Inference, in a statistical context, refers to drawing conclusions from data containing an element of randomness introduced by e.g. measurement error, sampling variation, or assignment of experimental treatments. A common inferential paradigm is drawing conclusions about population parameters from ...

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2answers
63 views

Why we shouldn't be obsessed with unbiasedness

In my Bayesian statistics class, my professor makes the remark that we should not be obsessed with unbiased estimator. First: I understand this statement in the sense of trading biasedness for ...
2
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0answers
22 views

Importance of multivariate normality assumption for BIC-like sparse model selection inference with PCA

I am reading a paper for robust, sparse PCA in which they propose a BIC-like criterion for selecting the appropriate value of the sparsity parameter $\lambda$. They define this as: ...
4
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1answer
35 views

Testing equality of coefficients from two different regressions

This seems to be a basic issue, but I just realized that I actually don't know how to test equality of coefficients from two different regressions. Can anyone shed some light on this? More formally, ...
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0answers
19 views

Consistency of an order statistic in exponential distribution

I have two questions. 1) If $X_1,X_2,X_3,...,X_n$ constitute a random sample of size $n$ from an exponential distribution, show that $\bar X$ is a consistent estimator of the parameter $\lambda$. ...
2
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0answers
21 views

How do I check for variation of a distribution over spatial scales?

I have about 30000 particles distributed (not randomly) in space; I have their vector positions and velocities. I'm trying to characterize if and how the (underlying) velocity (magnitude) distribution ...
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1answer
18 views

Inferring testlet structure in item response theory

Is it possible to infer the testlet structure in a set of items using item response theory? Specifically, I've created a lot of variations on the story recall task, each variation being scored on 25 ...
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0answers
15 views

Standard Deviation Grows Quadratically with Input Variable

I take an input x, based on which I do an experiment that gives me several data points. I compute the standard deviation of these data points. Then, I change ...
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0answers
27 views

How to model to improve the room usage efficiency based on motion sensor history

To reduce the confusion, I changed my application from traffic to meeting room, so this application is about modeling a meeting room efficiency , the data collection is built by placing a kind of ...
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0answers
22 views

Any fancy application of convergence (in probability, law, CLT, etc)?

As part of the inference course in an applied stats masters degree, we've to prepare a talk about convergence (see, for example, Lehmann 1999 Chapter 2). We'll be explaining to other students some ...
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1answer
54 views

Does R have post hoc tests robust to unequal sample sizes/population variances?

While reading Discovering Statistics Using R pp. 431-432, Dr. Field says that "There are a variety of tests designed to deal with these situations [multiple comparison procedures with unequal ...
0
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1answer
24 views

How to obtain the elasticity from a log-level regression

I have forgotten my undergrad econometrics, and was hoping that someone could help to refresh my memory. If I have a regression $\ln y=a+bX+e$, and want to evaluate the elasticity of $y$ with ...
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0answers
30 views

Find the best critical region for testing H0: $\sigma^2=2$ against H1: $\sigma^2=4$ and H1: $\sigma^2=1$

I've attempted to take the ratio of the distribution for the null hypothesis to the distribution of the alternative hypothesis, but then I'm not sure where to go.
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1answer
52 views

When does drawing additional samples not cause much benefit in estimating the population probability distribution?

Suppose I have a random variable X that either evaluates to A, B, or C when I realize it (each with its own fixed probability). Now let's say I have drawn 100 samples and the frequency distribution is ...
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0answers
9 views

Gaussian Copula Approximation of an intractable distribution

I am currently encountering this problem: I have an intractable distribution and I want to minimize the KL divergence of this distribution and a Gaussian Copula(or 0 mean gaussian distribution). So ...
1
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2answers
36 views

Paired t-test of medians

I need to run an inferential test on some large data where the individual data points have a heavily skewed distribution. I'm considering doing a paired t-test across a number of days comparing the ...
3
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2answers
57 views

Where is traditional inference really relevant?

