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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Statistical Inference

I am not able to understand terms like Probability calculus and especially the 2nd paragraph starting from Remember. Copied from book-Statistical inference for data science by Brian Caffo If someone ...
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34 views

Distribution of the sum of the two dependent bivariate gaussian distributions and related questions

This is something I was thinking about and I decided to modify a question from a mid-term to ask this. Suppose $X_{1}$ and $X_{2}$ are two bivariate gaussian variables, decribed as $$ X_{i}=\begin{...
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13 views

Make inference on overall density of duplicate records from a sample

I have a file, typically of several million records, for which I need to make an inference on the percent of duplicates (perhaps testing for whether the rate exceeds a certain percent, or just coming ...
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57 views

What is wrong with “PROC fishing” syndrome?

RE: https://www.quora.com/What-do-statisticians-e-g-Stats-PhDs-think-of-data-scientists-in-industry-without-stats-backgrounds There are several comments made regarding "PROC FISH syndrome", whereby ...
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32 views

Vector Outcome Logistic Regression

Question: What model (Likelihood/prior family) is appropriate to use when attempting to do inference on a vector of boolean outcomes given continuous factors? Elaboration: I am only aware of ...
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63 views

Can you get the probability of an event happening before n days using its empirical cumulative distribution?

I have data of the number of days it takes an object to change from state A to state B, and I am interested in knowing what is the probability that this change of states happens before n days. Can I ...
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13 views

What's the best way to compute the offset of a time series?

Say that I have a signal $f(t)$ composed of an offset, another signal and noise: $$ f(t) = offset + g(t) + \epsilon(t) $$ The function $g(t)$ is strictly possitive but the epsilon can make the ...
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20 views

How to check the assumptions behind an inference procedure, in the case of very large data sets

On this site it has been confirmed multiple times that, contrary to what is often heard, hypothesis tests don't have any issues with large sample sizes. As a matter of fact, the probability of Type 1 ...
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58 views

How do I perform Bayesian Updating for a function of multiple parameters, each with its own distribution?

I have a variable that is a recursive function involving other variables with known distributions (see problem below). Let $b(t+1) = b(t) + C \sqrt{b(t)}$ where I know $C \sim N(1.82, .0298)$ and ...
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43 views

On randomized estimators

I been looking at this for a few days; I cant understand how the pseudo-random generator comes into play, why do we need it? Is it just in order to have an actual $X^{'}=X \mid t$ in a real life ...
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1answer
44 views

On theorem on characterization of MRE estimaters

I have some trouble with understand the second equality in the proof of theorem 6; Using the lemma we can just plug in $\delta_{0}-v$ and minimize over that w.r.t $v$, but howcome we have the ...
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1answer
77 views

GLM Categorical Variable Level grouping / simplification

I am trying to find information regarding a technique which is commonly used in the insurance pricing industry. This relates to a GLM model where a categorical variable is used in the model. The ...
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23 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
73 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
34 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
64 views

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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19 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
22 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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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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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 $\sigma^2$ known....
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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. \frac{\partial^...
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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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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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36 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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60 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 with ...
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79 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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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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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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70 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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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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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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29 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 season ...
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21 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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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
32 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
48 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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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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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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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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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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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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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, ...