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.

learn more… | top users | synonyms

0
votes
2answers
35 views

recommended books for preliminary concepts of Bayesian Statistics [duplicate]

I am interested in learning Bayesian Statistics related for my CS career. I have a very little background on frequentist statistics, which I know differs from the bayesian approach. The reason of my ...
2
votes
0answers
19 views

Bayesian Linear Model Posterior as Sum of Squares?

As part of a homework, I am asked to do the math from the Normal-Inverse Gamma linear regression model. Starting from priors $N(\beta_0, \sigma^2 A)$ and $IG(\alpha_0, \delta_0)$ and with the help ...
0
votes
0answers
9 views

When to pick Scale or Rate for Gamma/ Inverse Gamma parameters? Picking up the correct conjugate prior

I am very confused about the following problem. I think my question is both theoretical and applied. When I model a Gamma distribution, when do I use this model, so I guess Inverse Gamma: ...
0
votes
2answers
42 views

(Failure) probability calculation

I am working on mortality in 12 hospitals performing cardiac surgery in babies. The dataset is available here: Surg dataset. The dataset is structured in this way: ...
2
votes
0answers
40 views

Is a Bayesian estimate with a “flat prior” the same as a maximum likelihood estimate?

In phylogenetics, phylogenetic trees are often constructed using MLE or Bayesian analysis. Oftentimes, a flat prior is used in the Bayesian estimate. As I understand it, a Bayesian estimate is a ...
0
votes
0answers
20 views

Inferring the bias of two types of coin

I would like to find the bias of a type of coin, when there is uncertainty about which kind of coin I am testing. The scenario is as follows, there are 2 mints in my neighbourhood that produce ...
0
votes
0answers
19 views

guidance for picking Likelihood in Bayesian analysis

I'm doing a Bayesian analysis for a time series response and wonder whether it is possible to get the Likelihood function without making distributional assumptions. I suppose my response is ...
0
votes
1answer
25 views

High dimensional sampling with low measurement noise

Assume that you have a model $$ Y = G(\Theta) + \varepsilon,$$ where $\Theta$ is a parameter vector with $\sim 8$ dimensions, $G$ is a highly nonlinear function of the parameters, $Y$ is observed ...
2
votes
1answer
68 views

How to score predictions in test set taking into account the full predictive posterior distribution?

I have three predictive models (regressions) which parameters are estimated by Markov Chain Monte Carlo. Predictions are made over a test set of size $N$. Since I compare the models under different ...
3
votes
0answers
67 views

How to do inference over two steps in a graphical model simultaneously?

I have observed data $D$ about a physical object described by $M$. I would like to determine the posterior distribution of $M$ given $D$, or $p(M|D)$. Now I can't infer this directly because unknown ...
0
votes
0answers
22 views

How to fit a Gaussian Mixture Model to data with correlated errors?

I'm restating this question in the hope of getting more interest. The usual function for scoring a Gaussian mixture model assumes independent measurements. But what if we have correlated measurements? ...
4
votes
1answer
47 views

completing the square for Gaussian multivariate estimation

I have been trying to derive the posterior distribution in the case of weighted Bayesian regression in the case of multivariate normal distribution for a few days and have been stuck. I am not sure if ...
1
vote
1answer
42 views

Computing the conditional distribution for the mean of a Gaussian

I have the following distributional assumptions on some on my RV and model parameters: $$ y_i \sim N(\beta x_i, w_i^{-1}\Sigma_y) $$ There is a normal prior on the parameters $\beta$ as well: $$ ...
0
votes
0answers
16 views

Can I have a Bayesian approach to analyse my data set? [closed]

I have a data set with tax incomes from different types of taxes(eg: Income tax, VAT, Goods & services).I want to forecast the each tax revenue for next 10 years using an statistical approach.Can ...
0
votes
0answers
6 views

computing expectations in variational updates

I have a complete log-likelihood expression as follows: $$ L = \sum_{i=1}^N \log P(y_i|x_i, w_i, \beta) + \log P(\beta) + \sum_{i=1}^N \log P(w_i) $$ Now, I need to compute the expectation of these ...
0
votes
1answer
30 views

PyMC consistently under estimating results found in paper. Possibly not sampling enough?