I have been occupied with a fairly simple question regarding ordinary inference procedures where my own, and many others, practice feels slightly uncomfortable. We know that the purpose of ordinary ...
1
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0answers
30 views

Efficient estimators

let $x_{1},..,x_{n}$ be iid with cauchy distribution. Let $y=median(x_{1},..,x_{n})$ , $z=MLE$. I get that $y$ is not an asymptotically efficient estimator to the location of a cauchy distribution ...
2
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0answers
21 views

Ways the likelihood ratio test may fail

I have a question related to: Why is a likelihood-ratio test distributed chi-squared? On point 2 of @StasK's answer, he states: The theorem assumes that all the relevant derivatives are ...
1
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1answer
87 views

Comparing estimators of location of the Cauchy distribution

I'm comparing the following 4 estimators of location of the Cauchy distribution: Let $x_{1},..x_{n}$ be observations and $l$ be the log likelihood function. $x=median(x_{1},..x_{n})$, ...
5
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2answers
159 views

Bayesian inferencing: how iterative parameter updates work?

I have been struggling with this for a while. A typical optimisation problem can be viewed as optimising some cost function which is a combination of a data term and a penalty term which encourages ...
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0answers
20 views

Exact inference in a Factorial HMM with 2 hidden state chains

I am trying to understand the process of exact inference in Factorial HMM models. While it is explained here (Appendix B, page 20). I think my goal is slightly different and I am struggling to fill in ...
3
votes
1answer
86 views

How to compute marginals in Sum-Product Networks?

This should be fairly easy, but for some reason i'm having hard time getting it to work and I've spent a long time trying to figure it out myself. In the last paragraph of page 4 of the original ...
1
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1answer
51 views

What are the important conditions in ANOVA fixed effects?

I am working with an ANOVA model. I want to run a fixed effects ANOVA in which I have a ratio dependent variable and three independent variables with two and three levels. Obviously, before analyzing ...
3
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1answer
131 views

Statistical analysis on several data sources - possible?

I have a formulation of a statistical problem in mind and haven't been able to find any literature/references about it. As professors that I asked also couldn't help, I thought I'd ask here. Consider ...
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1answer
32 views

Transformation of skewed data shows strong linear relationship

The dataset comprises bandwidth usage for each customer. There is also a hybrid metric based on the distance covered by each traffic flow and aggregated to obtain 'Bit-Miles' for each customer (sum of ...
2
votes
1answer
60 views

Compare two (or more?) groups of regression coefficients

Short version: I need to compare two small (~10) groups of numbers, usual setup for a non-paired t-test, or Mann-Whitney. But -- the numbers come each with its own SE, and since the groups are small, ...
4
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1answer
73 views

Do concepts in probability help us understand when an analogical inference is acceptable?

I'm a philosophy undergraduate. I've recently read about analogical inferences. When making inferences by analogy, we observe that many of the properties of the analogues are the same, then infer that ...
3
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1answer
166 views

How to interpret Cochran-Mantel-Haenszel test?

I'm testing the independence of two variables, A and B, stratified by C. A and B are binary variables and C is categorical (5 values). Running Fisher's exact test for A and B (all strata combined), I ...
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0answers
41 views

What sample size do I need?

I have a population of 709 and the ability to draw a truly random stratified sample. I understand how to do the stratified part once I determine the sample size. One calculation indicated that I need ...
0
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1answer
67 views

Understanding Latent Dirichlet Allocation Inference

I'm reading the wikipedia page about how Latent Dirichlet Allocation assigns a topic distribution to a document after the model's been learnt (see this link). I'm very confused by this part of it: ...
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0answers
9 views

FactorGraph approximations: Binary variables to unary

I am reading the Expectation Propagation chapter in Chris Bishop's book and there is a bit on approximating factor graphs. So, the original factor graph and the approximating factor graph looks as ...
2
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0answers
31 views

Guessing test question answers from scores

My teacher likes to give online quizzes that are about 20-30 questions long. Every student has the same questions in the same order. We are not told after taking the quiz which questions we got wrong, ...
6
votes
1answer
99 views

How to measure uncertainty of a parameter when false positives exist?

