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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Fundamental question about applying Anova

I have a fundamental question about applying ANOVA. Suppose we are testing 4 drugs which reduce blood pressure. Our experiment contains 4 drugs + 1 Placebo. We give these to 3 types of patients ...
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25 views

How do I calculate the Cramér–Rao bound of a function of a parameter?

I have, say, $Y_i \stackrel{iid}{\sim} \mathcal{B}(1, p)$ and I want to calculate the lower bound of variance of an estimator of $\theta = p(1 - p)$ (which happens to be $Var[Y_i]$). If $\theta = p$, ...
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26 views

Minimal sufficiency with indicator functions

The following theorem can be used to demonstrate that a statistic is minimal sufficient: Let $f(X|\theta)$ be the pmf or pdf of a sample X. Suppose $\exists$ a function $T(X)$ such that, for ...
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2answers
36 views

Parametric vs Non parametric test difference

I'm reading PDQ Statistics[1], I have a small base of statistics and I can't figure out this statement from the book. They assure in the book that It seems that most people who have taken a stats ...
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1answer
34 views

How to combine two measurements of the same quantity with different confidences in order to obtain a single value and confidence

Back in the lab at university, we were taught to measure the quantity of interest some number of times (call this N), and then calculate the standard error. The underlying assumption here is that you ...
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24 views

Confidence intervals and p-values of multiple factor analysis lead to different conclusions?

I have the following model: man94_141 <- glmer(richness ~ year*block + (1|tr) , family=poisson , data=datasan94_14) where richness is the number of species ...
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15 views

Composition of Normals

I.e., the data was generated from 5 normal distributions: ...
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1answer
24 views

Is this the correct likelihood equation?

Consider a 2x2 contingency table with X having two categories {men,women} and Y having categories {yes,no}. For each category of X the observations was fixed (so the rows had fixed totals).The ...
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1answer
32 views

On One-to-One Functions of Complete Statistics

Why is a one-to-one function of complete statistic also complete? How might you go about proving this?
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25 views

FInd the sufficient statistic

I am familiar with sufficient statistics, doing questions out of textbooks with not much problems, but ran into this question and its a very different setup, and not sure how to start going about ...
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2answers
40 views

Identifying a confounder

I'm trying to check whether a variable is a confounder or not. Specifically, for a randomized trial where I want to investigate the effects of a reduction in class size on student performance, would ...
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8 views

Assessing variable importance in generalized additive models (GAM)

In a linear model, it's easy to assess the importance of each explanatory variable. If the assumptions of the model are met, given two explanatory variables $x_1$ and $x_2$, both with a regression ...
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31 views

Is there any real statistics behind “the Pythagorean theorem of baseball”?

I'm reading a book about sabermetrics, specifically Mathletics by Wayne Winston, and in the first chapter he introduces a quantity that can be used to predict the win rate of teams: ...
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30 views

Analytical properties of sample quantiles in statistical packages

When studying and proving properties of sample quantiles, such as its consistency or its asymptotic normality, every text I have seen uses the standard definition of this estimators. This is, given a ...
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1answer
45 views

Post Model Selection Inference problems - which remedies exist?

Recently, Hannes Leeb from Yale University and Benedikt Pötscher from the University of Vienna have published a series of papers dealing with what they call Post Model Selection Inference problems.* ...
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18 views

one-sided survival log rank test p-value

I want to compare two treatments for an oncology indication. I used a log rank test as two treatments (variable treatment) with time (variable month) and censor status (variable censor). Below is the ...
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9 views

How do you figure out the form of the variational distribution in variational inference?

