# Latest News on Bayesian Estimation Research: Oct – 2019

Recursive Bayesian Estimation: Navigation and Tracking Applications

Recursive estimation deals with the matter of extracting data regarding parameters, or states, of a phase space in real time, given rackety measurements of the system output. algorithmic estimation plays a central role in several applications of signal process, system identification and automatic management. during this thesis we tend to study nonlinear and non-Gaussian algorithmic estimation issues in separate time. Our interest in these issues stems from the mobile applications of target chase, and autonomous craft navigation exploitation parcel data. [1]

Nonlinear Bayesian estimation using Gaussian sum approximations

Knowledge of the likelihood density perform of the state conditioned on all on the market mensuration knowledge provides the foremost complete doable description of the state, and from this density any of the common forms of estimates (e.g., minimum variance or most a posteriori) is determined. Except within the linear mathematician case, it’s extraordinarily tough to work out this density perform. during this paper associate degree approximation that allows the specific calculation of the a posteriori density from the Bayesian formula relations is mentioned and applied to the answer of the nonlinear filtering drawback. specially, it’s noted that a weighted add of mathematician likelihood density performs is accustomed approximate at random closely another density function. This illustration provides the premise for procedure that’s developed and mentioned. [2]

Bayesian Estimation and Prediction Using Asymmetric Loss Functions

Estimators and predictors that ar best relative to Varian’s uneven LINEX loss perform ar derived for variety of well-known models. Their risk functions and Thomas Bayes risks ar derived and compared with those of usual estimators and predictors. it’s shown that some usual estimators, for instance, a scalar sample mean or a scalar method of least squares parametric statistic computer, ar impermissible relative to uneven LINEX loss by providing different estimators that dominate them uniformly in terms of risk. [3]

Collective Animal Behavior from Bayesian Estimation and Probability Matching

Animals living in teams create movement choices that rely, among different factors, on social interactions with different cluster members. Our gift understanding of social rules in animal collectives is especially supported empirical fits to observations, with less stress in getting first-principles approaches that permit their derivation. Here we have a tendency to show that patterns of collective choices are often derived from the essential ability of animals to form probabilistic estimations within the presence of uncertainty. we have a tendency to build a decision-making model with 2 stages: Bayesian estimation and probabilistic matching.In the initial stage, every animal makes a Bayesian estimation of that behavior is best to perform taking into consideration personal data regarding the setting and social data collected by observant the behaviors of different animals. within the likelihood matching stage, every animal chooses a behavior with a likelihood adequate the Bayesian-estimated likelihood that this behavior is that the most acceptable one. [4]

A Comparison between Maximum Likelihood and Bayesian Estimation Methods for a Shape Parameter of the Weibull-Exponential Distribution

We thought-about the theorem analysis of a form parameter of the we have a tendency toibull-Exponential distribution during this paper. we have a tendency to assumed a category of non-informative priors in etymologizing the corresponding posterior distributions. specifically, the Thomas Bayes estimators and associated risks were calculated underneath 3 completely different loss functions. The performance of the Thomas Bayes estimators was evaluated and compared to the tactic of most chance underneath a comprehensive simulation study. it had been discovered that for the same parameters to be calculable, the quadratic loss operate underneath each uniform and Jeffrey’s priors ought to be used for decreasing parameter values whereas the employment of precautional loss operate are often most popular for increasing parameter values no matter the variations in sample size. [5]

Reference

[1] Bergman, N., 1999. Recursive Bayesian estimation: Navigation and tracking applications (Doctoral dissertation, Linköping University). (Web Link)

[2] Alspach, D. and Sorenson, H., 1972. Nonlinear Bayesian estimation using Gaussian sum approximations. IEEE transactions on automatic control, 17(4), (Web Link)

[3] Zellner, A., 1986. Bayesian estimation and prediction using asymmetric loss functions. Journal of the American Statistical Association, 81(394), (Web Link)

[4] Collective Animal Behavior from Bayesian Estimation and Probability Matching
Alfonso Perez-Escudero & Gonzalo de Polavieja