ARMCMC: Online Model Parameters full probability Estimation in Bayesian Paradigm
Authors: Pedram Agand
Mo Chen
Hamid D. Taghirad
Venue:  (2021)
Keywords: Bayesian estimation
Full probability distribution
MCMC
Hybrid non-Gaussian system

Abstract: Although the Bayesian paradigm provides a rigorous framework to estimate the full probability distribution over unknown parameters,  its online  implementation can be challenging due to heavy computational costs. This paper proposes Adaptive Recursive Markov Chain Monte Carlo (ARMCMC) which estimates full probability density of model parameters while alleviating  shortcomings of conventional online approaches. These shortcomings include: being solely able to account for Gaussian noise, being applicable to systems with linear in the parameters (LIP) constraint, or having requirements on persistence excitation (PE). In ARMCMC, we propose a variable jump distribution, which depends on a temporal forgetting factor.  This allows one to adjust the trade-off between exploitation and exploration, depending on whether there is an abrupt change to the parameter being estimated. We prove that ARMCMC requires fewer samples to achieve the same precision and reliability compared to conventional MCMC approaches.  We demonstrate our approach on two challenging benchmark:  the estimation of parameters in a soft bending actuator and the Hunt-Crossley dynamic model. Our method shows at-least 70% improvement in parameter point estimation accuracy and approximately 55% reduction in tracking error of the value of interest compared to recursive least squares and conventional MCMC.

Under review as a conference paper at ICLR 2021
ARMCMC: ONLINE MODEL PARAMETERS FULL PROBABILITY ESTIMATION IN BAYESIAN PARADIGM
Anonymous authors
Paper under double-blind review
ABSTRACT
Although the Bayesian paradigm provides a rigorous framework to estimate the full probability distribution over unknown parameters, its online implementation can be challenging due to heavy computational costs. This paper proposes Adap- tive Recursive Markov Chain Monte Carlo (ARMCMC) which estimates full probability density of model parameters while alleviating shortcomings of con- ventional online approaches. These shortcomings include: being solely able to account for Gaussian noise, being applicable to systems with linear in the param- eters (LIP) constraint, or having requirements on persistence excitation (PE). In ARMCMC, we propose variable jump distribution, which depends on tempo- ral forgetting factor. This allows one to adjust the trade-off between exploitation and exploration, depending on whether there is an abrupt change to the parame- ter being estimated. We prove that ARMCMC requires fewer samples to achieve the same precision and reliability compared to conventional MCMC approaches. We demonstrate our approach on two challenging benchmark: the estimation of parameters in a soft bending actuator and the Hunt-Crossley dynamic model. Our method shows at-least 70% improvement in parameter point estimation accuracy and approximately 55% reduction tracking error of the value of interest com- pared to recursive least squares and conventional MCMC.
INTRODUCTION
Bayesian methods are powerful tools to not only obtain numerical estimate of parameter but also to give measure of confidence (Kušmierezyk et al. 2019 Bishop 2006 JJhho et al. (003)). In particular, Bayesian inferences calculate the probability distribution of parameters rather than point estimate, which is prevalent in frequentist paradigms (Tobar 2018). One of the main advantages of probabilistic frameworks is that they enable decision making under uncertainty (Noormohammadi: Asi & Taghirad| 2019). In addition, knowledge fusion is significantly facilitated in probabilistic frameworks; different sources of data observations
be combined according to their level of certainty in a principled manner (Agand & Shoorehdeli, 2019). Nonetheless, Bayesian inferences require high computational effort for obtaining the whole probability distribution and prior general knowledge on noise distribution before estimation.
One of the most effective methods for Bayesian inferences is the Markov Chain Monte Carlo (MCMC) methods. In the field of system identification, MCMC variants such as the one recently proposed by Green (2015) are mostly focused on offline system identification. This is partly due to computational challenges which prevent real-time use (Kuindersma et al. 2012). The standard
MCMC algorithm not suitable for model variation since different candidates do not share the same parameter set. Green 1995) first introduced reversible jump Markov chain Monte Carlo (RJMCMC) as method address the model selection problem. In this method, an extra pseudo random variable is defined to handle dimension mismatch. There are further extensions of MCMC in the literature, however, an online implication of it has yet to be reported.
Motion filtering and force prediction of robotic manipulators are important fields of study with inter-
esting challenges suitable for Bayesian inferences to address (Saar et al. 2018). ). Here, measurements inherently noisy, which is not desirable for control purposes. Likewise, inaccuracy, inaccessibil- ity, and costs are typical challenges that make force measurement not ideal for practical use (Agand) et al. 2016). Different environmental identification methods have been proposed in the literature

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for linear and Gaussian noise (Wang al. 2018): however, in cases of nonlinear models like Hunt-
Crossley that does not have Gaussian noise (c.g. impulsive disorder), there is no optimal solution for the identification problem. Diolaiti et al. (2005) proposed double-stage bootstrapped method for online identification of the Hunt-Crossley model, which is sensitive to parameter initial conditions.
Carvalho & Martins (2199) proposed method to determine the damping term in the Hunt-Crossie
model. A neural network-bbseed approach was introduced to control the contac/noon-onntac Hunt-
Crossley model in (Bhasin al. 2008
This paper proposes a new technique, Adaptive Recursive Markov Chain Monte Carlo (ARMCMC), to address address certain weaknesses of traditional online identification methods, such as only being appllicable to systems Linear in Parameter (LIP), having Persistent Excitation (PE) requirements, and assuming Gaussian noise. ARMCMC is an online method that takes advantage the previous posterior distribution, given that there is no sudden change in the parameter distribution. To achieve this, we deñne new variable jump distribution that accounts for the degree of model mismatch using a temporal forgetting factor. The temporal forgetting factor is computed from a model mis- match index and determines whether ARMCMC employs modification or reinforcement to either restart or refine parameter distribution. As this factor is a function of the observed data rather than a simple user-defined constant, it can effectively adapt to the underlying dynamics of the system. We demonstrate our method using two different examples: soft bending actuator and Hunt-Crossley model and show favorable performance compared to state-of-the-art baselines.
