Bayesian inference is a method of statistical inference that relies on turning the model parameters into random variables and applying Bayes' theorem to deduce probability statements about the parameters or hypotheses, conditional on the observed dataset.

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Unrealistically high significance when marginalizing over large number of parameters

The setup I've tried to reduce the problem to a self-contained subset for this question, but it still ended up being pretty long. Sorry about that! I have a set of observations of a set of objects ...
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1answer
18 views

Fitting a mixture model to spatially correlated data

When the data are spatially correlated, is the usual GMM likelihood function overweighted? The data. Scattering experiment, sensor is like a CCD. Can't see individual events, only density estimate ...
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1answer
11 views

What is the difference between R hat and psrf?

In convergence diagnosis in WinBUGS/JAGS/Stan, there are different statistics reported for each variable. In WinBUGS/Stan, Rhat ($\hat{R}$) is reported. In JAGS with the ...
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1answer
27 views

General questions on rejection sampling

I am new to Bayesian methods. I was going through a chapter on sampling. I have a few questions related to it. Please help me get these clarified. As far as I understand, rejection sampling will not ...
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30 views

How to estimate the correlated individual components from a sum, for a random process?

Assume that there are $N$ realisations of five individual, random variables$X_1$, $X_2$, $X_3$, $X_4$ and $X_5$, which in general could be correlated. We define another random variable ...
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1answer
50 views

Bayesian Estimation: Bernoulli and Quadratic Loss Function

I am trying to understand a solution to this problem (I am a very beginner in Bayesian statistics) and I am terribly confused so I would appreciate it if someone could explain to me how exactly this ...
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21 views

Conjugate Distribution for Tracy-Widom Distribution?

Does anybody know if there is a distribution conjugate to the Tracy-Widom (in the Bayesian context)?
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1answer
14 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 ...
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1answer
122 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 ...
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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 ...
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1answer
14 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
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1answer
63 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 ...
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1answer
66 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 ...
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2answers
88 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 ...
4
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1answer
143 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 ...
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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 ...
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15 views

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

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 ...
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1answer
29 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
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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, ...
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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 ...
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25 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 ...
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31 views

Identifiability issues for linear mixed models with cross-classified data

I have a dataset that could be easily simulated like this: ...
0
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1answer
46 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 ...
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1answer
49 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 ...
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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 ...
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0answers
18 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
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1answer
51 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 ...
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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 ...
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1answer
33 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
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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?
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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: ...
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2answers
71 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
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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 ...
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1answer
45 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 ...
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2answers
105 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: ...
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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 \\ ...
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1answer
28 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
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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
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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 ...
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22 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 ...
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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
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1answer
21 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 ...
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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
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2answers
65 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
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0answers
66 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, ...
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27 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
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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) ...
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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
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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' &= ...
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1answer
22 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 ...