# Questions tagged [linear-dynamical-system]

Dynamic linear models refers to modeling problems where coefficients (as in regression) are allowed to vary with time. This is the so called state-space approach.

27 questions
Filter by
Sorted by
Tagged with
18 views

### Compute initial value in Kalman Smoother

Suppose we observe data $y_t$ and $X_t$ from $t=1,...,T$ and want to estimate a dynamic linear model of the form $y_t = X_t\beta_t + \epsilon_t$ $\beta_t = \beta_{t-1} + \omega_t$ where $\epsilon_t$...
26 views

### Examples of Real Applications for Time-series with Continuous-valued Targets and Continuous-valued Observations

Suppose that we are interested in estimating continuous-valued targets $y_t$ from continuous-valued observations $x_t$ over discrete time steps $t = \{1,2,3,\dots,T\}$. Could you give me some ...
11 views

### Online learning from a Bayesian Perspective in a State-Space Model

I'm trying to learn how to do online learning from a Bayesian Perspective. My main interest is to use it for a State-Space model. However, any explanation/reference in a different context, which may ...
99 views

20 views

### How to model this as a POMDP?

I would like to fit a DLM to a dataset in R but I don't know the underlying transition matrices between states nor do I have a guess for the emission matrix (given a state, what responses should I see)...
39 views

### Understanding the DLM

The DLM model in my notes is described as: $f_k(\theta,u)=F_k\theta+u$ and $h_k(\theta,v)=H_k\theta+v$, where $F_k$ is a $d\times d$ matrix and $H_k$ is a $d'\times d$ matrix, respectively called ...
94 views

### How to numerically solve a matrix differential equation in R? [closed]

I have interest in using the R language and environment to numerically solve a system of linear ordinary differential equations. The numerical solver, deSolve, ...
27 views

### How important is research on model selection methods in Statistics?

My question is nothing technical. I just wanted your opinion on how important is the model selection problem in the field of Statistics considering the age of big data. Are the current methods such as ...
241 views

I have a state space model of the form \begin{align} x_{t+1} &= Ax_t + Bu_t + w_t\\ y_t &= Cx_t + Du_t + v_t \end{align} where $u$ is the exogenous input. Also, $w_t \sim N(0, Q)$ and $v_t \... 0answers 78 views ### How does one approximate$\mu$and$\sigma$in an arithmetic Brownian motion using a Kalman filter? My concern arises from the fact that in the following system:$x_k = (\mu, \sigma)^T = x_{k-1}Y_k = Y_{k-1} + \mu + \sigma Z_k \quad Z_k \sim N(0,1)$that I cannot separate the states I want to ... 0answers 360 views ### How to ensure covariance matrix is positive semi definite in linear dynamical model learning? I am trying to learn a linear dynamical model for a data using expectation-maximization algorithm. The model is defined as follows: $$x_0 \sim \mathcal{N}(\mu_0 ,\Sigma_0)$$ $$x_{t+1} = Fx_t + w_t, \... 1answer 53 views ### Help on statistical modeling of pedestrian flow in subways I'm a New Yorker and take the subways every day. I have a growing interest in understanding the distribution of paths people take on the subways to work every day. I.e. if there are n subway ... 0answers 35 views ### Determining state space for a dynamic linear model Are there any techniques for determining a good state space to use for a dynamic linear model? I'm trying to model ad-clicks with observed values being whether a user clicked on an ad and I'm curious ... 0answers 60 views ### What should be the termination criteria for my problem with a closed loop system identification? I have modelled a dynamic system which needs to be validated against test data. A closed loop system identification process is used for the validation. In this process, the time domain simulation of ... 0answers 191 views ### How to add stochastic drift in dynamic linear model? As I'm not able to comment (yet), my question follows the one raised by @mzuba here I would like to use the DLM R package to model the local linear trend model, which unlike mzuba specified, has a ... 0answers 35 views ### Predictions in a control loop like airconditions I wonder if there are special things to consider with predictions in a control loop, e.g. An airconditioner trys to hold the target temperature at 20 degrees. I want to predict the energy consumption,... 1answer 414 views ### How to estimate coefficients of a state space when relevant data is provided? I have a state space system \dot{x} = Ax + Bu y = Cx I know C matrix exactly. And A matrix looks something like this, and some of the x_{ij} in A are known as well. Same goes with B. \... 1answer 124 views ### Help in CRLB for linear model The model is an FIR (MA) filter$$x(t) = h_1 u(t-1) + h_2 u(t-2) + u(t) \tag{1} y(t) = h^T x(t) + v(t) \tag{2}$$u(t) is a pseudo-random binary signal (PRBS) that excites/ drives the ... 1answer 93 views ### Simulating a dynamical system Basically I need to replicate Hartley's 'A User's Guide to Solving Real Business Cycle Models' . Specifically (to make question relevant to stats.stackexchange), I want to simulate the dynamical ... 0answers 156 views ### State Space model question [closed] I am looking for some help with estimating Space state model of this form: r_{t} = r^{*}_{t} + \pi + \varepsilon_{1} R_{t}= r^{*}_{t} + \alpha + \pi + \varepsilon_{2} r^{*}_{t} = r^{*}_{t-... 2answers 2k views ### Forward Filtering Backwards Sampling (FFBS) and Look-Ahead Bias Assumptions / Context: Let's assume that I have data that can be modeled as a dynamic linear model. To estimate the parameters (e.g., covariance matrix of the state/system equation), I use a Gibbs ... 1answer 353 views ### Model selection and parameter estimation in forecasting with a Dynamic Linear Model I am implementing a general purpose prediction tool for time series. I want to tolerate missing values, so I decided to settle for DLMs. To make it as relevant as possible on a large number of ... 0answers 52 views ### Estimation from two observations [closed] Suppose there are two vector signals x, z. The observer 1 receives a linear version of x plus Gaussian noise. Observer 2 receives a linear sum of both x and z plus Gaussian noise as shown ... 0answers 69 views ### How to include prior knowledge that a model might be able to figure out itself I have a problem where I want to predict the outcome of a sequence given another sequence online. Let (x_1, x_2, ... x_T) be denoted by x_{1:T}, then I am estimating:$$ p(y_T|x_{1:T})$$where$...
I am interested in finding the relation between two (possibly multi dimensional) time series $x_{1:T}$ and $y_{1:T}$. I wonder how I can do that with a linear dynamical system/Kalman filter. My ...