Inference, in a statistical context, refers to drawing conclusions about a population from information about a sample from that population.
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877 views
Why would someone use a Bayesian approach with a 'noninformative' improper prior instead of the classical approach?
If the interest is merely estimating the parameters of a model (pointwise and/or interval estimation) and the prior information is not reliable, weak, (I know this is a bit vague but I am trying to ...
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5answers
3k views
Understanding “variance” intuitively
What is the cleanest, easiest way to explain someone the concept of variance? What does it intuitively mean? If one is to explain this to their mom or child how would one go about it?
It's a concept ...
19
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3answers
984 views
What if your random sample is clearly not representative?
What if you take a random sample and you can see it is clearly not representative, as in a recent question. For example, what if the population distribution is supposed to be symmetric around 0 and ...
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2answers
317 views
Accommodating entrenched views of p-values
Sometimes in reports I include a disclaimer about the p-values and other inferential statistics I've provided. I say that since the sample wasn't random, then such statistics would not strictly ...
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3answers
609 views
What is the fiducial argument and why has it not been accepted?
One of the late contributions of R.A. Fisher was fiducial intervals and fiducial principled arguments. This approach however is nowhere near as popular as frequentist or Bayesian principled arguments. ...
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3answers
788 views
Comparison between MaxEnt, ML, Bayes and other kind of statistical inference methods
I'm in no way a statistician (I've had a course in mathematical statistics but nothing more than that), and recently, while studying information theory and statistical mechanics, I met this thing ...
10
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1answer
599 views
Do likelihood ratios and Bayesian model comparison provide superior & sufficient alternatives to null-hypothesis testing?
In response to a growing body of statisticians and researchers that criticize the utility of null-hypothesis testing (NHT) for science as a cumulative endeavour, the American Psychological Association ...
9
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3answers
292 views
Good summaries (reviews, books) on various applications of Markov chain Monte Carlo (MCMC)?
Are there any good summaries (reviews, books) on various applications of Markov chain Monte Carlo (MCMC)?
I've seen Markov Chain Monte Carlo in Practice, but this books seems a bit old.
Are there ...
9
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2answers
396 views
Optimal software package for bayesian analysis
I was wondering which software statistical package do you guys recommend for performing Bayesian Inference.
For example, I know that you can run openBUGS or winBUGS as standalones or you can also ...
9
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1answer
236 views
If a tennis match was a single large set, how many games would give the same accuracy?
Tennis has a peculiar three tier scoring system, and I wonder if this has any statistical benefit, from the point of view of a match as an experiment to determine the better player.
For those ...
8
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2answers
278 views
Why is the Fisher Information matrix positive semidefinite?
Let $\theta \in R^{n}$. The Fisher Information Matrix is defined as:
$$I(\theta)_{i,j} = -E\left[\frac{\partial^{2} \log(f(X|\theta))}{\partial \theta_{i} \partial \theta_{j}}\bigg|\theta\right]$$
...
8
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2answers
258 views
Behrens–Fisher problem
Is there a good published expository account, with mathematical details, of the various approaches that have been taken to the Behrens–Fisher problem?
8
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1answer
272 views
Is it acceptable to run two linear models on the same data set?
For a linear regression with multiple groups (natural groups defined a priori) is it acceptable to run two different models on the same data set to answer the following two questions?
Does each ...
7
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3answers
478 views
Mixture Models and Dirichlet Process Mixtures (beginner lectures or papers)
In the context of online clustering, I often find many papers talking about: "dirichlet process" and "finite/infinite mixture models".
Given that I've never used or read about dirichlet process or ...
7
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1answer
207 views
If the likelihood principle clashes with frequentist probability then do we discard one of them?
In a comment recently posted here one commenter pointed to a blog by Larry Wasserman who points out (without any sources) that frequentist inference clashes with the likelihood principle.
The ...
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2answers
157 views
Inference with Gaussian Random Variable
Let $X = N(0,\frac{1}{\alpha})$, $Y = 2X + 8 + N_{y}$, and $N_{y}$ be a noise $N_{y} = N(0,1)$. Then, $P(y|x) = \frac{1}{\sqrt{2\pi}}exp\{ -\frac{1}{2}(y - 2x - 8)^{2} \}$
and $P(x) = ...
