# Tagged Questions

Inference, in a statistical context, refers to drawing conclusions about a population from information about a sample from that population.

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### 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 ...
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### 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 ...
359 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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### 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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### 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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### 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 ...
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### 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 ...
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### Inference for the skeptical (but not math-averse) reader

I just watched a lecture on statistical inference ("comparing proportions and means"), part of an intro to stats online course. The material made as little sense to me as it always does (by now I ...
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### Why is the Fisher Information matrix positive semidefinite?

Let $\theta \in R^{n}$. The Fisher Information Matrix is defined as: $$I(\theta)_{i,j} = -E\left[\frac{\partial^{2} \log(f(X|\theta))}{\partial \theta_{i} \partial \theta_{j}}\bigg|\theta\right]$$ ...
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### Does “Inference” include estimation or only testing?

Does the term "statistical inference" include only hypothesis testing or does it also include point estimation, interval estimation etc. Authoritative references will be greatly appreciated.
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### 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 ...
552 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 ...
324 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 ...
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### What does “fiducial” mean (in the context of statistics)?

When I Google for "fisher" "fiducial" ...I sure get a lot of hits, but all the ones I've followed are utterly beyond my comprehension. All these hits do seem to ...
301 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?
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### 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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### 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 ...
942 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 ...
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### Implications of current debate on statistical significance

In the past few years, various scholars have raised a detrimental problem of scientific hypothesis testing, dubbed "researcher degree of freedom," meaning that scientists have numerous choices to make ...
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### 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 ...
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### What can be concluded from small sample size?

I had just conducted a test where the customer wants to see a 20% improvement in perforation length from a baseline perforator. The baseline perforator has not been tested in the customer's specific ...
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### (interacting) MCMC for multimodal posterior

I am trying to sample from a posterior having many modes particularly far from each others using MCMC. It appears that in most cases, only one of these modes contains the 95% hpd I am looking for. I ...
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### Inference on fixed effects in a mixed effects model

I have correlated data and am using a logistic regression mixed effects model to estimate the individual level (conditional) effect for a predictor of interest. I know that for standard marginal ...
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### 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 ...
183 views

### Maximum Likelihood estimator - confidence interval

How can I construct an asymptotic confidence interval for a real parameter, starting from the MLE for that parameter?
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### 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 ...
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### Resampling within a survey to account for missing data

Suppose I have survey responses that look like this: ...
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### Simple linear regression with a random predictor

We understand a SLR model as $$y_i = \alpha + \beta x_i + \varepsilon_i$$ with $\varepsilon_i$ i.i.d with equal variance. Suppose I have two instruments measuring a common entity, say, density of ...
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### Inference on random graph, with an application to mobile sensors

I've attended a course on Machine Learning and another one in Network Analysis, and I wonder if this two topics already intersect, in particular I'm interested in the following model: we have a ...
122 views

### Choosing non-informative priors

I am working on a model relying on an ugly parametrized function acting as a calibration function on a part of the model. Using a Bayesian setting, I need to get non-informative priors for the ...
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### 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 ...
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### 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 ...
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### How to measure student skill level based on a set of questions answered at different points in time and of different difficulties levels?

I am working on an e-learning system with a friend for our final year (Computer Science) project which is part of the under-graduate programs mandatory 'courses'. I have a question about making ...
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### 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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### 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 ...
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### 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 ...
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### Is it invalid to use a single sample to estimate more than one proportion?

Lets say that I have a jar of white, black and red marbles (1000 total) but I don't know the quantity of each colour. I now take a sample of 10 marbles from the jar which contains 3 x white, 4 x ...
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### 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 ...
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### 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 ...
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### What is the name/relevant details of this exponential-family related structure?

Suppose that $X$ comes from an exponential family $$p_\theta(x) = h(x)\exp(\theta x - A(\theta)),$$ and that, conditional on $X$, $Y$ also comes from an exponential family of the form  ...
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### 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 ...
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### 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 ...
573 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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### Why is using cross-sectional data to infer / predict longitudinal changes a Bad Thing?

I'm looking for a paper which I hope exists, but don't know if it does. It could be a set of case studies, and / or an argument from probability theory, about why using cross-sectional data to infer / ...