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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9 views

Bootstrap in meta-analysis

I am conducting a network meta-analysis of clinical trials on cardioprotective drugs in patients undergoing chemotherapy (see PROSPERO protocol CRD42015029915), and I was wondering whether it would ...
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1answer
65 views

On the Bayesian setup in inference

I've been trying to get into the chapter 4 in Lehmann's Theory of point estimation, but I can't seem to understand his presentation of the Bayesian setup. He starts of by the introduction below and ...
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1answer
31 views

Using a point estimate in confidence interval calculation

In order to estimate a population parameter(say mean), I read that we use the point estimate and confidence intervals to come up with a range within which the population estimate may lie. However, my ...
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1answer
42 views
+50

How to reconcile results from many incremental hypothesis tests?

I'm considering a series of controlled experiments (e.g. A/B tests) measuring the performance of a system. Each time a change to the system is found significant (via statistical inference) the test ...
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13 views

Causal Impact and using multiple control series with their regressors

Hi all I am analyzing several DMA's for campaign effectiveness using the CausalImpact package by Kay Brodersen. I have data for participants and non-participants INCLUDING their contemporaneous ...
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1answer
18 views

How do GBR trees differ from random forests regression in terms of predictive performance?

Is there a case when one would use gradient boosted regression trees instead of random forests regression (or vice versa)? It appears gradient boosted regression trees have done far better in ...
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40 views

Bayesian Approach To Combine Multiple Weighted Inputs

I'm beginning to learn about Bayesian theory but I'm stumped on the ideal approach for combining multiple weighted inputs. Here's an example to make this more concrete. Let's say that I want to ...
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35 views

How does one infer the noise/error model given measurements?

What resources are available for applying inference/computational statistics to infer the underlying error/noise model, given X measurements from some apparatus? (Below, I am mostly referring to ...
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50 views

For a Fisher Information matrix $I(\theta)$ of multiple variables, is it true that $I(\theta) = nI_1(\theta)$?

For a Fisher Information matrix $I(\theta)$ of multiple variables, is it true that $I(\theta) = nI_1(\theta)$? That is, if $\theta = (\theta_1, \ldots, \theta_k)$, will it be the case that the fisher ...
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20 views

How can we find the Fisher Information Matrix of a linear regression model?

Suppose we have a sequence of random variables $y_1, \ldots, y_n$ such that $y_i = \beta_0 + \beta_1 x_i + \epsilon_i$ where $\epsilon_i$ is assumed to be i.i.d. $N(0,\sigma^2)$, with $\sigma^2$ ...
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9 views

Why is the Fisher Information sometimes written as a conditional expectation?

I was looking at the Fisher Information entry on Wikipedia just now, and saw that the Fisher Information Matrix was written as: $$ \mathcal{I}(\theta) = - \operatorname{E} \left[\left. ...
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17 views

How to compare two test according to power?

I know the expectation calculates the power of the test, but how can i find a test that is as good as the given one based on the power?
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18 views

Can we calculate the MLE of $\mu$ and $\sigma^2$ of normally distributed data using the profile likelihood approach?

My definition of profile likelihood is that given a vector of parameters $(\theta_1, \theta_2)$, with $\theta_1$ the parameter of interest, and $\theta_2$ a nuisance parameter -- If $L(\theta_1, ...
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32 views

General approach to learning a graphical model

Lately I've been reading a lot about inference and learning in probabilistic graphical models. I mostly understand specific methods (e.g. junction tree, message passing, MCMC; gradient descent, ...
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31 views

Can an independent t-test be used on paired data when the pairing is unknown?

Suppose the effectiveness of a training course is examined, and performance of each individual in a group is taken both before and after, and the differences are compared in a paired $t$-test. Would ...
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2answers
59 views

Point null hypothesis in Bayesian statistics

Let $X\sim N(\theta,1)$ and consider 5 independent observations $X=(4.9,5.6,5.1,4.6,3.6)$. The prior probability that $\theta=4.01$ is $0.5$. The remain values of $\theta$ are given a prior ...
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2answers
75 views

Does zero correlation mean no causation? [duplicate]

If I demonstrated that there is no correlation between two random variables, does that mean that there is no cause and effect relation between them ?
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18 views

Can supervised machine learning techniques infer the formula (if it exists) for a statistical model?

