Questions tagged [sequential-analysis]

Hypothesis testing without a fixed sample size.

103 questions
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Calculating alpha values from group sequential boundaries

I'm using the Lan-DeMets alpha spending function method for determining when I should stop a trial. I found this R package for calculating the boundaries: https://cran.r-project.org/web/packages/...
10 views

Detecting changing mean and variance using Sequential Probability Ratio Test (SPRT)

I have a process that outputs values that should conform to a normal distribution with a known mean and variance. I would like to perform sequential testing in order to detect changes in the mean and/...
59 views

What are disadvantages of “Sequential analysis”

Sequential analysis involves performing sequential interim analysis till results are significant or till a maximum number of interim analyses is reached. Sequential analysis sounds appealing ...
20 views

Representative Pattern Extraction from Time Series using LSTM

I am interested in extracting a representative pattern from time series having variable time periods. I have attached an image for reference. I would like to know if a LSTM would be the appropriate ...
27 views

Is there a name for this? Updating class probabilities, online

An object is of an unknown class $y$. We receive a stream of measurements $x_1, x_2, ...$ of the object. Every time we receive a new measurement, we want to update our estimate of the class label $y$ (...
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Average Sample Number using Page's CUSUM procedure?

I am trying reproduce the Table 1 results from the page 12 using the equation given the page 13.To access the journal article please click https://arxiv.org/pdf/math/0605322.pdf. The corresponding ...
17 views

Does an interim sample size re-estimation increase type 1 error if based on the overall event rate?

Suppose that a sample size is to be calculated for a trial: a presumed effect size summarizes the effect of intervention (relative risk RR $\exp(\theta_1)$), and background gives the rate of events in ...
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Sequence Prediction with noise / gap using markov models

I'm trying to understand if Markov models can account for a "noise event" when predicting the next item in a sequence. For instance, if i have very frequently occurring (noise) event "F", can a ...
31 views

Mixed-effects modelling in a sequential analysis design

I'm planning a study and am considering going with a sequential analysis design (as described here: https://psyarxiv.com/9yegd/download?format=pdf). This design allows one to take multiple looks at ...
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How to methodologically show that a given 'time-series/sequential' data is not really sequential?

I have an apparent time-series/sequencial (supervised: multi-class classification problem) dataset with each data-point time-stamped. However, some domain intuition tells me that the data is static ...
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Reverse the shuffling phase

It is very convenient to have sklearn library to split and shuffle the data with ...
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How to encode text and categorical variables together?

I have two groups of texts that are very similar (e.g. reviews written on fridays and reviews written on mondays), and I want to build a LSTM that can classify them into positive and negative reviews. ...
75 views

Can the Bayesian but not the frequentist “just add more observations”?

Since the frequentist's p-values are uniformly distributed under the null hypothesis, it is a highly problematic practice to add more and more data to your sample until you find a significant result. ...
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Sequential mining technique for categorical events?

I'm facing a problem where I have a short (2-8) sequence of discrete events, of variable length, and a final state. Ex.: cold, warm, warm -> soft clothing. I would like to determine what are the main ...
48 views

Predicting elections with a random sample

If I have a population of exactly 100.000 voters, and I know they all voted in either candidate A, B, C, D or E. (e.g where the results of a random sample of 100 voters are A = 40%, B = 30%, C = 10%, ...
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Applying Sequential Probability Ratio Test (SPRT) on a Vector Signal?

I am trying to apply SPRT on a vector signal (of residual) for detecting faults occurring in the sensors' measurement of an aircraft. The vector signal contains measurements from five different ...
183 views

Stopping rules in group sequential designs

I have read that in group sequential designs, having a maximum of $k$ stops, for the $j$-th stop $j < k$ there are 4 bounds chosen $a_j,b_j, c_j, d_j$ such that the three decisions are considered. ...
22 views

power calculation for two stage binomial type model

This is a power-type calculation for a Bernoulli/binomial question in two stages. Suppose you are planning an experiment which starts with a test for an event on $N$ experimental units. The event ...
1k views

Determining sample size before starting an experiment or run the experiment indefinitely?

I studied statistics years ago and have forgotten it all so these may seem like general conceptual questions than anything specific but here is my issue. I work for an e-commerce website as a UX ...
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How many samples do I need to estimate a gaussian distribution?

Background: I'm comparing the performance of two algorithms. The data is noisy so the results tend to form a nice normal distribution. I'd like to estimate the mean with a high confidence: up to 1% ...
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Advice for conducting the same experiment several times?

