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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Predict app downloads based on a set of search-rankings

I am facing a problem with mobile-application data. I want to build a model to predict the number of daily downloads of an application on the App Store, using as predictors the daily rankings of the ...
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4 views

Stats test needed with population of treatment group but sample of comparison group?

I want to compare outcomes of a treatment group and a comparison group. The pilot program serves about a thousand clients, all of whom we are surveying. The comparison group is drawn from a similar ...
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114 views

Are we frequentists really just implicit/unwitting Bayesians?

For a given inference problem, we know that a Bayesian approach usually differ in both form and results from a fequentist approach. Frequentists (usually includes me) often point out that their ...
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9 views

Application of Barndorf-Nielsen Formula for Maximum Likliehood Inference and Confidence Intervals

I've seen various forms of what is called the $p^*$ or Barndorff-Nielsen formula for the conditional distribution of the MLE. The most general form I've found is here. I'll reproduce it below: $$ f(\...
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18 views

Purposeful model building for prediction and inference

What are some of the best practices and steps to building models for prediction and or inferences? What have been taught to me during my classes was the steps outlined in Chapter 4 of Hosmer et al. ...
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1answer
27 views

Geometry of Rejection regions for tests (NP lemma, Karl-Rubin, UMPU, LMP, etc)?

The Neyman-Pearson lemma, the Karlin-Rubin theorem, and the other for UMPU tests for the exponential family, etc. They all define a most powerful Rejection Region (RR), in a certain class of tests. I ...
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27 views

Most reliable method to compute 95% confidence intervals of proportions for small samples

I am planning a prospective trial for CE mark of a new cardiovascular device, and wish to use 95% confidence intervals to present, once data are collected, the inferential estimate for the occurrence ...
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172 views

Is frequentist conditional inference still being used in practice?

I've recently reviewed some old papers by Nancy Reid, Barndorff-Nielsen, Richard Cox and, yes, a little Ronald Fisher on the concept of "conditional inference" in the frequentist paradigm, which ...
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39 views

y and x axes coupled by two experimental measurables, how to determine if the trend is due to the coupling or not?

If, in a plot of $y$ versus $x$ where $y=f(a,b)$ and $x=g(a,b)$ such that $f{\ne}g$, a clear trend arises, how can one show that the trend is either a) probably due to the axes sharing the variables ...
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1answer
12 views

HMM with random process that determines how long you stay in a state

I have a situation that is reasonably well-modelled by a discrete Hidden Markov Model (HMM), but with one twist: when you enter a state, the amount of time that you spend there is given by some ...
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2answers
194 views

How to define a Rejection Region when there's no UMP?

Consider the linear regression model $\mathbf{y}=\mathbf{X\beta}+\mathbf{u}$, $\mathbf{u}\sim N(\mathbf{0},\sigma^2\mathbf{I})$, $E(\mathbf{u}\mid\mathbf{X})=\mathbf{0}$. Let $H_0: \sigma_0^2=\...
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2answers
95 views

How to define a rejection region?

This has always troubled me a bit. When I choose my hypothesis, do I define in some way the rejection region [RR], or, do I do that by choosing the test statistic I want to use? By fixing the ...
2
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1answer
41 views

An example of the differences in frequentist and bayesian perspectives

The following is an example from a book I'm reading. Let there be a sequence of throws of an unfair coin, and $\theta$ be the prob. of getting head. Imagine the observer gets: $x=(T,H,T,T,H,H,T,H,H,H)...
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14 views

Estimator's Efficiency vs. Consistency

I know the definition of both (I think), but they seem so equal at the same time. Any clarification? I know that as the sample size goes to infinity; the estimator converges to the population ...
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1answer
46 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{...
2
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1answer
14 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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2answers
60 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 ...
2
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1answer
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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82 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 ...
3
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0answers
24 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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2answers
60 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 ...
3
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1answer
46 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
89 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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24 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
36 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 ...
2
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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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22 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
24 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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36 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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51 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 $\sigma^2$ known....
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12 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. \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?
3
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23 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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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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2answers
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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2answers
81 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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19 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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0answers
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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43 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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1answer
68 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 ...
5
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1answer
85 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
29 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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28 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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7 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 ...