The rest of this paper is organized as follows: In Sec. 2, introductory context about the Bayesian approach and MCMC is presented. Sec 3 is devoted to presenting the proposed ARMCMC approach in step-by-step algorithm. Simulation results on soft bending actuator with empirical results on reality-based model of a soft contact environment capturing Hunt-Crossley dynamic are presented in Sec. 4. Lastly, the final remarks and future directions are concluded in See 5.
PRELIMINARIES
2.1 PROBLEM STATEMENT
In the Bayesian paradigm, estimates of parameters are given in the form of the posterior probabil- ity density function (pdf); this pdf can be continuously updated as new data points are received. Consider the following general model:
= F(X,)) 0) +v,
(1)
where Y, Xx 0, and v/ are concurrent output, input, model parameters and noise vector, respectively.
To calculate the posterior probability, the observed data along with a prior distribution are combined via Bayes' rule (Khatibisepehr et al. (2013). The data includes input/output data pairs (X, Y). We
will be applying updates the posterior pdf using batches of data points; hence, it will be convenient to partition the data as follows:
D ((XY)).. (), (X, y)
where N₂- = TT/T is the number of data points in each data pack with T,To being the data and algorithm sampling times, respectively. This partitioning is convenient for online applications, as D should have been previously collected so that the algorithm can be executed from fm to f. +
N. 1 1 or algorithm time step t. Ultimately, inferences are completed at t,, +N, 22 Fig. D Iillustrates the timeline for the data and the algorithm. is worth mentioning that the computation can be done in parallel by rendering the task of the adjacent algorithm step (e.g. phase A of algorithm I, phase B of algorithm / 1 and phase C of algorithm / - 2 can all be done simultaneously) According to Bayes' rule and assuming data points are independent and identically distributed (iiid) in equation] I we have
P(D'10 DC P(( D1-1) Di-11)00
D'))
where He denotes the parameters at current time step. P D(-1) is the prior distribution over parameters, which is also the posterior distribution the previous algorithm sampling time. P(D'(0' DD-1) is the likelihood function which is obtained by the one-step-ahead prediction:
d- F(D .0')
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interoa Incerval
Ingortttonn
Data
6m
Phose:
time
Figure 1:
Timeline for data and different phase of ARMCMC algorithm. For algorithm at time
Phase (A) Data collection [pack N₂ data points], Phase (B) Running [apply the method on the data
pack], (C) Execution [update the algorithm results parameters].
where y-llt1 is the prediction of the output in 11. If the model in 4 is valid, then the difference between the real output and predicted should be measurement noise, (i.e., yd prljt11 1\).
Therefore, the model parameter may be updated as follows:
Im +NN+++
P( ('-1)
II fm
-
(5)
where Pe is the probability distribution of noise. Note that there is no restriction on the type of noise probability distribution.
Remark 1: As it was mentioned before, there is no need to know the exact probability distribution of noise. This probability distribution can be simply substituted with Gaussian distribution, if one has minimal knowledge of the mean and variance of the data which can be easily obtained with preprocessing (Bishop. 2006).
2.2 MARKOV CHAIN MONTE CARLO
MCMC is often employed compute the posterior pdf numerically. The multidimensional inte- gral in 33 is approximated by samples drawn from the posterior pdf. The samples are first drawn from different distribution called proposal distribution, denoted q(-), which can be sampled easier compared to the posterior. Brooks et al. (201T) discuss different types of MCMC implementations which may employ various proposal distributions and corresponding acceptance criteria. The main steps of the Metropolis-Hastinng algorithm are listed as follows (Ninness & Henriksen, 2010):
1. Set initial guess Ag while P(folY) > for iteration k
2. Draw candidate parameter Pend. at iteration k, from the proposal distribution, g(Oend (00emnn(@k1) (
3. Compute the acceptance probability,
a( min {1, D)g (eea) )
(6)
P(0x-1 D)q (Bend (e-n
4. Generate a uniform random number 7 in [0, 1].
5. 'Accept' candidate if S a and 'ignore' it if y > a.
6. Set iteration to & and go step 2.
2.3 PRECISION AND RELIABILITY
Two important notions in probabilistic framework to compare results are precision (c) and reliability (0). The former represents the proximity of sample to the ground truth, and the latter represents the probability that an accepted sample lies within of the ground truth.
Lemma: Let Ps be k samples from MCMC, and IE(P;) denote its expected value. According to Chernoff bound (Tempo et al. 2012), given 6, & [0, 1]. the number of samples (k) satisfies
2
k 2
log(
(7)
2
then Pr B(Pp) se 28.
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Algorithm 1 ARMCMC
Assumptions: 1) roughly noise mean (H₂) 2) roughly noise variance (o,,) 3) desired precision and reliability (cg: 6n) 4) desired threshold for model mismatch (Sra)
Goul: Online calculation of parameters posterior distribution given the consecutive I-th pack of
data (P()))D*)
Initialization: Prior knowledge for 0%. n=0
Consider desire precision and reliability (c, d) repeat
Put tu = n N₂ + from n++
Add new data pack dataset D
Model mismatch index: Ç² from (10)
if Ç Sah then
Reinforcement: set prior knowledge equal to the latest posterior of previous pack Temporal forgetting forgetting factor: X from
else
Modification: set prior knowledge 07
Temporal forgetting factor: X 0
end if
Set minimum iteration kmin from 12
for to kmaz do
Proposal distribution:
draw X ~ (0,
Variable jump distribution: (-) from 8
Draw 0% ~ G))
Acceptance rate: a()) from (6)
Draw y ~ (O)
if y S a then
'Accept' the proposal
end if end for
Wait to build D 1- (algorithm sample time) until No data is obtained
3 ARMCMC ALGORITHM
At each time interval, ARMCMC recursively estimates the posterior distribution by drawing sam- ples. The number of samples drawn constrained by the desired precision and reliability, and the real-time requirement. On the other hand, the maximum number of data points in each data pack, N,, is limited by the frequency of model variation, and the minimum is confined by the shortest required time such that the algorithm is real-time We propose variable jump distribution that en- ables both enriching and exploring. This will necessitate the definition of the temporal forgetting factor measure reflect current underlying dynamics of the data. In other words, this parame- ter will show the validity of the previous model for the current data. We also prove that ARMCMC achieves the same precision and reliability with fewer samples compared the traditional MCMC. Algorithm summarizes ARMCMC.