I'm very new to Bayesian statistics, but I've found myself in a situation where they might be able to help. I'll be running the same experiment repeatedly and analyzing the data every few months. The ...
157 views

Understanding interim analysis and alpha spending functions

I have to perform an A/B test with interim analysis and found some literature about methods designed to preserve the global Type I error rate by adjusting the $\alpha$ level for each peeking. ...
37 views

Convergence of a sequence in finite number of steps

Here is the setup of my problem. It is a sequential problem and there are two possible actions A and B. Now, when either action $A$ or $B$ is taken at the $j$th time point, we observe some outcome say ...
39 views

Optimal denoising of a few features for latent variable modeling

I am fitting latent variable models to noisy, high-dimensional data. The dimension is 15,000 to 20,000; there are 2,000 observations. There is a certain latent structure that I observe -- essentially, ...
347 views

Bayesian updating with discrete priors + possibly unknown classes

I'm following along with some lecture notes on Bayesian updating with discrete priors. They give an example problem to illustrate some of these concepts, which I briefly restate here: Someone tells ...
85 views

sample size calculation for one-sample log rank test with interims (ie group sequential)

I wonder if there is any advice for performing a sample size calculation for survival data using the one-sample log rank test with interims (ie group sequential) - ie with O'Brien-Fleming or some ...
36 views

Finding expected value with $3$ unknown variables

Question: There are n marbles in a bag, player $1$ picks out $x$ marbles where $x \leq n$, marks them, and puts them back. Player $2$ picks out $y$ marbles where $y \leq n$. What is the expected ...
390 views

Complexities of interpreting A/B testing power & significance calculations

Apologies up front for not being a statistician. I've been searching high and low and I cannot find a sufficiently detailed explanation how to interpret differences in A/B testing power and ...
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Just how bad is it to determine when to stop data collection based on the resulting CI?

Say I want to be $95\%$ sure of the mean $\bar X$, with a CI of size $2$ ($1$ in each direction). The following is bad practice: collect data until $1.96\frac{s}{\sqrt{n}}=1$. What is the extent ...
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Building RNNs on mixed sequential and non-sequential data

I have a data set that is a bunch of windows, for each window I want to perform regression. The windows themselves have four sequential features that span back about 24 time steps. Additionally each ...
73 views

substring clustering with noise

I have sequence which is a repetition of a few strings. I have identified the start and end markers of these strings in the sequence and now, I want to cluster similar strings together. The problem is ...
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Derive sequencing probabilities from univariate data

Given a variable measured sequentially e.g. -6,-3,0,2,-3,1,-5,7,-47.. etc, what are some methods to derive some reliable sequencing probabilities? e.g. if i-2>0 and i-1 >0 then i>0 etc.
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How to compute expected value?

Hi I am trying to compute this: It's a denominator of ANS function in sequential statistics.The result is: I set "sigma1"=1 and "mi" is considered as a constant.Do you have any idea how to get the ...
69 views

Determining the number of days to reach significance

Apologies for what I think will be a simple question - it has been some years since I've take statistics. I run a business and we are attempting to determine the number of days required to reach a ...
2k views

How to use LSTM/GRU/RNN for sequence classification with Tensorflow/keras? [closed]

I want to use LSTMs and RNNs for sequence classification problem. I have features extracted from video segment of 10 sec @ 30 fps i.e. total of 300 frames. For each frame I have a feature ...
102 views

How can I make a mean sequential estimation?

I am an agronomist trying to estimate the average weight of fruit in a orchard. My first option is to grab 1000 fruit and get their weight mean. But as you can see, if i can get this with less fruits, ...
32 views

Group sequential method subjecting to non-normality

In the context of group sequential methods(GSM) for a clinical trial with two treatment arms, it is usually assumed that data follows normal distribution $N(\mu,\sigma^2)$. Then GSM such as Pocock's ...
27 views

maximum cumulative decision limit

It is well-known that it is problematic to stop an A/B test before we obtain a required number of samples. This website "A/B Testing Rigorously (without losing your job)" explains how to stop safely ...
175 views

How can I solve the sequence prediction problem?

Let's say I'm given a stream of characters, one at a time. Some example strings of characters that could occur might be "01234" or "hello how are". They might even be encodings of waveforms as ...
410 views

High autocorrelation when taking the L-th order of difference of a sequence of independent random numbers

To explain this question in more detail, I'll first elaborate my approach: I simulated a sequence of independent random numbers $X = \{x_1,...,x_N\}$. I then take $L$ times the difference; i.e. I ...
53 views

Terminology for sequential estimation with randomized stopping time

Consider a sequence of i.i.d Bernoulli RV's $\{X_i\}_{i \in \mathbb N}$ with parameter $p$. Based on this sequence we build a sequential estimator of $p$ (using inverse binomial sampling for example). ...
176 views

Testing for Benford Law in real time

Suppose I have data of a certain quantity $X$, given by $x_1,...,x_n$. Now, I take the first digit $d_i$ of each quantity $x_i$, and I want to study the relationship between the empirical distribution ...
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What type of analysis for sequential data can I use to identify patterns in collaborative activities

I have a data set, which is collected every 5 second for a total of one hour using a special type of wearable device. Each data point is the amount of verbal participation ratio (measured as percent) ...
740 views

Bayesian Q-learning

Suppose that, for every state $s$, there is a set of actions $\mathcal{A}(s)$ that can be chosen in that state. Let $Q(s, a)$ denote the expected utility of choosing action $a \in \mathcal{A}(s)$ in ...
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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 ...
507 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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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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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 ...
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 ...