Hypothesis testing without a fixed sample size.

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18 views

Is there a statistical correction that works if the number of experiments depends on the result of the experiments?

Suppose that I am running an experiment that gives us some confidence $c$ about a hypothesis. If I intend to run the experiment $n$ times, I understand there are some ways of choosing a $c'$ so that ...
4
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0answers
55 views

Expectation and variance of sample mean with random sample size

I have a question regarding sampling where the sample size itself is a random variable. Say I have two sub-populations $A$ and $B$ from which I can sample a real valued random variable with ...
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0answers
13 views

changepoint detection and its analysis

I applied changepoint detection provided by ecp package against a given time series. The time series plot marked with identified change points is shown as follows. ...
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1answer
22 views

Should one adjust analyses if interim analysis is planned for an outcome other than the primary outcome?

It is widely accepted that analyses of clinical trials have to be adjusted if interim analyses are planned in order to decide if early termination is necessary due to evidence for superiority of one ...
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1answer
43 views

Sequential parameter estimation of multiple discrete random walks

We have $M$ Bernoulli random walks, $X_1$ has parameter $p< 1/2$ and all the rest have parameter $1/2$. The steps are $\pm 1$. I want to identify the parameter $p$ random walk with probability of ...
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12 views

Sequential Probability Ratio Test for a learning curve

In the experiment is an animal in an rectangle cage. In the rewarded corner is water (in the other 3 not). Now, I want to check how many visits the animal need to learn or not to find the water. ...
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24 views

Sequential classification methods

I am curious to know if there are methods that exists for sequential modeling of binary outputs? Let me give an example to help further clarify the question: I have a problem where I have binary ...
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0answers
12 views

modeling sequential decisions

I am trying to model a 3 sequential decision. In my data context, there are two stores A and B. A consumer first decide to choose a store either A or B to visit, and then he decide to purchase a ...
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0answers
13 views

Question regarding p-value interpretation in Group Sequential Designs

I have a general question that I would appreciate any input on: Suppose we design a typical group sequential design and to stop (for efficacy or futility) at the first interim analysis the result has ...
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57 views

textbooks/literature/resources for online learning/ time series/ sequential analysis?

I have read (the contents of) machine learning introductory textbooks such as Pattern Recognition and Machine Learning, Machine Learning A Probabilistic Perspective, and The Elements of Statistical ...
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3answers
101 views

How do I compute/estimate the variance of sequential data?

Say I have a (infinite) sequences like, 1,3,2,2,1,3... I want to estimate their mean and variance of the sequence at time $t$. But I won't have enough storage to keep all the data seen ...
3
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1answer
38 views

Determining Optimal Step Size for Sequential Analysis

Consider the following problem: Suppose someone wanted to determine the ideal dosage of an epinephrine shot in order for the shot to be successful 90% of the time. The person is also not willing to ...
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1answer
52 views

Interim analyses without any stopping rules

I've got some questions about interim analysis rules. Do I need to make alpha/beta corrections in the following situation: One interim analysis is planned in the study The interim analysis is ...
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0answers
44 views

Sequential hypothesis testing with independent but non-identically distributed samples

I want to apply the hypothesis for my problem. According to A. Wald regarding sequential hypothesis, he used independent and identically distributed (iid) observations or samples but in my case my ...
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2answers
80 views

Are bayesian methods inherently sequential?

Ie, to do sequential analysis (you don't know ahead of time exactly how much data you will collect) with frequentist methods requires special care; you can't just collect data until the p-value gets ...
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0answers
24 views

Interim Analysis for Futility in a 1-Arm Trial with a Binomial Outcome

I am planning a 1-arm trial that tests a response rate in patients to a drug. The response rate indicative of the drug working would be 30%, and 10% would be considered the null response rate (i.e., ...
2
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0answers
60 views

Random walk with continuously distributed steps on $[-1,1]$

A simple random walk $S_n = X_1 +\cdots +X_n$, where $P(X_i = 1) = p \not = 0.5$ and $P(X_i=-1)= q \triangleq 1-p$, admits the following probability $$P(S_n \textrm{ reaches } a \textrm{ before} -b) =...
2
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1answer
51 views

sequential estimators for a proportion

Does anyone have any reference for a sequential estimator for proportions? I am planning an experiment to measure the probability of a certain event happening and would like to know how many ...
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0answers
13 views

Modelling distributions evolving with time

Say we have N probability vectors of dimensionality D describing how a process evolves in N time steps, something like multidimensional time series. What's the best way to model this sequence in ...
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0answers
32 views

How can Neyman-Pearson and Wald both be optimal?