3.1 VARIABLE JUMP DISTRIBUTION
We propose variable jump distribution (also known as a proposal distribution) to achieve faster convergence, thereby enabling real-time parameter estimation:
[P(O--ID--)) (N(UD.O))
d < X A X
(000000))))
(8)
where 05- the (A 1) parameter sample which is given by the t-th data pack throughout the MCMC evaluation. Averaging the second half of this quantity will construct 0¹. P(@t-1| ( is the posterior distribution the parameters at the previous algorithm time step, and N NHu,. o.) is a Gaussian distribution with uu, a. computed using sample-based mean and variance of 1
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The hyperparameter X (temporal forgetting factor), is an adaptive threshold for the t-th pack that takes inspiration from in the classical system identification terminology; regulates how previous knowledge affects the posterior distribution. Smaller values of X' intuitively means that there may be a large sudden change in 0, and thus more exploration is needed. Conversely, larger values of X is appropriate when is changing slowly, and thus previous knowledge should be exploited. As more data is obtained, better precision and reliability can be achieved.
3.2 TEMPORAL FORGETTING FACTOR
Depending on whether the distribution of the parameter has changed significantly, new sample can be drawn according to the modification or the reinforcement mode. Reinforcement is employed to make the identified probability distribution more precise when it is not undergoing sudden change. Modification is employed otherwise to re-identify the distribution "from scratch". Therefore, define a model mismatch index, denoted ç², such that when surpasses predefined threshold (ç' Stn), modification is applied. In other respects, if Ç* I Sth, then Ç" is used to determine X as follows:
=' 10- -
(9)
where H, is estimation of the noise mean, by calculation of the expected value in relation (I Note that employing modification is equivalent to setting X = 0. The model mismatch index itself is calculated by averaging the errors of the previous model given the current data:
1/N,
yn Σ
(F(D
(10)
BEGE-1
Remark 2:
The model mismatch index accounts for all sources of uncertainty in the system. To calculate Seh, one needs to precalculate the persisting error between the designated modeled and measured data. In other words, Çsh. is basically upper bound for the unmodeled dynamics, distur- bances, noises, and any other source of uncertainty in the system.
To avoid numerical issues, the summation of probability logarithms calculated. In addition, each pair in the algorithm time sample is weighted based on its temporal distance to con- current time. Therefore Eq. 5 is modified as
Remark 3:
Im +N,
log (P(-))
Σ
log Po
(11)
P' ((Ns-)))
where p E 1] design parameter that reflects the volatility of the model parameters, and e lef: ...,.. <'n ....... efx For systems with fast-paced parameters, P should take larger values. We are trying to solve the Bayesian optimization problem that gives us the pdf the model parameters (0), when given the data pairs in the presence of uncertainty.
3.3 MINIMUM REQUIRED EVALUATIOON
Theorem 1. Let and be the desired precision and reliability. Furthermore, it can be assumed that the initial sample has enough number of evaluations (as in (7)). To satisfy the inequality in Eq. 7 the minimum number of samples k in ARMCMC is calculated using this implicit relation:
2
Kmin
2e log(
(12)
N(1 - 8) + 2(1 A0)e 21 3Kmmmn
Proof. Samples from previous pdf: According to the variable jump distribution in ( given k sam- ples, the expected number of samples drawn from the previous posterior probability (P())D)) is Akk. By assumption, the algorithm has already drawn at least samples in the previous algorithm time-step. Consequently, by (7). the expected number of samples with distances less than from E Px) drawn from previous distribution is at least Ake5.

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Samples Gaussian: By ( there are ku (1 X samples drawn in expectation. According to 113, we have Pr PPx - E(p))
of 2 g0. where dg is given by rearranging 7):
60 = 2e 2o
(13)
Thus, the expected number of samples with distances less than from E(Px) are least (111-1)
Overall reliability: The total expected number of samples with distances less than from IE((k) is the summation of the two parts mentioned above. Hence it obtained through dividing by k:
81 (X*Rō) + (6o X²)
(14)
k
Given the new obtained reliability, which is greater than the desired one, helps decrease the number of evaluations. For the sake of illustration, Fig. preseenss the minimum required number of for different precisions and reliabilities. As can be seen, the MCMC
evaluations with respect is equal to ARMCM if À is always set to one. The number of evaluations in ARMCMC mitigates as the validity of the previous model increases.
2.5
cm.00
Minimum number of samples
1.5
0.5
0.3
0.4
0.5
Figure 2: Knan with respect to for some values of 6, in ARMCMC. (for À evaluation for ARMCMC is equivalent to MCMC)
RESULTS
In this section, we demonstrate the priority of the proposed approach given two different examples. First, we employ the proposed method to identify the soft bending actuator model and compare the results with a Recursive Least Squares (RLS). the second example, we evaluate it on the Hlunt-Crossley model given reality-based based data and compare it with simple MCMC and RLS.
