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Fitting a Discrete-time survival analysis

I am trying to fit a discrete-time survival analysis using R. My overall goal is to check if the variable pain impacts smoking. Every time I include the variable ...
Gabriel Costa's user avatar
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1 answer
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How to show that a stable discrete stochastic process converges to a stationary process?

So I have a discrete stochastic process defined by $x_{k+1}=Ax_k+Bw_k$ where $w_k$ is zero mean Gaussian white noise with covariance $R_w$, and where $A$ has its eigenvalues in the unit disk. I can ...
Minecraft dirt block's user avatar
3 votes
1 answer
33 views

Discrete vs. Continuous Survival regression - for business case / subscription churn

I'm trying apply a survival analysis to a churn problem - customer subscriptions. There's nothing particularly unusual about these subscription - customers either pay, or leave, monthly, or annually, ...
user45867's user avatar
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0 answers
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Modeling probability of bird species detection across the day

I am looking for guidance on constructing a statistical model for the following problem, motivated by bird watching. There is a very large database of bird "checklists". For the sake of this ...
Aldo Leopold's user avatar
3 votes
3 answers
201 views

Which error bars to use when comparing only two subjects when many replicates?

I want to plot discrete time measurements made for two subjects, but where many cells were observed for each subject in triplicate. I think the experimental unit is the subject, so I should just get a ...
maglorismyspiritanimal's user avatar
3 votes
1 answer
133 views

Is my data interval-censored data or discrete-time data?

I am trying to analyze my data using survival analysis in R and I am curious about how to identify my data. My research is an 11-month longitudinal study, and me and my colleagues collected data for ...
Han's user avatar
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0 answers
55 views

What is the distribution of completed parts by a given machine after t minutes in SimPy's Machine Shop example?

Question You can read the Machine Shop example in the SimPy documentation, however I have tried to put it into its mathematical description below so that reading Python is not necessary. Suppose a ...
Galen's user avatar
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35 views

Combination of a discrete and a continuous Markov Chain in a MCMC

Recently, I've been questioning myself on the possibility of combining a discrete update and a continuous update on a single MCMC. Stephens (2000) in Algorithm 3.2 runs the process for a fixed amount ...
nico's user avatar
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1 answer
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Discrete-time survival model output doesn't match Cox proportional-hazards model - problem with input of data?

I'm trying to construct a discrete-time survival model to analyse some mating data. I've used a Cox proportional hazards model previously but got some input that the discrete-time survival model would ...
Blanca's user avatar
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1 vote
0 answers
73 views

Average time in which a product random variable becomes zero

Im looking for the optimal time in which a process should be cancelled before it results on financial losses. Say M_n=X_n*Y_n-c(n) for for n =1 to 12 which is the number of hours the process gets ...
Vacoiide's user avatar
1 vote
1 answer
654 views

Discrete time survival analysis or Cox regression?

In an RCT, I want to find out whether the treatment (treatment vs control) has an effect on the uptake of aftercare (yes/no + time). I have five measurement points, which are not equidistant (i.e., ...
Sebastian's user avatar
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Basic Kaplan-Meier survival analysis input data interpretation with discrete time periods

I am trying to apply Kaplan-Meier survival analysis from the Reliability package in Python to a problem with discrete time periods, and I'm having some trouble understanding which periods to list ...
Alejandro Erickson's user avatar
2 votes
1 answer
755 views

Survival analysis: difference between GLM clog-log family binomial vs GLM clog-log family Poisson

I'm trying to find ways to do survival analysis on data with asynchronous interval-censored outcomes and time-varying covariates. I know that GLM binomial with a complementary log-log link function ...
Wojty's user avatar
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1 vote
1 answer
154 views

Training discrete time hazard model with xgboost on right censored loan data

I am currently developing a loan default risk model using a discrete time hazard approach with xgboost. The goal is to generate a series of predicted monthly default probabilities using a new ...
tatakae888's user avatar
3 votes
1 answer
214 views

Censoring in a discrete-time hazard model of time-to-drop-out of a clinical trial

I am conducting a discrete-time hazard model where the outcome being analysed is time to drop out of treatment during a 12-week clinical trial examining the effect of an agonist drug on days of ...
llewmills's user avatar
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3 votes
2 answers
1k views

Is is acceptable to use cox proportional hazard regression when time-to-event is a discrete, numeric variable?

I recently submitted a paper where I performed a cox proportional hazards regression model modelling the effect of group allocation in a randomised controlled trial on treatment retention. The event ...
llewmills's user avatar
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1 vote
0 answers
69 views

When are continuous-time models important?