The main goal of my research is to measure the percentage of brown dwarf stars in the Pleiades star forming cluster that are actually double stars (i.e. the brown dwarf star has a companion brown ...
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0answers
13 views

Maximum Margin of Error

Here's a stats question I'm having trouble with: Suppose the researchers plan to do a follow-up study in the future to once again estimate π = the true proportion of the population that gets help for ...
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5answers
200 views

Rule of thumb for number of bootstrap samples

I wonder if someone knows any general rules of thumb regarding the number of bootstrap samples one should use, based on characteristics of the data (number of observations, etc.) and/or the variables ...
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0answers
20 views

How different is training a factor graph with discriminative features?

Many of the people define graphical models with factors, each with 'conditional probability tables' (CPT) and perform inference on them. But more realistic case is when you can't define full ...
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0answers
30 views

Bonferroni correction: control vs. groups?

I'm trying to understand how to set up a Bonferroni correction on several different groups and compare it to the control group. The groups and observations are as follows (with Group 0 being the ...
6
votes
1answer
258 views

Conditioning on independent random variables

I am in a situation where I have to compute: $$E(u(x_1)|\bar{X},S^2)$$ where $X_1$ is a normally distributed random variable and $u(.)$ some function. I know that by the student's theorem the sample ...
0
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0answers
24 views

Expectation Propagation when the likelihood is already Gaussian

What happens with EP when the likelihood terms and the priors are already Gaussian. So, if we imagine that the posterior is given by: $$ P(\theta|y) = ...
1
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1answer
110 views

Expectation Propagation and multivariate priors

I have been struggling with this for weeks now. All EP examples that I have found on the net seem to deal with univariate priors and I am really at a loss as to how to make it work with a multivariate ...
5
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0answers
61 views

What is the difference between Inference and Machine Learning? [duplicate]

I have seen some classes in my University labeled as an "Inference class" and others as "Machine learning" classes, but I was not sure if appreciated the core difference between these two labelings? ...
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0answers
44 views

Does confirmatory = inferential, and exploratory = descriptive analysis / statistics?

Reading this webpage, I wonder: Are confirmatory analysis / statistics and inferential analysis / statistics the same concept? Are exploratory analysis / statistics and descriptive analysis / ...
6
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2answers
258 views

Is confirmatory vs exploratory statistics “induction vs deduction”?

This webpage says: Inferential Statistics - Deductive Approach Descriptive Statistics - Inductive Approach But I doubt it. If I understand correctly, Inferential Statistics is "given ...
1
vote
1answer
60 views

Regression test coefficient on variable is greater than coefficient on interaction term

With a model such as: $y \approx B_0 + B_1\cdot \log(x) + B_i\cdot \log(x):\text{group}_i +B_j\cdot group_i$, where group can take on several values ($i = 2$ to $15$, let's say): In an OLS ...
0
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0answers
28 views

If Maria performs more observations per unit of time than Maximilien, how can he estimates the Maria's results from his own?

General problem Having a sequence of values $v_0, v_\Delta, v_{2\Delta}, \ldots, v_{N\Delta}$, which are measured every $\Delta$ units of time, usually we are interested in the prediction of the ...
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0answers
21 views

Regression: Mean Response Confidence Interval vs Confidence Intervals of Each Predictor

I have a regression of costs on volume and some interactions (costs ~ volume + volume:year + year) Often times when I do a regression, I expect a negatively sloped relationship and the model ...
6
votes
2answers
220 views

Are sampling distributions legitimate for inference?

Some Bayesians attack frequentist inference stating that "there is no unique sampling distribution" because it depends on the intentions of the researcher (Kruschke, Aguinis, & Joo, 2012, p. 733). ...
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2answers
132 views

Which Distribution Does the Data Point Belong to?

I have two distributions which are derived from 2 separate sets of data. These distributions are not normal, and it is not clear at this point if they belong to any family of known pdfs (they are not ...
0
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1answer
25 views

Global search operators for approximate MAP inference?

In complicated Bayesian models, like for instance a hierarchical nonparameteric one, often times it's intractable to do Gibbs or other MCMC sampling methods to convergence. Rather, people tend to do ...
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1answer
30 views

Posterior distribution for true population variance

I have a process which may be assumed Gaussian - for now I'm assuming it to be zero-mean. The variance is unknown. I will estimate variance in the usual unbiased way to give the sample variance and ...