4.1 SIMULATION RESULTS
For this part, we consider the dynamic model of a fluid soft bending actuator. The dynamic is given by the following relation: (Wang et al. 2019)
á qi(p Patm) ) - q2 93a
U. sign(p= p) lp - pl =qp + qstp, = 0
(15)
Ue uasign(p Patm) V h/ppppaate Patml = 96p qnpp, Uc O,
where a the angle of the actuator, Me, Ue are the control inputs, and p. Ps Patm are the current, compressor and atmosphere pressure respectively. For this example, assume a1 1408.50, d2 132.28, f3 = 3319.40 are known and Patm 101.3/111 101.3kpa, four other parameters (q4,.., 97). To this end, we assume the hybrid model below:
800kpa. We are trying to identify the
sign(p. p) pps pl 0. + Ozip, {ue, Ud)
(16)

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1.6
AR-MAPS FILS
(95.0
1.4
64
(060)
-11
-15
Wh
4 1,000
0.2
(loc)
(b) Angle of the actuator
(a) Parameter variation RLSS and AR-MAPS
Figure 3: Comparison of RLS and AR-MAPS for soft bending actuator
As the range of these parameters are small, we scale the input vector by the factor of 107 for RLS. Given the input Ud) Ua) and the output (p, want to identify the parameter and estimate the current angle of actuator knowing its initial position at the origin. The data sample time T = ms and each data pack includes 100 samples which results in an algorithm sample time equal to T. 0.1 sec. The point estimation obtained by considering the mode at the modification phase and the medium during the reinforcement phase in ARMCMC is denoted as AR-MAPS. The point estimate results for the parameter estimation are shown in Fig. Ba The true parameters are qs -2.14 x 10-4, Y6 = 6.12 x 10-9, 9 '77 = -9.76 x 10-5 48
1.90 x 10-9, The second norm of the parameters' errors are 0.0235, 6.0053 x 10-7 for 0₁, 02 in RLS and 0.0089. 1.1840 x 10-7 in AR-MAPS, respectively. Moreover, the estimation of the angle plotted Fig. 3b
4.2 EMPIRICAL RESULTS
In this section, we demonstrate ARMCMC by identifying parameters of the Hunt-Crossley model, which represents environment involving needle contacting soft material. The needle is mounted as an end-effector on a high preciprcision translational robot, which switches between two modes: free motion and contact. Due abrupt changes in the model parameters when the contact is established or lost, online estimation of the force is extremely challenging.
4.2.1 CONTACT DYNAMIC MODEL
Consider the dynamic of contact as described by the Hunt- Mout-Crossley model which is more consistent with the physics of contact than classical linear models such as Kelvin- Kelvin-Voigt (Haddadi Hashtrudi- Zaad (2012). In order to overcome the shortcomings of linear models, Hunt & Crossley (1975)
proposed the following hybrid/nonlinear model:
fe(x(t)) - Ka ( B.r
x(t) 0 (x) 0'
(17)
0
in which Kg. B.x² denote the nonlinear clastic and viscous force coefficients, respectively. The parameter p is typically between I and 2, depending on the material and the geometric properties of contact. Also (t), (t)), fe are the current position, velocity (as inputs X) and contact force (as output (Y' in [T] of a needle near or inside the soft material, with r 2 0 representing the needle being move freely in open space or penetrate the soft material; the forces on this needle are modeled using the Hunt-Crose Cruns-Crsssle model. The practical problem we consider is to estimate the force at the tip of the needle by identifying the model parameters. Ke. Be, p three unknown parameters (0 in Eq. (T)) that needs to be estimated. An online estimate of environment force plays pivotal role in stable interaction between robotic manipulators and unknown environments.
inside. This needle

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To make the parameters ready for the regression problem we have
log(fe) log K Ka= Bebg log(fe) =p (zg + log K. + B.
(18)
We will use the RLS method proposed in (Haddadi & Hashtrudi-Zaad 2012) as a baseline of com- parison where it is needed to make the assumption that Fe << I. It should be noticed that the vector of parameters (0) in the following relation are not independent, which may lead to divergence. With this assumption, we have
log(1 + Be/Kat,) Be/ Ke/K
(19)
log(Je) (o, )+ log(Ke)) + Bel Re/.....
6 = [,, [n(
(20)
0 = log(KK), Be/ Ke.p
4.2.2 SETUP
The data structure is same as previous simulation. Prior knowledge of all three parameters (Ke, Be. p) are initialized to N (1,0.11 0.1) (a normal distribution with μ and a = 0.1) More- over, more data is collected, the spread of the posterior pdf decreases. A bit after seconds, the needle goes outside of the soft material, and experiences zero force; this is equivalent to all param- eters being set to zero. The color-based visualization of probability distribution over time used for the three parameters in Fig. 4al probability density), there is no contact and the parameter values are equal to zero.
During the period of time that the whole space is blue (zero
Since are taking Bayesian approach, are able to estimate the entire posterior pdf. However, for the sake of illustration, the point estimates are computed by using AR-MAPS method which is shown in Fig. 4b for the time-varying parameters 0 = Key 02 Bz,0s p. During the times that RLS results are chattering due to the use of saturation (if not, the results would have diverged), the needle is transitioning from being inside the soft material to the outside vice versa. In addition, due to the assumption 19). performance can deteriorate even when there is no mode transition. Furthermore, in the RLS approach, estimated parameters suddenly diverged during free motion, since the regression vectors are linear dependent. In contrast, with the Bayesian approach, this issue can be easily resolved. The result of ARMCMC is presented in Fig. [5] which shows the force estimation with two different identification approaches. This probability of interest can be easily obtained by deriving the parameter density at one's disposal.
4.2.3 QUANTITATIVE COMPARISON
Quantitative details of comparing a naive point estimate of the ARMCMC algorithm by averaging the particles (AR-APS) and the RLS method are listed in Table [ This reveals more than 70% improvement in the precision of all model parameters throughout the study by using the Mean Ab- solute Error (MAE) criteria and also more than a 55% improvements in the second norm of force estimation error. Among parameters, the viscose (B.) has the largest error in the RLS method since it is underestimated due the restrictive assumption in Eq. (19). The AR-MAPS approach uplifts the performance of the parameter identification and the force estimation.