So - generally for any difficult to factorize joint distributions (implying difficult to normalize) , variational inference proceeds by assuming there is a variational distribution of the latent ...
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1answer
34 views

Choosing a model for a relationship between academic prestige and public visibility

I have data frame in which I would like to analyse the correlation between academic prestige (factor analysis scores) and public visibility. These scatter plots reveal different patterns in the ...
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20 views

Identifiability of regression parameter in multinomial logistic regression

In simple logistic model, we have $\log (\frac{\pi}{1-\pi})=\alpha+\beta t$. If we allow our parameters $\alpha$ and $\beta$ to take value in $[-\infty,\infty]$, there will be identifiability problem. ...
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24 views

Why sampling for inference of a new document in LDA?

Given a standard LDA model with few 1000 topics and few millions of documents, trained with Mallet / collapsed Gibbs sampler: When inferring a new document: Why not just skip sampling and simply use ...
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20 views

Identifiability of multinomial logistic regression

What are the sufficient conditions for identifiability of regression coefficients in multinomial logistic regression generally?
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8 views

interpreting R plot of 100 t-confidence intervals on same graph. [duplicate]

I have drawn 100 sample of size 10 from standard normal distribution using r . after that for each repetition the 95% t-confidence intervals have been plotted on the same graph paper and those ...
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25 views

get probabilities of inference in bayesian network in R

I have a question about how continuous variables can be used for building models and prediction in a bayesian network. With some help, I was able to get it to work for continuous variables as follows ...
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1answer
39 views

E-step in EM algorithm with non trivial latent variables

I am trying to derive the E-step for an EM algorithm for this model: The interesting fact is that there are two sets of latent variables: $z$ and $y$. The E-step involve a derivation of the ...
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1answer
100 views

Law of large numbers and convergence

Suppose $X{\sim}N(\mu_1,\sigma_1^2)$ and $Y{\sim}N(\mu_2,\sigma_2^2)$, $x_1,...x_n$ and $y_1,...,y_n$ are i.i.d samples from X and Y, respectively. Consider the estimator ...
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111 views

Can prior distributions incorporate uncertainty AND variability in parameters?

I am trying to understand how to interpret Bayesian prior and posterior distributions in situations where there is believed to be variability in model parameters (due to variation in the population ...
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12 views

Inference arrival rate by samples of forward recurrence time for renewal process

There is a regenerative renewal process with iid. inter arrival time $X$, which follow the distribution $F(x)$. $N(t)$ is the counting process and $S_{N(t)} = X_0+X_1+\dots+X_{N(t)-1}$ is the time ...
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1answer
27 views

Parameter Inference when Model is a bad fit to the data.

I am working with gamma-ray data from the Fermi Satellite. The data has been binned into energy dependent maps of the sky -- e.g. three dimensions (energy, latitude, longitude) and is extremely high ...
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Covariance of parameter estimates in Method of Moments

I have a $3\times1$ vector function $f(x_i;\theta)$ where $X$ is a rv and $\theta$ is $3 \times 1$ parameter vector, such that \begin{equation} E \, f(X;\theta) = {\bf 0}.\end{equation} If I have a ...
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21 views

Classification using HMM

I would like to use HMM to classify a sequence of alphabets while preserving their orders. Just to put it formally, I am looking to compute $p(c|x_{1},x_{2}\ldots, x_{n})$ where ${x_{1},x_{2}\ldots, ...
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19 views

Inferring values based on rankings

I'm looking to infer items' values from only ranked lists of these items. I'm assuming that each item has some value, for which a higher value makes it more likely to appear first. This value can be ...
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18 views

Confidence intervals and Central Limit Theorem with only one sample

I know that to erect confidence intervals, standard errors must be calculated, a process which in turn makes use of the CLT (but I am not clear how). I also understand that, very generally, the CLT ...
2
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1answer
43 views

Inferring the convex combination parameter of two Poissons

Suppose I am interested in estimating an unknown quantity $p\in[0,1]$. I am limited to drawing three random samples, $X\sim\mathrm{Pois}(\alpha)$, $Y\sim\mathrm{Pois}(\beta)$, and ...
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10 views