I see optimality mentioned in the context of both Neyman-Pearson tests and Wald tests. Neyman Pearson is a fixed sample test, while Wald is a sequential test. The Neyman-Pearson lemma states that no ...
3
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0answers
81 views

updating a Bayes factor

A Bayes factor is defined in Bayesian testing of hypothesis and Bayesian model selection by the ratio of two marginal likelihoods: given an iid sample $(x_1,\ldots,x_n)$ and respective sampling ...
2
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0answers
123 views

Estimation on evolving distribution with small updates

I have a set $X$ of $10^6$ elements and a time series of probability distributions $\mu_1,\mu_2,\ldots$ on $X$. I want to estimate the expected value of a function $f$ over each $\mu_t$. It is easy to ...
2
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0answers
19 views

Hypothesis test based on (random) result of previous experiment: can I multiply confidence levels?

Consider an i.i.d. sequence of Bernoulli random variables $\{Z_i\}$ with Bernoulli parameter $x$. By a certain procedure (experiment A) I obtain a random set S such that $\mathrm{Pr}[x \in S] \geq c_A$...
4
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1answer
148 views

When to stop an ad campaign?

I have a campaign and I am trying to decide whether to terminate or not, with profit maximization in mind. There is cost associated with every time the ad is shown, and a reward once it converts (...
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0answers
95 views

What are few techniques that use sequential pattern mining for predicting location?

I found many sequential pattern techniques like GSP Algorithm Sequential PŠttern Discovery using Equivalence classes (SPADE) Apriori algorithm etc But they all work for data with certainty like ...
10
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1answer
166 views

How to test if “previous state” has influence on “subsequent state” in R

Imagine a situation: We have historical records (20 years) of three mines. Does the presence of silver increases the probability of finding gold in next year? How to test such question? Here is ...
2
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0answers
189 views

Sequential Probability Ratio Test (or other Sequential Sampling techniques) for testing difference

I have the results from running two algorithms and I want to be able to say that there is, say, a 95% probability that one of the sets of results is different to the other where different means A > B ...
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20 views

Interim analysis and CI

A trial was planned and designed to be a single arm trial (one group), and the sample size was calculating using a confidence interval to achieve some accuracy in the estimation of the unknown ...
2
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0answers
22 views

Test that does not based on sufficient statistics [closed]

In the context of adaptive clinical trials, inverse normal method/test was addressed as not based on sufficient statistics, while sequential tests do. Is it because in adaptive design, the test is not ...
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0answers
38 views

Closed form Pocock Rejection Region solution for joint MVN correlated RVs?

This is related to my previous question (link), but I have a simpler way of expressing it. Suppose $ \left( \begin{array}{ccc} \ Z_1 \\ Z_2 \end{array} \right)$ follows a Bivariate standard normal ...
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0answers
40 views

How can I maintain a streaming value and be 95% confident that the measure for the population dropped below some value?

