# Questions tagged [sequential-analysis]

Hypothesis testing without a fixed sample size.

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84 views

### How to distinguish between two biased coins

I have two very biased coins: The first coin (C1) lands on heads 95% of the time. The second coin (C2) lands on heads only 1% of the time. One of the coins has been selected and I want to determine ...
48 views

### Term for when hypothesis testing is conducted repeatedly until an interesting result is found?

What is the term for when, through accident or intent, many hypothesis tests are conducted until an 'interesting' result is found? That is, the experiment (or variations on it) are repeated until a ...
28 views

### In R, why do the p-values from anova() change when you add more predictors?

When conducting linear regression in R, I am trying to understand how certain p-values are calculated and what they represent. So far this is my understanding: The p-values from summary() correspond ...
98 views

### Equivalence of Contextual Bandit formulations

I find two different type of Contextual Bandit problem formulations in the literature: Definition 1: (https://hunch.net/~jl/projects/interactive/sidebandits/bandit.pdf) In a contextual bandits problem,...
54 views

### Is sequential probability ratio test bayesian or frequentist or both?

Is sequential probability ratio test bayesian or frequentist or both? Is there a way to implement a bayes decision rule with "sprt"?
47 views

### How long will it take to detect that the parameters in a normal distribution have changed, given online sampling?

Let's say, for instance, you have normally distributed data that is coming in one at a time. At some unknown instance, the distribution parameters (mean and variance) change. Assuming that there is ...
15 views

### Markov model for multiple cases

I was wondering if the markovchain r package can handle multiple cases with unequal length of sequences. If so, how to perform that in r? If not, any other markov packages in r can do that? Many ...
18 views

### Early stopping in wilcoxon signed rank test?

I have decided to acquire N joint samples of variables X and Y (for example, N=200), and test whether their means are different using the signed-rank test. I will repeat this procedure many times, ...
198 views

### O'Brien Fleming Interim Analysis Interpretation with PROC SEQDESIGN

Quick question about the output of PROC SEQDESIGN. I was playing around with the O'Brien Fleming method trying to understand how we can interpret the results spit out by SAS for a mock study with ...
48 views

### How to recursively filter sequential predictions of binary classifier?

Problem My goal is to estimate binary state using entire observation history. Observations are coming sequentially with fixed interval (~1 sec). I have xgboost model which predicts the state given a ...
86 views

### To improve the posterior belief receiving a time-series from a fixed data source

Let data $\mathbf{X}\in \mathbb{R}^d$ come from one of the $K$ possible sources $\mathsf{S}\in \{1,2,...,K\}$. The true $\mathsf{S}$ is unknown but it is fixed. The main task is to infer the true ...
25 views

### extension of sequential probability ratio tests to particle filters?

I've been wondering if there are extensions of the sequential probability ratio test to account for particle filters. I ask because, in my research, I'm working with distributions that cannot be ...
30 views

### Binary Sequence Prediction Model with Time dependant features

I got a very long sequence of binary items (0 or 1). Each item is associated to a timestamp. For example : ...
300 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 ...
26 views

### 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 ...
58 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 ...
45 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 ...
25 views

### 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 ...
231 views

### Reverse the shuffling phase

It is very convenient to have sklearn library to split and shuffle the data with ...
95 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. ...
13 views

### 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 ...
60 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%, ...
34 views

### 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 ...
252 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. ...
26 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 ...
569 views

### 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% ...
25 views

### 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 ...
304 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. ...
51 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 ...
47 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, ...
622 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 ...
192 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 ...
591 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 ...
27 views

### 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 ...
201 views

### 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 ...
127 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 ...
17 views

### 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.
65 views

### 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 ...
82 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 ...
137 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, ...
36 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 ...
28 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 ...
189 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 ...
548 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 ...
57 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). ...
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 ...