In Econometrics, majority of the models are in discrete-time setting, whereas when you move on to quantitative finance, continuous-time models are most prevalent. I get the theory and idea behind ...
Carl's user avatar
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Determine order of events happening in discrete timespace

At $t=0$ I have a certain (active) population, lets say 1,000 customers. In each time step I expect a certain amount I have a probability of death of 1% and a prepayment rate of 5%. At the end of each ...
Siddler's user avatar
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Probability $X_n=k$ for a Markov Chain over the integers

Let $\{X_n\}$ be a Markov chain with state space $\mathcal{S}=\mathbb{Z}$, and $X_0=0,$ and $p_{0,1}=p_{0,-1}=1/2,$ and $p_{i,i+1}=1$ for all $i \ge 1,$ and $p_{i,i-1}=1$ for all $i\le -1.$ The ...
Trevor Mason's user avatar
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0 answers
107 views

Proving positive recurrence for a finite state space DTMC

Let $$P = \begin{pmatrix} 0.3 & 0.5 & 0 & 0 & 0 & 0.2 \\ 0 & 0.5 & 0 & 0.5 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0.3 & 0 & 0 &...
hkj447's user avatar
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4 votes
1 answer
728 views

Calculating the expected number of visits to a state by a DTMC

Suppose we have a DTMC $X$ : $\{X_n : n = 0, 1,2,\dots\}$, a transition probability matrix $P$, and state space $S = \{1,2,3\}$. Suppose I want to calculate the expected amount of times we visit state ...
hkj447's user avatar
  • 447
3 votes
1 answer
223 views

Conditional probabilities with Discrete Time Markov Chain non-perishable inventory

Suppose $\{X_n : n =0,1,2,\dots \}$ is a DTMC that represents the inventory level at the end of day $n$. We have inventory policy $(2,4)$, i.e., if $X_n < 2$, we order enough units to have ...
hkj447's user avatar
  • 447
4 votes
1 answer
231 views

What statistical tests allow for a comparison of the "roughness" of discrete functions?

I have a data set of the revenues of 10 different large companies from the years 2000 through 2019. Here they are all plotted in one graph. The y-axis has a unit of billions of Euros:                  ...
Max Muller's user avatar
1 vote
1 answer
45 views

Using test hypothesis to prove I ran a sufficient number of simulations

I simulated a system using discrete-events simulation, more particularly next-event simulation. The system is M/M/1 (infinite FIFO waiting room). Whenever the system is jobless, the server shutdowns. ...
Adrien H's user avatar
  • 111
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0 answers
45 views

Discrete Time Logistic

I'm trying to use panel survey data to determine married event in life using discrete logistic regression. However, some observations enter the survey not the same time as other i.e. some enter in ...
Natacha's user avatar
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0 answers
97 views

Generating correlated discrete random variables

Suppose that we have $q_t \in \{-1, 1\}$ where $\mathbb{P}(q_t = -1) = \mathbb{P}(q_t = 1) = \frac{1}{2}$. Further, assume that \begin{align} Cor\left( q_t, q_{t-k} \right) = \begin{cases} ...
Stéphane's user avatar
  • 258
3 votes
1 answer
926 views

Z transform of $ 2^{-|n|} $

Dears, I'm trying to compute the Z-transform of $$ x(n) = 2^{-|n|} $$. My procedure is as follows: Using definition of Z transform: $$ X(z) = \sum_{n=-\infty}^{\infty}2^{-|n|} z^{-n} = \sum_{n=-\infty}...
Julius Max's user avatar
2 votes
1 answer
34 views

Variable data measured discretely with poor resolution

Is there an appropriate method for estimating variation when variable data is measured discretely where the resolution is poor. Here's an example: You are looking at how long it takes for a solid to ...
KoldBeans's user avatar
3 votes
0 answers
178 views

Negative Binomial vs. Discrete Survival

I am trying to model a discrete duration variable (number of weeks) and I am not sure which model to use. Many would argue that durations are modeled using survival models. However, in J. Hilbes ...
C. Sebastian's user avatar
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0 answers
39 views

Any methods for clustering short time series data

I have around 200 different sets of time series data with a semi-annual periodicity. The length of each series varies from 1 to 6 years. I essentially want to build unsupervised clusters by grouping ...
Sid's user avatar
  • 21
2 votes
0 answers
335 views

Proving/showing that the Markov property holds in discrete time Markov chain example

I am currently studying the textbook Introduction to Modeling and Analysis of Stochastic Systems, Second Edition, by V. G. Kulkarni. In a section on discrete-time Markov chains, the author presents ...
The Pointer's user avatar
  • 2,096
1 vote
1 answer
2k views

Rows and columns of the one-step transition probability matrix

I am currently studying the textbook Introduction to Modeling and Analysis of Stochastic Systems, Second Edition, by V. G. Kulkarni. In a section on discrete-time Markov chains, the author introduces ...
The Pointer's user avatar
  • 2,096
1 vote
1 answer
2k views

Regression analysis with small data set

We've performed a regression analysis with 14 data points (Y's) that originate from 9 X's (plant batches were split up). I'm well aware that this is a small data set and there are caveats. However, ...
Beerhunter's user avatar
2 votes
1 answer
90 views