I weigh hail stones one at a time, producing a sequence of weights. I want to tell the weatherman when I'm 95% confident that hail stones are less than 50g in weight based on the previous $K$ hail ...
1
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2answers
242 views

Cluster Sequences of data with different length

I need to cluster sequences of data that have different length. I am using Matlab and my first question is related to the method. Is KMeans sufficient to achieve this? IN KMeans I have to use the ...
2
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0answers
143 views

rejection region for correlated bivariate normal

STATEMENT OF PROBLEM: Suppose $ \left( \begin{array}{ccc} \ Z_1 \\ Z_2 \end{array} \right)$ follows a Bivariate standard normal with covariance $ \rho $ $ \left( \begin{array}{ccc} \ Z_1 \\ Z_2 \...
2
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0answers
58 views

Running sequential tests as data is collected - practical advice for researchers

I've observed that many experimental labs in my field don't do a power analysis before they start collecting data. In practice, it seems that many researchers collect data and periodically run ...
3
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1answer
198 views

Sequential testing for a Bernoulli variable

Suppose $T$ is a Bernoulli random variable, such that $T = 1$ with probability $s$, $s$ is not known. I am interested in checking hypothesis $H_1$ that $s \neq 1/2$ ($H_0$ is that $s = 1/2$). One way ...
6
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0answers
62 views

bias of an estimator when using stopping rules

Consider the setting where $X_1,X_2,...$ are i.i.d. real-valued random variables with $\mathbb{E}[X_i] = \theta$ and let the random variable $\tau$ be an associated stopping time. I'm wondering what ...
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0answers
113 views

Method for detecting anomalies in timeseries?

I am exploring creating alerts for anomalies in a timeseries. Say that I have a graph like this: There are two anomalies here that I would wanted to be alerted on: First, on April 7th with there ...
4
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1answer
487 views

What's the algorithm for finding sequences used by TraMineR?

I'm working an analysis about finding frequent sequences in a event-state dataset using the R package TraMineR (and ...
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1answer
66 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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167 views

One pass distributed clustering algorithm

I am working on clustering of data streams. For my purpose Sequential Leader Clustering (SLC) have given fair result, as i need not give number of clusters (like k in k means), which require some ...
2
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0answers
154 views

Sequential Inference And Evidence (Jaynes 2003): Is it valid? Is it used?

Exploring the work of ET Jaynes, Probability Theory (11th Printing 2013) has led to consideration of the technique he identifies as Sequential Inference (p. 96); where the evidence, in decibels, ...
2
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1answer
153 views

Runs test for randomness for k elements

Say I have a sequence of length $n$ of $k$ different elements, s.t. $n > k, k > 2$. I want to show this sequence is random, based on the number of runs. I found this paper by AM Mood which ...
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0answers
25 views

Statistical similarity on sequences

What are the methods that can be used for evaluating the similarity of the sequences? Lets say that we have three sequences; I want to be able to say that "statistically" the sequence number 1 and the ...
7
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0answers
444 views

Understanding Sequential Probability Ratio Test (SPRT) Likelihood Ratio

I am a software developer looking to develop an alternative for the simple hypothesis testing scheme described here. In short, the test works as follows: Two URLs are compared for their ability to ...
13
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4answers
574 views

How could one develop a stopping rule in a power analysis of two independent proportions?

I am a software developer working on A/B testing systems. I don't have a solid stats background but have been picking up knowledge over the past few months. A typical test scenario involves comparing ...
6
votes
1answer
361 views

Speed up web a/b tests with sample size checkpoints

Before starting an a/b test with a control and one experimental route, I can calculate a required sample size based on conversion rate estimates for both routes. I can get a good estimate of the ...
2
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0answers
87 views

Performing a Wald's group sequential test in R (for complex hypothesis)

The settings: we have a sequence of numbers generated from a normal distribution with $\mu=1;\sigma^2 = 1 $. And with every new observation collected, we'd like to test for: $H_0:\mu_0=0$ (two-sided)....
3
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1answer
285 views

Sequential testing of multiple probabilities (binomial variables)

Task: I have e.g. 1 control group and 7 experimental groups which are treated differently. All groups have a dependent binomial variable: 1 = success, 0 = no success. I want to conduct sequential ...
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1answer
70 views

Group sequential Design

Can anyone recommend a paper which provides a nice introduction or summary of group sequential design.
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0answers
110 views

Statistic describes the sharpness or dispersion of sequential data?

I want to find an existed statistic that can clearly describe the sharpness or dispersion of a peak-shape signal. To state this question more clearly, I plotted two different types (sharp and broad) ...