6
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1answer
121 views
Understanding the Behrens–Fisher problem
This section of this article says:
Ronald Fisher in 1935 introduced fiducial inference in order to apply it to this problem. He referred to an earlier paper by W. V. Behrens from 1929. Behrens and ...
6
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1answer
387 views
Estimating probability of success, given a reference population
Suppose you have the following situation:
You observed over time 1000 bowling players, who each played a relatively small number of games (say 1 to 20). You noted the strike percentage for each of ...
6
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3answers
361 views
Bayesian inference on a sum of iid real-valued random variables
Let $X_1$, $X_2$, ..., $X_n$ be iid RV's with range $[0,1]$ but
unknown distribution. (I'm OK with assuming that the distribution
is continuous, etc., if necessary.)
Define $S_n = X_1 + \cdots + ...
6
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1answer
295 views
How much can the “pyramid of evidence” be applied to economics and political sciences?
When trying to assess a validity of a claim relying on statistics, I was taught (in the school of epidemiology) that the scale to use is “the pyramid of evidence“
However, when conducting a ...
5
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1answer
185 views
Expectation of an estimator?
When evaluating an estimator in a frequentist setting, using MSE and let say to compute the Bias of the estimator we compute the expectation of this estimator, are we supposing that the estimator has ...
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2answers
137 views
Resampling within a survey to account for missing data
Suppose I have survey responses that look like this:
...
4
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1answer
159 views
When will a less true model predict better than a truer model?
In "To Explain or to Predict?", Pr. Galit Shmueli said that sometimes a less true model can predict better than a truer model. Why is it so? When will it happen? How does it happen? Is explanation a ...
4
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1answer
177 views
Bayesian analysis of data
I have a big dataset in the form: $X_1, X_2, X_3, X_4, Y$. All the $X_i, i \in {1,...,4}$ come from different unknown distributions and $Y$ follows a bernoulli distribution, so it can take only values ...
4
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1answer
163 views
Means of groups A and B differ significantly. I want to classify values into A or B
My data look like this.
The variable on the $x$ axis is height in inches. The variable on the $y$ axis is whether someone hovers when urinating at a public toilet. Each of the 103 points is a ...
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4answers
314 views
Why does continuous Bayesian analysis seem to give this contradictory result?
Let's say you have a process that generates data according to r = sin(t) + epsilon, where epsilon ~ N(0,V) is Gaussian noise. The unconditional variance of r is 0.5 + V.
Let's say we're forecasting ...
4
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1answer
138 views
Does Loopy BP give the same solutions as a Gibbs sampler?
The literature in MCMC and LBP never refer to the fact that the two methods look (on expectation) exactly the same. To illustrate, first consider a simple Ising model, that is, a graphical model ...
4
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1answer
558 views
How to write a poker player using Bayes networks
This is my first question on stackexchange and also my first time implementing a Bayesian network so I will apologize ahead of time for any novice mistakes I make.
The goal of my project is to ...
4
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1answer
72 views
Inference from conditional observations
Let $(x_1, \ldots, x_n)$ be an i.i.d. random sampling from a conditional normal distribution ${\cal N}(\mu,\sigma^2)$ distribution given some event $A$ possibly parameter-dependent: for instance when ...
4
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1answer
81 views
Inferring multiple ratios and binomial proportions with missing data
I have a number of studies describing families tested for a genetic condition. For each study the following data are described:
$n_p$, number of probands (the proband is the first person in a family ...
4
votes
2answers
459 views
Standardized residuals vs. regular residuals
I've got an easy question concerning residual analysis. So when I compute a QQ-Plot with standardized residuals $\widehat{d}$ on the y-axis and I observe normal distributed standardized residuals, why ...
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6answers
338 views
Inference to the population when the survey response rate is only 30%
I have conducted a survey in which the questionnaires were sent out to 450 individuals, but only 30% of them answered the questionnaires.
Is it still valid to interpret the usual inference analysis ...
3
votes
4answers
223 views
What if your randomly formed groups are clearly not similar?
What if, before you begin the data collection for an experiment, you randomly divide your subject pool into two (or more) groups. Before implementing the experimental manipulation you notice the ...
