at a data set where the posterior mode has noticeably less "bias" than the posterior mean and posterior median, and somewhat less error. However, the posterior mode is not invariant under ...
0
votes
1answer
19 views

Does Accept - Reject Algorithm Monte Carlo help fit a distribution to the data?

As far as I understand the Accept - Rejection Algorithm is used to help us simulate hard to simulate densities or unknown densities by first simulating an easy density and then accepting or rejecting ...
2
votes
2answers
63 views

Re-estimating a probability distribution with additional priors

I have a 3D dataset with at least millions of data points (scatter events from atoms, approximately Gaussian). I am modeling this data with a Gaussian Mixture Model. The usual approach would be to ...
4
votes
0answers
65 views

Optimal Stopping for Bernoulli One-Armed Bandit with a Fixed, Known Payout

I'm very new to bandit problems (apologies if I've formatted my question incorrectly), but I have to solve the optimal stopping of what I think is a very simple case. Suppose I have two arms $k = {1, ...
0
votes
0answers
25 views

Marginal Distribution of Sample Variance with Inverse Gamma Prior on $\sigma^2$

Assume the following model with $S^2$ being the sample variance based on $n$ samples. \begin{align*} S^2 & \mid \sigma^2 \sim \sigma^2 \chi_{n-1}^2/(n-1)\\ \sigma^2 & \sim \textrm{inverse ...
0
votes
0answers
18 views

Gibbs within Metropolis

Consider a model with two parameters, $\alpha$ and $\beta$. We want to sample these two parameters conditioning on two data points, $d_1$ and $d_2$. Is it possible to use an algorithm like this: 1) ...
1
vote
0answers
21 views

Fitting multiple models to a noisy measurement

I have measured a quantity for a set of data contains couple of thousands objects. Since the measurement is very noisy, I need a set of data contains a lot of objects. Then I have a model based on the ...
3
votes
0answers
39 views

Methods of fitting a dynamic linear model

I'm taking a time series course and am learning about exchangeable time series form of dynamic linear models (DLMs). This is given by: \begin{align*} \mathbf{y}_t' &= ...
0
votes
1answer
21 views

Degree of belief in fuzzy modelling

I’ was reading a paper on fuzzy regression. In that paper, and many other papers on fuzzy regression, the authors use most of the time a $h$ to indicate a certain degree of belief. Unfortunately the ...
2
votes
2answers
55 views

Predictive with uniform likelihood

I'm trying to get a predictive density and currently getting something which I know can't be true (based on both logic and simulation based techniques. Here's the relevant information. $\theta$ is a ...
1
vote
1answer
32 views

Imputation of a binary variable by Bayesian logistic regression

In the book "Flexible Imputation of Missing Data" by Van Buuren, the following algorithm is presented I think I understand the algorithm as given, but I would like to know what is the "more ...
1
vote
1answer
68 views

Simple model selection example in PYMC

I am currently experimenting with PYMC and I am trying out a simple example so that I start learning how things work (I am also a Python beginner, but an experienced machine learner). I have set ...
2
votes
2answers
182 views

Problem interpreting the Beta distribution

On p38 of Lee and Wagenmakers (2012) "Bayesian Cognitive Modeling: A Practical Course" the following passage appears: "One of the nice properties of using the θ ~ Beta (α,β) prior distribution ...
0
votes
1answer
17 views

Expectation propagation for feature selection

I'm using Expectation propagation algorithm (infer.net library) for my feature selection problem. I generate input data and test my model. The thing is that when ...
3
votes
2answers
36 views

Can quadratic constraints be handled by Bayesian methods?

I want to solve a regression method whose parameters are under quadratic constraint a'*a=1. Is there any method in Bayesian statistics to handle this constraint? Thank you in advance.
-1
votes
1answer
35 views

compute Expectation Propagation messages for sum

Can anyone help me in understanding how Expectation Propagation updates are computed when we have a function on several variables? Like this example: ...