Testing for Exponential Growth in Groups

I have data on population of professionals that change jobs from a few large consulting firms (about 30) to enter private equity. In making a bar plot of which consulting firms produce the most PE ...
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29 views

Finding the uniformly most powerful test

Let $X_1,X_2,...,X_n$ denote a random sample from density, $f(x;\theta)={1\over 2\theta}$, $0<x<2\theta.$ Find the uniformly most powerful test for testing $H_0:\theta<=\theta_0$ vs ...
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21 views

finding the critical region of most powerful test

Let $X_1,X_2,...,X_n$ be from a density function $f(x;\theta)=3\theta x^2e^{-\theta x^3} ;x>0,\theta>0$. From the Neyman-Pearson Lemma the most powerful test to test $H_0:\theta=\theta_0$ vs ...
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1answer
171 views

How does the inverse transform method work?

How does the inversion method work? Say I have a random sample $X_1,X_2,...,X_n$ with density $f(x;\theta)={1\over \theta} x^{(1-\theta)\over \theta}$ over $0<x<1$ and therefore with cdf ...
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43 views

Hamiltonian Monte Carlo with large parameter values fail to converge

I'm trying to learn about Hamiltonian Monte Carlo. Therefore I tried to infer the Parameters of a Multivariate Normal given some samples. My procedure is the following: Define $\mu$ and $\Sigma$ ...
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1answer
50 views

Uniformly most powerful test in poisson

This is example in Hogg and Craig's book page 254 I have shown that the best critical region is $\sum X_i>=3$. I don't understand why, after finding $\sum X_i>=3$ is the best ...
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56 views

Time series forecasting with OpenBUGS

My background is in applied math, not stats, so forgive my nontechnical terms throughout. For a work presentation on Monday I have to prepare a brief example of forecasting time-series data with ...
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16 views

Is there a proper interpretation of ordered multinomial variables in binomial Logit model?

I am using a binomial Logit model to make inferences about how respondents of a survey use the Internet based on differences in their financial well-being and income. My dependent variable measures ...
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1answer
41 views

Most powerful test

I don't understand what is meant by a most powerful test. I was reading the article here and the definition of most powerful test is given as, Definition. Consider the test of the simple null ...
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13 views

how can I check the bias between two groups

I have a presentation at the firm... using the stata. I want to check is there any bias between unweighted mean and weighted mean. and I already calculated the means between them..by common method ...
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11 views

Inference, effect of diet on performance

I'm new to statistics and inference, now taking my first course. I'm having trouble in this exercise to even determine what I'm supposed to be looking at: ...
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1answer
69 views

Bayesian vs. frequentist estimation

I don't really understand the connection between bayesian to "normal" frequentist estimation. Suppose we want to estimate the expected value of a population given a sample. In frequentist statisics ...
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1answer
40 views

Is it justified to include non significant predictors in a model if it decreases the fit criteria (AIC)?

During analysis of a high dimensional dataset (92 cases, 400+ variables) with the goal of statistical inference, I first used a bootstrapped LASSO (bolasso) to select predictors, and then did an ...
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2answers
32 views

(CDF Quantile) Understanding an example from a swirl lesson

I need to understand an explanation from a swirl() lesson in course "Statistical Inference", menu option "Probability2". At 76% of completion, there is a question: "The quantile v of a CDF is the ...
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11 views

Statistical inference on multiple dependent events

I am analysing a set of ~70 subjects. Each subject has been followed for 24 hours, and the times of a reoccuring event have been collected. Each event lasts 0.5 hr, and another event can start during ...
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98 views

Bayesian vs. Frequentist calculation steps

This article contains an example of Bayesian vs. Frequentist philosophies. An old drug successfully treats 70% of patients. To test a new drug, researchers give it to 100 patients, 83 of whom ...
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13 views

Statistics Theory and probability [duplicate]

Show that the order statistics are minimal sufficient f_θ (x)= (1+θx)/2 |x|<1 where -1 ≤θ≤1