We also compare ARMCMC to MCMC. For the algorithm to run in real-time, MCMC requires more time to converge. For this example, with X = 0.7, the value of Kmin is 15000 for MCMC but only 6000 for ARMCMC (more than two times faster) with e = 0.01, 5 = 0.9. Two approaches that can be used to fix this drawback are to reduce the number of samples, which results in worse precision and reliability compared to ARMCMC, or to increase the algorithm sample time which would cause more delay in the estimation result and slower responses to changes in the parameter.
CONCLUSIONS
This paper presented an algorithm for an online identification of full probability distribution of model parameters in a Bayesian paradigm using adaptive recursive MCMC. Due to the abrupt
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15
(b) Model parameters point estimation in AR-MAPS.
(a) Probability distribution using ARMCMC.
Figure 4: Estimation of model parameters (0) Ke. 02 Be. 0z for Hunt-Crossley
2
1.5
Force estimation error (mN)
-0.5
-1.5
(N~5000)
MCMC (T=200ms)
-2.
RLS
2
10
12
14
16
18
20
Time (Sec)
Figure 5: Force prediction error in RLS, AR-APS, and MCMC
Table 1: Comparison of RLSS Haddadi & Hashtrudi-Zaad 2012) and point estimate of ARMCMC and MCMC for environment identification.
ERRORS
MAE K.
MAE
MAE p
RMS F, (MN)
RLS
0.5793
0.9642
0.3124
51.745
MCMC (N=5000)
0.6846
0,8392
0.3783
76.695
MCMC (T, 0.2)
0.7294
0.9964
0.4195
101,88
AR-APS
0.0774
0.0347
0.0945
33.774
AR-MAPS
0.0617
0.0316
0.0756
31.659
change of model parameters such as contact with soft environment when it established/lost. con- ventional approaches suffer from low performance. Empirical results on the Hunt-Crossley model as a nonlinear hybrid dynamic model was compared with a well-known conventional identification process and revealed proficiency of the proposed algorithm. The proposed method provides sys- tematic strategy for handling abrupt changes which relaxes the pre-requirement conditions in the parameters. As future work, deploying fully probabilistic framework from identification to control and decision-maaee stage considered to exploit the full potentials of the Bayesian optimization. Additionally, employing method compensate the delay will be taken into consideration.

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REFERENCES
Niki Abolhassani, Rajni Patel, and Mehrdad Moallem. Needle insertion into soft tissue: A survey. Medical Engineering and Physics, 29(4):413-431, 2007.
Pedram Agand and Mahdi Aliyari Shoorchdeli. Adaptive model learning of neural networks with uub stability for robot dynamic estimation. In 2019 International Joint Conference on Neural
Networks (IJCNN), pp. 1-6. IEEE, 2019.
Pedram Agand, Hamid D Taghirad, and Ali Khaki-Sedigh. Particle filters for non- con-gaussian hunt- crossley model of environment in bilateral teleoperation. In 4th International Conference Robotics and Mechatronics (ICROM), pp. 512-517. IEEE, 2016.
Bhasin, Dupree, PM Patre, and WE Dixon. Neural network control of robot interacting with an uncertain hunt-crossley viscoelastic environment. In Dynamic Systems and Control Conference, volume 43352, pp. 875-882, 2008.
Christopher M Bishop. Pattern recognition. Machine Learning, 128, 2006.
Steve Brooks, Andrew Gelman, Galin Jones, and Xiao-Li Meng. Handbook of markov chain monte carlo. CRC press, 2011.
André S Carvalho and Jorge M Martins. Exact restitution and generalizations for the hunt-crossley contact model. Mechanism and Machine Theory, 139:174-194, 2019.
Noah J Cowan, Ken Goldberg, Gregory S Chirikjian, Gabor Fichtinger, Ron Alterovitz, Kyle B Reed, Vinutha Kallem, Wooram Park, Sarthak Misra, and Allison M Okamura. Robotic needle steering: Design, modeling, planning, and image guidance. In Surgical Robotics, pp. 557-582. Springer, 2011.
Nicola Diolaiti, Claudio Melchiorri, and Stefano Stramigioli. Contact impedance estimation for robotic systems. IEEE Transactions Robotics, 21(5):925-95) 9355, 2005.
Peter Green. Reversible jump markov chain monte carlo computation and bayesian model deter- mination. Biometrika, 82(4):711-732, 1995.
Peter L Green. Bayesian system identification of a nonlinear dynamical system using novel variant of simulated annealing. Mechanical Systems and Signal Processing, 52:133-146, 2015.
Amir Haddadi and Keyvan Hashtrudi-Zaad Real-time identification of hunt-crossley dynamic mod- els contact environments. IEEE transactions on robotics, 28(3):555-566 2012.
KH Hunt and FRE Crossley. Coefficient of restitution interpreted as damping in vibroimpact. Jour- nal of applied mechanics, 42(2):440 445, 1975.
Dominik Joho, Gian Diego Tipaldi, Nikolas Engelhard, Cyrill Stachniss, and Wolfram Burgard. Nonparametric bayesian models for unsupervised scene analysis and reconstruction. Robotics: Science and Systems VIII. pp. 161, 2013.
Shima Khatibisepehr, Biao Huang, and Swanand Khare. Design of inferential sensors in the process industry: A review of bayesian methods. Journal of Process Control, 23(10):1555-156 2013.
Scott Kuindersma, Roderic Grupen, and Andrew Barto. Variational bayesian optimization for run- time sensitene control. Roboties: Science and Systems VIII, 2012.
Tomasz Kuśmierezyk, Joseph Sakaya, and Arto Klami. Variational bayesian decision-making for continuous utilities. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d Alché-Buc, E. Fox, and R. Garnett (eds.), Advances in Neural Information Processing Systems 32, pp. 6392-6402. Curran Associates, Inc., 2019.