3
votes
1answer
63 views
Neg Binomial and the Jeffreys' Prior
I'm trying to obtain the Jeffreys' prior for a negative binomial distribution. I can't see where I go wrong, so if someone could help point that out that would be appreciated.
Okay, so the situation ...
3
votes
2answers
456 views
How would you do Bayesian ANOVA and regression in R?
I have a fairly simple dataset consisting of one independent variable, one dependent variable, and a categorical variable.
I have plenty of experience running frequentist tests like ...
3
votes
2answers
100 views
How to go about selecting an algorithm for approximate Bayesian inference
I am wondering if there are any good rules of thumb for how to go about selecting an approximate inference algorithm for a problem/model (specifically when exact inference is intractable)? When you ...
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2answers
140 views
MRF MAP inference for non-submodular pairwise terms
I have a multilabel MRF MAP inference problem (a labeling problem). The graph has relatively few nodes, about a thousand or so. The pairwise term is (very) not submodular (it does not satisfy the ...
3
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1answer
64 views
Fiducial Inference in Machine Learning
I was looking at the Fiducial Inference page on wikipedia, which is an alternative to the traditional Frequentist and Bayesian standpoints. Although it was out of favour in mainstream statistics for ...
3
votes
1answer
47 views
How often is data corrupted given how often a 3-way vote passes incorrect data?
Assume we have a noisy system where data is available via sample() and in order to filter out the noise someone has implemented the following voting algorithm:
...
3
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1answer
209 views
Property of entropy
When characterizing an information measure one desires to have the following 'Grouping' property (cf., Cover&Thomas, Ch.2 exercise 46)
$$H(p_1, p_2,\dots, p_n)=H(p_1+p_2, p_3,\dots, ...
3
votes
1answer
91 views
Estimating an unknown restricted Markov Chain from partial measurements
There is an Markov chain $M$ defined on states $1, ..., N$ with the special property that it only has transitions $p_i$ from $i$ to $i + 1$ , $q_{i + 1}$ from $i + 1$ to $i$, and $r_i = 1 - p_i - q_i$ ...
3
votes
1answer
128 views
Designing an inference engine for unknown items with known probabilities
I have done some AI projects involving inference, neural networks, etc., but I'm not sure what the right algorithm would be for this problem.
Say there is a set of pills, where each type is visually ...
2
votes
1answer
266 views
Are there problems with inference using linear regression on observational data with highly skewed distributions of predictor values?
I am using a linear regression model to perform inference on some observational data. The samples are from an observational study and highly skewed along some of the dummy variables in the regression.
...
2
votes
2answers
238 views
Bayesian inference of parameters: residuals are independent but not normally distributed
I would like to compute belief intervals (confidence intervals; CI) for the parameters of an environmental dynamic model within the Bayes' theorem. The measurement model of the data is
$$
...
2
votes
1answer
247 views
Intractable posterior distributions
In Bayesian statistics, it is often mentioned that the posterior distribution is intractable and thus approximate inference must be applied. What are the factors that cause this intractability?
2
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1answer
31 views
Comparing results for computer and pen and paper writing
I am conducting a study to examine the differences between writing paragraphs in English among junior high school students in Japan.
We collected writing samples from four classes, approximately 38 ...
2
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2answers
70 views
Bayesian Inference Notation Confusion
In Bayesian Inference the following notation is quite common:
$P(H|D) = \frac{P(D|H)P(H)}{P(D)}$
where $D$ is data and $H$ is hypothesis. Moreover $P(D)$ is represented as total probability.
$P(D) ...
2
votes
1answer
78 views
Inference from linear regression slope and Pearson
Sorry if this has been asked before but I've already done quite a bit of work here and I feel like I'm quite close to an answer.
I am interested in testing whether the PHP function array_key_exists ...
2
votes
1answer
84 views
Can I insert an observation (evidence) to a Winbugs model?
Greetings,
Is it possible to use evidence in a Winbug model? For example, a random variable in a model has been observed, and I'd like to update the other variables in the model, pretty much the same ...
2
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1answer
84 views
Prior for Bayesian Inference on Failure Rate in Poisson Distribution
I'm trying to derive the posterior distribution for the failure rate (lambda) of a process with poisson distribution.
I have tried the use of an improper uniform distribution on lambda by letting the ...
