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1answer
53 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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1answer
60 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
59 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
104 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 ...
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0answers
23 views

Probability distribution of distances to micro-cluster centers using particle filtering

Is it possible, using particles filter, to get the probability distribution of distances to cluster centers in an online clustering process, where for each data-point x, if x is close enough to its ...
2
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0answers
59 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
477 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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0answers
145 views

particle filtering importance weights

In theory, 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 ...
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0answers
171 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
186 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 ...
1
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0answers
50 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
214 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
4k 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
316 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
393 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
112 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
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1answer
898 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
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2answers
864 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 ...
21
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1answer
3k 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 ...