Brett Ninness and Soren Henriksen. Bayesian system identification via markov chain monte carlo techniques. Automatica, 46(1) 1):40-5,,, 2010.
Ali Noormohammadi-Ae and Hamid D Taghirad. Multi-goal motion planning using traveling sales- problem in belief space. Information Sciences, 471:164-184 184 2019.
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Under review as a conference paper at ICLR 2021
Kaur Aare Saar, Fabio Giardina, and Fumiya lida. Model-free design optimization of a hopping robot and its comparison with a human designer. IEEE Robotics and Automation Letters, 3(2): 1245-1251, 2018.
Roberto Tempo, Giuseppe Calafiore, and Fabrizio Dabbene. Randomized algorithms for analysis and control of uncertain systems: with applications. Springer Science & Business Media, 2012.
Felipe Tobar. Bayesian nonparametric spectral estimation. In S. Bengio. H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett (eds.), Advances Neural Information Processing Systems 3/, pp. 10127-10137. Curran Associates, Inc., 2018.
Beilun Wang, Arshdeep Sekhon, and Yanjun Qi. A fast and scalable joint estimator for integrat- ing additional knowledge in learning multiple related sparse Gaussian graphical models. In Jennifer Dy and Andreas Krause (eds.), Proceedings of the 35th International Conference Machine Learning, volume 80 of Proceedings of Machine Learning Research, pp. 5161-5170, Stockholmsmässan, Stockholm Sweden, 10-15 Jul 2018. PMLR.
Tao Wang, Yunce Zhang, Zheng Chen, and Shiqiang Zhu. Parameter identification and model- based nonlinear robust control of fluidic soft bending actuators. IEEE/ASME Transactions on Mechatronics, (4(3):1346-11) 2019.
A APPENDIX
According to Abolhassani et al. (2007) a nonlinear hybrid model based on a reality-based soft environment considered follows:
fe = fm + (u( t,(
(21)
where x is the needle tip position and ip is the latest time of puncture. Initial position of the envi- ronment is assumed to be at the origin. The stiffiness of the force (fs) belongs a pre-puncture and the friction (ft)) and cutting forces (fez) belong to a post-puncture. The stiffness force is modeled using a nonlinear Hunt-Cront CrossCyyssley model:
x <<< 0
fal = (t)
(22)
12, t2pp
where Ke, p are the same parameters defined in (17). The maximum depth that the soft environment yields before the puncture and its position after it is denoted by 21, 22, respectively (0 < 22 < x1))
In this study, the needle insert up 16.65, 10.21 before and after penetration. A friction model is inspired from modified Karnopp model.
Cnsgn(i) + Ba max Fa)
i < Au//2 - <
f1)
(23)
max Fa)
0 à < Av/2
Cpsgn(i) + B.xa 2 Av/2
where C, 111.96 10-3 and Cp 10.57 10-3 are negative and positive values of dynamic friction, D, = -0.01823 and D, = 0.01845 are negative and positive values of static friction, and Be, p are same Eq. (17). The relative velocity between the needle and tissue denoted by and 2e/2 0.005 is the value below where the velocity is considered to be zero, and F, is the sum of non-frictional applied forces. The cutting force is considered as static force constant for the tissue and the needle geometry if soft tissues are not inhomogeneous and anisotropic Cowan et al. (2011)
t,
(0.04
S0
x x x1, hp
(24)
0.94 x x> 12, tp
According to the previous relations, the system is considered as a hybrid model while providing both free motion and in-contact environment. The manipulator is translational mechanism with a friction, slip, and hysteresis loop for the actuator. To present the superiority of the proposed algorithm, the results compared with the RLS method presented in (Haddadi & Hashtrudi-Zaud 2012). To prevent the results RLS from divergence in model mismatch sequences, saturation is applied in the outputs of the identifier.
11


Reviews:
[{"review_id": "jQrRDdrAO6c", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 7, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "**Quality**\nOverall, the technical content appears correct. The authors present results that show their proposed ARMCMC method outperforms RLS and conventional MCMC for a Hunt-Crossley problem. The results also show the robustness of the proposed algorithm to adapt to abrupt changes in the model parameters.  \n\n**Clarity**\nOverall, the paper is well written. Paper should be revised to improve clarity and correct typos (non-exhaustive):\n•\tPage 1: \"Besides, inaccuracy, inaccessibility, and cost are the typical shortcomings that make them not ideal for solely use\" What does \"them\" refer to. \n•\tPage 2: appllicable, performance, t_m in definition of D^t\n•\tPage 4: \\sigma_e or \\sigma_v?\n•\tDefine \\theta in Equation (1)\n•\tEquation (6): e^t vs e^t_n?\n•\tPage 6: k_{min} on both sides of (17)\n•\tPage 7: “\\theta_1 = K_e; \\theta_1 = B_e; \\theta_3 = p”\n•\tDefine all acronyms when first used (e.g., RLS).\n•\tConsistency in notation (ARMCMC-APS vs. AR-APS)\n•\tCaptions should be more explanatory to describe figure/table content. Define acronyms in figure/table captions so that the reader does not rely on information in the text to interpret the information in the figure. Increase the font size in figures. \no\tFigure 1: Scale on y-axis (fractional minimum number of samples?). Label x-axis.  \no\tFigures 2 and 3: Labels based on the actual parameters, not generic \\theta_1, \\theta_2, \\theta_3. A better layout is to time align probability distribution (top) with the corresponding parameter estimates (bottom).\no\tFigure 4: Plot the results separately to allow easier comparison\n\n**Originality**\nAuthors provide a summary of the prior work and outline the shortcomings that their proposed work addresses. The authors claim the proposed adaptive modifications to the MCMC provide the flexibility for exploitation or exploration based on the estimated model mismatch, updating the proposal distribution to better match the current data conditions, and selecting the number of iterations for parameter estimation based on a desired level of precision and reliability. \n\n**Significance**\nThis paper describes an adaptive recursive algorithm to address the restrictive requirements of MCMC in Bayesian parameter estimation (“systems Linear in Parameter (LIP), having Persistent Excitation (PE) requirements, and assuming Gaussian noise.”). The proposed algorithm can be applicable to other latent parameter inference problems.\n---------------------------------\n**Pros**\n•\tThe authors outline the proposed modifications, which includes some assumptions and derivations - the differences between MCMC and ARMCMC are highlighted.\n•\tThe proposed algorithm is compared with other algorithms. \n•\tThe authors provide code (however, should be better annotated).