Suppose that we have response data $y_i$ generated by a specific mathematical function $y_i=\mathcal{F}(X_i)+e_i$ where $X_i$ is a vector of predictor variables with random error term $e_i$. Without ...
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16 views

Non Parametric test for ranked data

I am working on a project on multi criteria decision modelling. The technique applied (Analytical Hierarchy Process) provides me with data in the form of normalised weights (sum=1) to a set of ...
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42 views

Bayes factor and hypothesis test in Bayesian inference

Let $$\pi_0=P(\theta\in\Theta_0)=\int_{\Theta_0}\pi(\theta)d\theta$$ $$\pi_1=P(\theta\in\Theta_1)=\int_{\Theta_1}\pi(\theta)d\theta$$ $$a_0=P(\theta\in \Theta_0|x)$$ $$a_1=P(\theta\in \Theta_1|x)$$ ...
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32 views

Understanding LDA inference

It is said that the key inferential problem that needs to be solved to use LDA (latent dirichlet allocation) is that of computing the posterior distribution $p(\theta,z | w, \alpha ,\beta)$. I know ...
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1answer
69 views

Why is the posterior distribution in Bayesian Inference often intractable?

I have a problem understanding why Bayesian Inference leads to intractable problems. The problem is often explained like this: What I don't understand is why this integral has to be evaluated in ...
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7 views

Corrections needed when performing multiple analyses on the same database? [duplicate]

I have access to data from various health-related surveys. Colleagues with a hypothesis in mind ask me to run their analyses. Even though each of them is unaware of the others' work, we are doing ...
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1answer
27 views

Understanding formulas for the sampling distribution of the mean

In the passage below, what does $k_c$ mean, and why (in "$σ_0/\sqrt n$") is $\sigma$ being divided by the square root of $n$? I got this form the book Principles of statistical inference.
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25 views

Problem in estimating parameters by moments methods

I am working on one of the discrete probability distribution having pmf as $P(x)=\{p^{\log(1+x^c)}\}-\{p^{\log(1+(x+1)^c)}\},\quad 0<p<1; c>0; \,x=0,1,2,...$ The moments of the distribution ...
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5 views

CausalImpact and choosing the start of effect time-frame

Is it probable, to experimentally choose a prior starting point to the factual starting point of a n effect in order to validate the package's results? I guess the point gets more clear if you look ...
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24 views

How does Causalimpact work? (please see more specific questions in the description)

How does CausalImpact behave when the number of data points in the time-series is unequal to n times the set length of a season (for example when there are 30 data points with the length of the ...
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0answers
19 views

how to maximize strength of inference in non-independent data

I have a large set of vectors, each one describing the shape of a different object. Each vector has 25 categorical descriptors for the shape of the object, with each position on the vector having ...
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29 views

Does an Efficient Unbiased Estimator exist for a function of a parameter of an exponential family distribution?

Say I have an i.i.d. sequence sequence $X_1,\ldots X_n \sim \text{Bernoulli}(p)$, and I am interested in estimating $p^2$. Let $T$ denote $\sum_{i=1}^n X_i$. It turns out that the mle $\bar X^2 = ...
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10 views

Class imbalance and standard errors

I'm building a logistic regression that models the probability of conversion when clicking on a website ad. I'm not that interested in building a great classifier, but I want to identify a set of the ...
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1answer
30 views

Understanding the statistical significance calculated in an experiment

I am trying to understand analysis in a paper which talks about statistical significance of a certain stimulus. I have used 'VALUE' in place of the specific variable that is being observed, and ...
3
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1answer
46 views

Strong Vs Weak law of large numbers, (looking for Stat help and R simulation.)

This rather looks quite basic, but when referring to weak and strong law of large numbers this is the definition I look at (Casella and Berger) Can you please give an 'intuition' in understanding ...
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29 views

Why don't I get intervals which don't contain parameter by simulation?