I have been trying to build confidence in (my ability to correctly use) PyMC by working examples. Namely, I have been working on Chickering and Pearl 1997, and more specifically on their 'artificial' ...
1
vote
2answers
27 views

Suspiciously high Multivariate PSRF from gelman.diag()

I am using "Multivariate PSRF" statistics from gelman.diag() function to analyze my MCMC chains. Now I analyzed convergence 471 variables (parameters for each ...
1
vote
1answer
36 views

How to calculate a sample size for validating correct/incorrectness of records in a data table?

I have read through existing answers on CrossValidated (plus elsewhere online) and can't find what I'm looking for, but do please point me to existing sources if I've missed them. Let's say I have a ...
6
votes
1answer
76 views

Parameters vs latent variables

I have asked about this before and have really been struggling with identifying what makes a model parameter and what makes it a latent variable. So looking at various threads on this topic on this ...
0
votes
0answers
19 views

Combining several posteriors

Is there an accepted method of combining the posterior distributions from a model fit to several participants to obtain a posterior for the entire group of participants? The reason I am asking is ...
2
votes
2answers
45 views

How might Google go about estimating and updating traffic speeds?

This is, I guess, a specific example of a wider class of problem, one to which there must be a well-established solution, but which I, as a relative layman when it comes to statistics have thus far ...
1
vote
1answer
27 views

How to rank rankings? Two factors - freq and rank but freq has to has much more weight

My respondents has to evaluate number of items (say, 20). Formerly they had to just check three that they liked (like/dislike) and I simply counted the most checked. I 'improved' survey by replacing ...
5
votes
2answers
282 views

Example for a prior, that unlike Jeffreys, leads to a posterior that is not invariant

I am reposting an "answer" to a question that I had given some two weeks ago here: Why is the Jeffreys prior useful? It really was a question (and I did not have the right to post comments at the ...
-1
votes
0answers
41 views

Bayes Test and decision regions

I'm given the following hypotheses: $$f(x|H_0) = e^{-x}u(x)$$ $$f(x|H_1) = 0.5\{u(x)-u(x-2)\}$$ and asked set up a Bayes Test for equally likely hypotheses and determine the decision regions. My ...
2
votes
1answer
51 views

How is ABC more computationally efficient than exact Bayesian Computation for parameter estimation in dynamical systems (ODE) models?

Approximate Bayesian Computation has been suggested as an approach to parameter estimation for computationally intensive simulations, most commonly in population genetics, but also in dynamical ...
0
votes
1answer
20 views

One-Step ahead predictive likelihood for time series forecasting

I am still new to Bayesian forecasting, so I am hoping to get some clarification on a simple concept (by the sounds of it). Suppose that we are interested in forecasting some time series one-step ...
0
votes
0answers
31 views

MCMC: The posteriors are too narrow

I have this very simple MCMC there I have ...
1
vote
0answers
32 views

Probability Interval for F(x) with Parameter Estimates from Bayesian Analyses

Problem: I estimated the shape $\alpha$ and scale $\lambda$ parameter of the Weibull distribution using Bayesian methods. That gave me a marginal posterior distributions for both parameters. ...
2
votes
2answers
88 views

Can my Bayesian prior reflect what the data should say rather than what it could say?

Can my Bayesian prior reflect what the data should say rather than what it could say? For example, assume I collect data where $Y_i$ is whether or not student $i$ passed the test and $X_i$ is whether ...
0
votes
0answers
34 views

Is is possible to determine conditional conjugacy in this case?

I'm working on a problem where I have to extract sufficient statistics for parameter estimation in a state-space model. Usually these come from the quantities used for conjugate updates. I'm OK with a ...
1
vote
1answer
37 views

Show posterior is proper for this poisson linear model

This question is 3.12 in Andrew Gelman's Bayesian Data Analysis 3rd edition. Let $y_i|\alpha,\beta \overset{iid}{\sim} \text{Poisson}$ with mean $\alpha+\beta t_i$. Find a prior distribution that ...
0
votes
0answers
33 views

implementating the bayesian linear prediction with NIG prior

In Bayesian linear regression when the covariance of weights is unknown; one can set Normal-Inverse-Gamma prior. Based on "Machine Learning: a Probabilistic Perspective", Page 235, \begin{equation} ...
0
votes
0answers
15 views

Factorization of probability distribution and its Bayesian Network

My question is if we have a distribution $P$ that can be factorized into cond. distributions, can we model it with Bayesian Networks? I mean, $P(X_1,X_2,...,X_n) = \prod_{i=1}^n P(X_i|Cond(X_i))$ ...
3
votes
1answer
49 views

Bayesian regression with independent variable drawn from distribution

I'm trying to set up a bayesian regression of the form $y_i \sim f(\beta_0 + \beta_1 x_i)$ but rather than $x_i$ fixed, they themselves are drawn from a distribution of (known) mean $x_i \sim ...
14
votes
4answers
1k views

What is a good book about the philosophy behind Bayesian thinking?