\n\n**Cons**\n•\tIt is difficult to assess the generality/utility of the proposed modifications (e.g., variable jump distribution) to other applications as the performance of the proposed method is only demonstrated in a specific case. A more comprehensive analysis is needed to assess the implications of the various approximations on model performance (e.g., model initialisation, substitution with a Gaussian distribution in (15), forgetting factor). \n•\tIt is not clear how some of the parameters are chosen, e.g., threshold (\\zeta_{th}).\n•\tAuthors should first describe the methods of the experiment before presenting results to facilitate reproducibility. \n•\tProvide quantitative results for the claim: \"For the algorithm to run realtime, MCMC requires more time to converge.\" (page 7).\n", "extra_scores": {}, "extra_text": {}}, {"review_id": "bsedsh35gir", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The paper introduces a new Markov chain Monte-Carlo (MCMC) algorithm to obtain and track the posterior distribution over unknown parameters in a non-linear system. Despite its simple elegance, i.e., the introduction of a data-driven _temporal forgetting factor_ into the usual Metropolis-Hastings algorithm, the approach is, to my knowledge, novel. Its discovery seems to be the result of the intersection between fields: system identification and Bayesian sampling techniques, leading to new bridges. \n\nIn fact, novelty and interdisciplinarity are the strong points of this paper, but mostly everything else is compromised due to a severe lack of clarity. Although Section 1 is clear and fulfills its role of contextualizing the paper well, from Section 2 onward the a) organization, b) notation, c) technical inaccuracies in writing, and d) lack of detail on the application make the paper hard to read. To give just one example in each category: a) a major change in the usual MCMC scheme is explained in (and only in) _Remark 2_, Section 2.1, which is supposed to be part of the preliminaries on MCMC, b) the number of different notations for the collected data is ludicrous, and they are impossible to distinguish, c) $P_k$ in $(9)$ is not a probability density function (PDF), simply a sample of the MCMC algorithm,  and d) Section 2.4 is confusing because $p$ and $n$ are sometimes interchanged, no contextualizing figure is provided, assumptions are not interpreted, etc.   \n\nI recommend to reject this paper, but only because I believe it should be rewritten to be exposed clearly. Although the contribution is worthwhile, the paper is confusing and misleading. I am open to changing my recommendation if the authors introduce major changes in the presentation, writing, and structure, while still presenting the same content.\n\nAmong writing inaccuracies, using the term \"density estimation\" in the title of the paper is among the worse. Any Bayesian approach obtains a posterior distribution (explicitly or implicitly), but this is not the same problem as estimating the probability distribution of some given data. \n\nThe following questions point to some of the key problems I have found in the paper, without any specific order:  \n* Have the authors evaluated the assumption that the Gaussian model for noise is sufficiently robust for the application even when other noise models are used for the empirical results?  \n* Could the authors define the times at which the algorithm is run and the times at which data is collected? as well as the relation between them? A simple, intuitive, and correct notation for the data is needed. That could be the first step towards obtaining it. \n* Could the authors clarify in which sense the minimum number of data points is restricted (not confined) by the fact that the algorithm is aiming at real-time operation? \n* Could the authors clarify the role of $\\rho$? It is mentioned in _Remark 2_ and does not seem to appear again. \n* Could the authors give some hints to the readers on how the expectation-maximization algorithm is used for delay compensation? This would greatly aid reproducibility. \n* Could the authors explain what is, and discuss the results of, AR-MAPS in Table 1? \n* Could the authors use clearer measures of improvement than percentages of improvement? These are ill-defined and it is hard to pin which percentages are being reported. \n* Is the resulting posterior as informative when the parameters are zero because the needle is not in contact with the soft surface? Could the vertical axes in Figure 2 be expanded to explore that? \n* Could the authors clarify in which sense their simulated data is realistic? The appendix is quite uninformative to non-experts in the application. \n\nSuggestions to improve the paper -  not specifically related to my recommendation: \n* Thoroughly revise the use of English: some sentences are missing key components.\n* Emphasize and clarify throughout the paper the role of the _temporal forgetting factor_, and the fact that it is not simply a user-defined constant, but a function of the observed model mismatch: this can be confusing to those that are not used to the concept.\n* Use the entire available horizontal space in Figures 2, 3 and 4: it will help visualize some of the key features and look better.\n* Use transparency for the line plots in Figures 3 and 4: it will allow to see their individual behavior better.\n* Resize the fonts in all plots to match the size of the Figure captions: this will make them much easier to read.\n* Correct the references (capitalization, etc.), e.g., Hunt-Crossley vs hunt-crossley in (Haddadi, Hashtrudi-Zaad, 2012).\n\n\n", "extra_scores": {}, "extra_text": {}}, {"review_id": "XmyPi4rrOe", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "**The changes of the review after rebuttal are  indicated in bold text.**\n\n### Summary of the contribution\nThis article proposes an algorithm called ARMCMC (Adaptive Recursive Markov Chain Monte Carlo\" in the context of contact dynamic, for example when detecting the presence/absence of contact over time between a needle and a soft material. \nARMCMC aims at estimating the parameters of the Hunt-Crossley model, related to the elasticity and the viscosity of the material.\nThe algorithm handles both a real time estimation, and the fact that there are sudden changes in the dynamic (contact/no contact).\nAfter reminding the basics of Bayesian estimation and MCMC, Section 2 finishes with the description of the contact dynamic model. Section 3 describes the ARMCMC algorithm and its main components, while Section 4 applies it to the example cited and compares it to Recursive Least-Squares (RLS).