I effect 100 simulations, and with a confidence level 95% I expected to get by simulation 5 coinfidence intervals approximately that not contain the paramater. I always get 100 confidence intervals ...
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1answer
61 views

Relationship between 0-1 Loss and error Type I and II in Neyman Pearson

In the context of hypothesis test $$H_0:\theta\in \Theta_0$$ $$H_1:\theta\notin \Theta_0$$. Find the relationship between the 0-1 loss defined by $$L(\theta,\delta)= \begin{cases} 1-\delta ...
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14 views

Extracting influence counts from Model variables or data

To idetifying the important activity performed from users who have been converted in last N days. So, I have tried GLM, Rpart and Random forest models which can give me the impoprtant activities (in ...
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36 views

How do you determine when to use certain test statistics?

I've been trying to formulate this question and have struggled, so if it seems ill-worded, I apologize: A statistics book I have has a table in the back that says: For an inference test regarding a ...
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1answer
74 views

Multilinear loss in Exponential-Uniform model

Let a prior $\pi(\theta)=\frac{1}{3}(\mathbb{I}_{[0,1]}(\theta)+\mathbb{I}_{[2,3]}(\theta)+\mathbb{I}_{[4,5]}(\theta))$ and $f(x\mid\theta)=\theta e^{-\theta x}$. Taking the multilinear loss ...
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1answer
14 views

posterior Gaussian distribution

I have quite a newbie doubt about Bayesian inference. Let's say that my prior data is composed by a Gaussian distribution (mean1, standard deviation1). My likelihood is another Gaussian with mean2, ...
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19 views

Comparing the rates of Poisson distribution using Bayesian inference

In the 'Theory of Probability' book by Sir Harold Jeffreys, (5.15), the form of the Bayes Factors that he derives for the comparison of Poisson rates is the same as that of Binomial rates. But I did ...
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1answer
34 views

Confusion regarding terminology related to the junction tree algorithm

As far as I understand, the "junction tree algorithm" is a general inference framework which roughly consists of the four steps 1) triangulate, 2) construct junction tree, 3) propagate ...
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1answer
52 views

Statistical Power and Type II Error

Let the power function be defined as $\beta(\theta)=P_{\theta}(\mathbf{X} \in R)$, where $R$ is the rejection region associated to the test being considered. Can I state that the Probability of type ...
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2answers
127 views

How is prior knowledge possible under a purely Bayesian framework?

This is more of a philosophical question, but from a purely Bayesian standpoint how does one actually form prior knowledge? If we need prior information to carry out valid inferences then there seems ...
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7 views

Inference of discrete-valued multivariate time series from asynchronous ticks

I am looking for a relevant model to do inference of a large multivariate time series whose values arrive asynchronously. To be more precise, let $X = (X_1,\ldots,X_N)$ be the multivariate time ...
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24 views

What is Maximum likelihood estimator (MLE) in plain language? [duplicate]

What is the plain meaning of Maximum Likelihood Estimator in point estimation.
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8 views

How to deal with the factors when moralize a directed network?

Consider we have a simple V-Structure Bayesian network which we use it for model some random variables. in other words we have a distribution $P(C|A,B)$ where A and B are the parents of C in the ...
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2answers
46 views

Calculating the risk of an estimator using zero-one loss

Consider two observations where $$P_\theta(x=\theta+1)=P_\theta(x=\theta-1)=0.5,\ \ \theta\in\mathbb{R}$$Let $\mathbb{D}=\Theta=\mathbb{R}$ the decision space. Suppose that the associated ...
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5answers
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What is a good, convincing example in which p-values are useful?

My question in the title is self explanatory, but I would like to give it some context. The ASA released a statement earlier this week “on p-values: context, process, and purpose”, outlining various ...
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1answer
87 views

Posterior distribution of normal with gamma prior on the precision

Find the posterior distribution when $$x|\sigma\sim \mathcal N(0,\sigma^2),\:\:\: 1/\sigma^2\sim \mathsf{Gamma}(1,2)$$ I'm stuck in this exercise, I know that $$\pi(x|\sigma)\approx ...
2
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1answer
35 views

How could I define this problem and what methods could be useful?

I have data that in hourly intervals tell me how many men or women are on a page on my site (well a third party's best guess - all noisy data). I also have the logs of users' ids (all anonymous ...
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16 views

model for two correlated noisy variables

Support I have two variables that I know are linearly correlated (unknown slope). I have a bunch of true value pairs as well as noisy measurements. When I get a new pair of noisy measurements I want ...