Statistical modeling multidimensional discrete system

I have a system which its state is described by a vector $v=(a, b, c)$, where $a$, $b$ and $c$ can take any value between $0$ and $100$ and where $a+b+c <= 100$. I have observations of the state ...
Giulia Martini's user avatar
0 votes
1 answer
100 views

Detecting Significant Changes in Time Series

I’m hoping someone might be able to point me in the right direction for this problem. I’ve anonymised the problem by describing it in terms of supermarket purchase data rather than the real context so ...
soundofsilence's user avatar
1 vote
1 answer
357 views

Posterior distribution from piecewise likelihood

Consider a hierarchical Bayesian model for analysing data from an inhomogeneous Poisson process that we observe in discrete time. Let $Y_i, i = 1,...,n$, be the number of events occurring in the time ...
Grautus's user avatar
  • 11
1 vote
0 answers
83 views

Modeling Time in the Discrete Time Analysis using Left-truncated Data

I am doing multiple-spell, discrete-time analysis to examine factors shaping time to exiting a renter spell, with time-varying covariates at monthly interval. My data has left-truncated spells, ...
Huiyun Kim's user avatar
-1 votes
1 answer
756 views

INAR(1) simulation in R [closed]

How do we simulate values of $Y_t$ for a maximum value of $t=60$ when we have an INAR(1) process as follows: $Y_t=ρ^*Y_{(t-1)}+R_t$ where $t$ takes values from 1 to 60, $ρ=0.3,0.8$, $ρ^*$ is ...
Shifa's user avatar
  • 1
0 votes
1 answer
415 views

Simulating a (discretized) Cox process via binomial sampling

Let X be a Cox process (doubly-stochastic Poisson process) driven by a Poisson process with fixed intensity(rate) $\lambda=50$ , and choose some small time interval $dt=0.01$ . Is the proper way to ...
crow's user avatar
  • 1
0 votes
1 answer
162 views

How to recognize an ARMA process?

By looking at the autocovariance, how could you recognise what discrete model (MA(q), AR(p), or ARMA(p,q)) is more appropriate to describe your data?
ilciavo's user avatar
  • 101
4 votes
2 answers
674 views

Simulation -Discrete Time Hazard model

How we can simulate the survival times for fitting discrete time hazard model?
has87's user avatar
  • 41
7 votes
2 answers
3k views

How to forecast integer time series in R?

For a while now I used to forecast integer/count time series as I would do for any other continuous time series, meaning : I use models like ARIMA, ETS, THETA, TBATS ... And then I simply round the ...
Taha 's user avatar
  • 183
3 votes
0 answers
94 views

best statistical approach to study the time evolution of clustering in a data set

I am using a stochastic method for the clustering of a data set. The number of clusters that this approach returns, can differ in each iteration. On the other hand, I would like to study the evolution ...
Dalek's user avatar
  • 117
7 votes
0 answers
130 views

Is average stopping time a continuous function of Bernoulli parameter?

Consider an infinite sequence $X = (X_i)_{i \in \mathbb N}$ of i.i.d. Bernoulli random variables with (unknown) parameter $p \in (0,1)$, and let $N$ be a stopping time on $X$. Is it always the case ...
Luis Mendo's user avatar
  • 1,099
2 votes
0 answers
30 views

Gaussian random variable over multiple periods

Let's assume that : $$X_0=X_0$$ $$X_1=(1+R_1)*X_0$$ $$...$$ $$X_N=(1+R_N)*X_{N-1}$$ where $R_i \sim \mathcal{N}(0,u^2)$. I am trying to compute the probability $P(X_N < a)$. How accurate is it to ...
Yuri's user avatar
  • 41
0 votes
1 answer
3k views

Linear mixed model: Time as continuous or discrete variable?

I am analysing a dataset from a randomised controlled trial (2 treatment groups) with measurements at 3 time points (weeks 0, 1 and 8). I am struggling with whether to analyse this with the three time ...
PeterS's user avatar
  • 11
0 votes
1 answer
198 views

Probability distribution for day of the year [closed]

"Day of the year" is an integer from 1 to 365, indicating the day within the year. I'd like to model the day of the year that a particular event occurs. The event must occur between day 100 and day ...
Jessica's user avatar
  • 1,251
5 votes
1 answer
3k views

discrete time survival analysis

I would greatly appreciate if you could let me know how to do discrete time survival analysis with time varying covariates. Some part of my data set is as follows: ...
ebrahimi's user avatar
  • 291
1 vote
1 answer
1k views

parametric survival regression and discrete time survival regression

I would greatly appreciate if you could let me know how to choose among different parametric distributions including gama, Weibull, lognormal, loglogistic and etc for panel (time series cross ...
ebrahimi's user avatar
  • 291
0 votes
0 answers
30 views

Looking for suitable method to update predictions

consider an e-commerce website which daily updates their transaction data. I take interest in predicting the revenue an account generates over a certain time range, say until the fifth year after the ...
MaHo's user avatar
  • 391