\n\n### Strengths\nThe paper is rather well written and interesting. \nIt tackles a problem that seems difficult, especially since it is discontinuous and it is treated in real time, hence the need for both accurate and fast estimation.\n\n### Weaknesses and concerns\n1. Organization of the paper and clarity \n- The title and introduction are a bit misleading as we expect to see a general method, while it appears later that it is designed specifically for the example given in the experiment.\nIf it is more general than that, I encouraged the authors to discuss other possible applications. \n\n**The authors added an experiment to show that the method is more general than it appeared in the first version, giving more strength to the paper.**\n\n- For a submission to a conference in artificial intelligence, it would be better to have less details on the well known MCMC (or at least put the details in appendix), \nand more details about the specific application. \n- The application envisioned is only specified in Section 4, while it would improve the comprehension were it already described in Section 2. \nIn particular, there is mention of a needle after Eq 10, the purpose of which we only understand 3 pages later. \n2. Related work\nOnly one other algorithm is compared with the one proposed (RLS) it seems to me that related work has been overlooked.\n- please discuss how ARMCMC differs from RJMCMC (Reversible Jump MCMC), where we could jump between model 1 (no contact) and model 2 (contact) back and forth.\n\n**The authors answered that comment a bit quickly, in my opinion, as RJMCMC has been applied to a change-point problem in the original paper, which seems to be similar to the one presented in the paper. However, their argument on realtime is valid.**\n\n- also, how does the proposed algorithm relate to the following ones?\n\to \"Particle filters for non-Gaussian hunt-crossley model of environment in bilateral teleoperation\", Agand et al (2016), which is cited for other reasons\n\to \"Neural Network Control of a Robot Interacting With an Uncertain Hunt-Crossley Viscoelastic Environment\", Bhasin et al (2008)\n\to \"Exact restitution and generalizations for the Hunt–Crossley contact model\", Carvalho and Martins (2019)\n\n**The authors agree that the work mentioned propose different approaches to the same model, but do not compare these approaches to the one they proposed in their experiment, and do not give enough details as to why.**\n\n3. Minimum number of evaluations\nFigure 1 shows an evaluation of the minimum number of evaluations depending on the values of the parameters: \n- how come there are values lower than 1? \n- In practice, was $k$ round up from $k_{min}$?\n- is it in purpose that it is called $k_{min}$ in Eq 17 and Figure 1, and $k_{max}$ in Algorithm 1?\n\n**The authors answered all the questions related to $k_{min}$, and it is now clearer.**\n\n4. Empirical results\n- The setting of the experiment is not specified: which material was used? Or was it synthetic data?\n- There is a mention of results without EM at the end of section 4.1, but are there any WITH EM, and if not why is it so?\n- In Table 1, why use different metrics for the parameters and for $F_e$? Why not use RMS everywhere? Does that mean that there are some points that are strongly over- or under-estimated? Or is it because of the lag (see comment below)?\n- In Figure 3: \n\to how come the lag for the absence of contact is so important with ARMCMC, while there is almost no lag for the beginning of contact? is it because of the temporal factor?\n\to Can you comment on why the RLS looks so unstable?\n\to also, which of the 2 versions of ARMCMC is presented here? APS or MAPS?\n\to Why is there no comparison with MCMC in Figure 3, whereas it appears in all other results?\n- Figure 4 is rather hard to read: please consider using doted/dashed lines and possibly markers to distinguish better between the estimators\n- There is mention in the introduction and in Section 2 that RLS requires some restrictive conditions:\n\to are they not realistic in practice?\n\to it would be interesting to see a case where those conditions are not met, showing the strength of the proposed algorithm\n\n### Question\nDo the parameters for viscosity and elasticity of a material vary in time? Is it really important to keep estimating them in real time, or can't they just be updated once in a while?\n\n### Minor comments\n- Eq. 8 and 9, please replace the implication sign by a sentence for better readibility.\n- In section 2.4, 2nd line: put the reference of Haddadi and Hashtrudi-Zaad in parenthesis to improve readibility.\n- After Eq.10, the third parameter is designed by $n$ instead of $p$.\n- After Eq 11, the acronym RLS is not defined: I had to go see the reference to see that the R stands for recursive, and not reweighted e.g.\n- Eq. 19 mentions the variables $\\delta_2$ and $\\delta_0$, but there are no $\\delta_1$ anywhere.\n- Please increase the fontsize of the axis and legends in Figures 2 to 4.\n- **Typo \"apllicable\" on page 2**\n\n### Overall evaluation\nWhile the topic and the approach are interesting, I believe the state of the art has not been discussed sufficiently. \nIf some of the suggested work indeed relate to the proposed one, they should be included in the experiment for comparison.\n\n**After rebuttal, I think the authors did a good job in clarifying some points and adding an example in the experiment, which is why I upgrade the score I gave. However, I don't understand why they don't compare in the experiment with some of the methods from the cited literature concerned with the same model, especially Diolaiti et al. (2005).**", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: Pros:
- The authors propose a novel method to perform MCMC in the condition where there is a distribution over models describing the data, rather than just a distribution over the parameters of a single consistent model (ie, in the theme of reversible jump MCMC). Sampling from the posterior of mixtures of parametric models is something current MCMC algorithms are very bad at, so this addresses an important need.
- Reviewers believed the proposed technique was novel and technically correct.
- The paper appears to build a bridge between the fields of system identification and Bayesian sampling techniques

Cons:
- Major concerns were raised about lack of clarity
- - From a *lightweight* read, I also had difficulty understanding what the paper was proposing, or even the precise problem it was tackling
- Experimental validation was limited, and missing baselines
- During discussion, the paper had no strong advocate
Decision: Reject