What is a good book about Bayesian philosophy, contrasting subjectivists against objectivists, explaining the view of probability as state of knowledge in Bayesian statistics, etc.? Maybe Savage's ...
2
votes
1answer
29 views

Marginalizing over a Chinese Restaurant Process prior

I am reading a paper by Kemp et al. and there is a part about marginalising over a Chinese Restaurant Process and I am quite clueless about how could one marginalise over such a prior! The details of ...
2
votes
1answer
67 views

Kalman filter with control inputs in python?

i am trying to fit a simple kalman filter with input controls (in this case step input) in python. i am using filterpy (http://filterpy.readthedocs.org/). my code is: ...
2
votes
0answers
32 views

MCMC convergence: why Heidelberg's test says normal samples are non-stationary?

I am learning about and playing with Heidelberg's convergence test to automatically stop a MCMC sampling. I would have said that if I sample, for instance, from a normal distribution, the test ...
0
votes
0answers
13 views

How to calculate the posterior probabilty of Gaussian Mixture Component

If the mean vector and the Covariance matrix of a Gaussian Mixture model are known, how could I calculate the posterior probability of each of the Gaussian Component in the mixture.
3
votes
1answer
35 views

Why is it called “mode” in MAP estimation?

When estimating parameters with MAP, why is it written that we are estimating the "mode"? I thought it would be the mean of the posterior distribution?
0
votes
1answer
33 views

Slope estimate dependent on covariance?

I am trying to perform a linear regression with equal errors on x and y (ex =1 and ey=1) in a Bayesian framework (using WinBugs). Using Winbugs (solid line in the Figure), I managed to reproduce the ...
0
votes
0answers
9 views

What models allow the study of the relation between a set of response variables and a set of covariates?

A first technique that comes to mind is Canonical Correlation Analysis. Bayesian Networks and other graphical models, I guess, can also be used to analyse such things. Any else that I should be aware ...
1
vote
1answer
13 views

Prior for gamma distribution in “mean form”

I need to specify priors for the parameters of a gamma distribution. Normally the gamma distribution is parametrized in either the "rate-form'': ...
2
votes
0answers
18 views

Do mildly informative prior distributions tend to mitigate false positives (i.e. Type I error rates)?

I am curious if others have sources that speak to the matter that providing informative and/or mildly informative prior distributions on a parameter tend to mitigate false alarm rates? I know from the ...
2
votes
0answers
19 views

Incorporating population priors into MLE fits with few/limited samples

I am fitting Beta distributions to data resulting from each of many experiments using maximum likelihood. My goal is for each experiment, given iid data $y_{1:k}$, fit a Beta distribution, and then ...
0
votes
0answers
21 views

Bayesian fixed effects model and invariant variables

Within a fixed effects approach, the effects of invariant variables cannot be estimated. Their effects are captured by the fixed effects. However, when I estimate following Bayesian fixed effects ...
4
votes
1answer
74 views

Gibbs Sampler transition kernel

Let $\pi$ be the target distribution on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R^d}))$ which is absolutely continuously wrt to the $d$-dimensional Lebesgue measure, i.e : $\pi$ admits a density ...
2
votes
0answers
19 views

prior for integer-valued random variable taking values 1 or greater

In my model I have an integer-valued random variable which should only take values one or greater. I would like to specify an appropriate prior for this which has most of the mass say around 1 to 5 ...
-1
votes
0answers
45 views

How I can analyze a data survey obtained with non probabilistic sampling?

I got data from a survey. The survey was designed with quotas of the population in that neighborhood (near the 10% of the total population of that place). But, the people was surveyed in the ...
5
votes
1answer
164 views

Gibbs Sampler contradiction proof

I want to prove that the systematic scan Gibbs sampler yields an aperiodic chain $X$ on a general state space. Let $\pi$ be the stationary distribution for the resulting chain. Suppose to get a ...