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0answers
15 views

How to find the pdf of a time-dependent parameter in a linear regression model with drift?

Suppose there exists a simple linear equation, where the dependent variable y(time series; measurements available) depends on x1 and x2. If the parameter multiplier of x2 is time dependent and the ...
0
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1answer
110 views

Particle filter (sequential Monte Carlo) for a non-Gaussian hierarchical model

I have the following, which I am attempting to model with a particle filter. \begin{align*} y_{i,t}&\sim\mathrm{Poisson}\left(\lambda_{i,j,t}\right)\\ ...
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0answers
16 views

Is it a problem to have non homogeneus sampling time in Bayes Filter?

I have a doubt related with Recursive State Estimation using Bayes Filter (actually using an aproximation to that through Particle Filters) This algorithm is explained in several sources with ...
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0answers
37 views

Covariance update from Jacobian of transition function

In this paper on particle filtering with gradient descent, the authors sample Xk+1 through gradient descent, then update the covariance matrix P associated with Xk+1 as follows: Pi+1(k + 1|k + 1) = ...
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0answers
22 views

Showing that the variance increases with the dimension of the random vector

This is actually related to a more complex question; but I want to re-ask it by trying to simplifying it as possible: 1- We have $n$ dimensional functions of the form $f_n:\mathbb{R}^{n} \mapsto ...
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0answers
19 views

How to show that the variance of Sequential Importance Sampling estimates increase with the dimension?

I am trying to understand the Particle Filter and the motivation to use it over the regular Sequential Importance Sampling. As far as I understand until now: 1- We try to estimate the expectation of ...
0
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1answer
75 views

Likelihood score function 101

I have some trouble with score functions in likelihood calculation. I'm not good at statistics or probability, so I'm still confused on formalism and mathematical-probabilistic language. Some ...
2
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2answers
101 views

Particle filters and loopy belief propagation

I want to implement a loopy belief propagation algorithm for factor graphs with continuous variables and messages represented using particles, that is vectors of samples for an empirical ...
5
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1answer
83 views

How is the number of particles decided in particle filtering?

Say the observations are $x_i$ and the states are $y_i$ in a sequential model. I understand that particle filtering works by generating "particles" from $p(y_i | x_1,\ldots,x_i)$ for approximating ...
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0answers
128 views

How to generalize Particle Filters (w.r.t. multiple states)

I'm using particle filters for inference in a hidden markov model with an infinite state-space. My current state-variable is multidimensional and there are interdependencies between some dimensions. I ...
2
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0answers
66 views

Rao-Blackwellising state space for a (marginalised) particle filter

I am starting to look at particle filtering for a problem that I have. In particular, I would like to reduce the dimensionality of the particles. The model that I have is able to be partitioned. ...
1
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1answer
729 views

Time series forecasting using particle filter

I have searched high and low for a practical example of using a particle filter to assist with short term price forecasting using the local trend of a time series. Could someone please share how a ...
1
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1answer
201 views

Particle filtering importance weights

In theory, the importance weight of a particle has to be a probability, i.e., $w_{s_t} = p(z_t|s_t)$. My question is: Since we eventually normalize the weights with their sum and get a probability ...
7
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0answers
220 views

Rao-Blackwellization of sequential Monte Carlo filters

In the seminal paper "Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks" by A. Doucet et. al. a sequential monte carlo filter (particle filter) is proposed, which makes use of a ...
4
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1answer
225 views

Using a particle filter for robot localization

I have a robot that has a GPS and velocity sensors. The GPS updates roughly every 1-2 seconds. I've been playing around with a Kalman filter that has been working pretty well. I just learned and ...
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0answers
53 views

A motion model to track a moving object using the condensation algorithm

I have implemented the condensation algorithm in order to track a moving object in video sequences, however the predictive step does not work properly, so the samples moves excessively compared to the ...
1
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1answer
236 views

clustering with particle filters

Suppose we want to cluster a data stream of unknown number of clusters, and estimate them using particle filters. With particle filters, we need to know $P(x_t | x_{t-1})$ and $P(z_t | x_t)$ (where z ...
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3answers
5k views

Very simple particle filters algorithm (sequential monte carlo method) implementation

I'm interested in the simple algorithm for particles filter given here. It seems very simple but I have no idea on how to do it practically. Any idea on how to implement it (just to better understand ...
2
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1answer
336 views

Forecasting a “chaotic” time series

Here are four graphs, 1, autocorrelation, autocovariance, partial-correlation and cross-correlation calculated from a time series are given. 2, The time series I need to do some predictions on ...
3
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1answer
489 views

Maximum likelihood estimation procedures for state-space linear models

State-space models are represented by a state equation and an observation equation (or system of equations to be more precise). These equations are parametarized by components including a transition ...
0
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1answer
121 views

Sense of correlation coefficient matrix of particle filter's parameters

I am using a particle filter to estimate the parameters($\Phi_{n\times1}$) of a non-linear model. Say my input (observations) is $t=1:k$, I will have a vector of length $k$ for each of the parameter ...
3
votes
1answer
1k views

Particle filter in Matlab - what is going wrong?

I posted this question on Electronics.Stackexchange and someone told me I'll be better off posting it here. Its an implementation of the Particle Filter using MATLAB but the results never follow the ...
6
votes
3answers
993 views

Estimating parameters of a dynamic linear model

I want to implement (in R) the following very simple Dynamic Linear Model for which I have 2 unknown time varying parameters (the variance of the observation error $\epsilon^1_t$ and the variance of ...
22
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1answer
5k views

What is the difference between a particle filter (sequential Monte Carlo) and a Kalman filter?

A particle filter and Kalman filter are both recursive Bayesian estimators. I often encounter Kalman filters in my field, but very rarely see the usage of a particle filter. When would one be used ...