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In statistics, sequential estimation refers to estimation methods in sequential analysis where the sample size is not fixed in advance. Instead, data is
Sequential_estimation
Statistical analysis where the sample size is not fixed in advance
classical hypothesis testing or estimation, at consequently lower financial and/or human cost. The method of sequential analysis is first attributed to
Sequential_analysis
Process of controlling orientation of an aerospace vehicle
Junkins.. Chapman and Hall/CRC, 2004. Kalman filtering can be used to sequentially estimate the attitude, as well as the angular rate. Because attitude
Spacecraft attitude determination and control
Spacecraft_attitude_determination_and_control
Method of data analysis
useful to make an estimate of the PCA projection that can be updated sequentially. This can be done efficiently, but requires different algorithms. In
Principal_component_analysis
Nonparametric measure of rank correlation
estimators. These estimators, based on Hermite polynomials, allow sequential estimation of the probability density function and cumulative distribution
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Branch of mathematics concerning probability
partial knowledge of their state, as in statistical mechanics or sequential estimation. A great discovery of twentieth-century physics was the probabilistic
Probability_theory
American mathematician and statistician (1919–2010)
Blackwell published the paper "Conditional Expectation and Unbiased Sequential Estimation", which outlined a technique that later became known as the Rao–Blackwell
David_Blackwell
Process for estimating a probability density function
PDF into a deterministic discrete grid Sequential Bayesian filtering is the extension of the Bayesian estimation for the case when the observed value changes
Recursive_Bayesian_estimation
Digital circuit design abstraction
A synchronous circuit consists of two kinds of elements: registers (sequential logic) and combinational logic. Registers (usually implemented as D flip-flops)
Register-transfer_level
Algorithm that estimates unknowns from a series of measurements over time
"Factorization Methods for Discrete Sequential Estimation". Factorization Methods for Discrete Sequential Estimation. Bibcode:1977fmds.book.....B. Bar-Shalom
Kalman_filter
Mathematical decision rule
for sequential estimation, where the posterior of the current measurement is used as the prior in the next measurement. In sequential estimation, unless
Bayes_estimator
Type of Monte Carlo algorithms for signal processing and statistical inference
localization Moving horizon estimation Recursive Bayesian estimation Wills, Adrian G.; Schön, Thomas B. (3 May 2023). "Sequential Monte Carlo: A Unified Review"
Particle_filter
Estimation method that minimizes the mean square error
estimates. One crucial difference between batch estimation and sequential estimation is that sequential estimation requires an additional Markov assumption.
Minimum mean square error estimator
Minimum_mean_square_error_estimator
British statistician (c. 1701 – 1761)
the core of almost every modern estimation approach that includes conditioned probabilities, such as sequential estimation, probabilistic machine learning
Thomas_Bayes
Structural estimation is a technique for estimating deep "structural" parameters of theoretical economic models. The term is inherited from the simultaneous
Structural_estimation
index Separation test Sequential analysis Sequential estimation Sequential Monte Carlo methods – redirects to Particle filter Sequential probability ratio
List_of_statistics_articles
although sequential versions were later developed, specifically the SNPHAP method. The most accurate and widely used methods for haplotype estimation utilize
Haplotype_estimation
Statistical experiment designs
GB; Chen, H; Vasudeva, RB (1966). "Sequential estimation of quantal response curves: a new method of estimation". Biometrika. 53 (3–4): 439–454. doi:10
Up-and-down_design
Theorem in statistics
(1955) Ghosh, Malay; Mukhopadhyay, Nitis; Sen, Pranab Kumar (2011), Sequential Estimation, Wiley Series in Probability and Statistics, vol. 904, John Wiley
Basu's_theorem
process has a finite state space. Magiera, R. (1998). "Optimal Sequential Estimation for Markov-Additive Processes". Advances in Stochastic Models for
Markov_additive_process
Polish mathematician and statistician (1932–2008)
Doktoraty". www.impan.pl. Retrieved 2025-02-24. Trybuła, Stanisław. "Sequential estimation in processes with independent increments". Dissertationes Mathematicae
Stanisław_Trybuła
Hypothesis test in mathematics
The sequential probability ratio test (SPRT) is a specific sequential hypothesis test, developed by Abraham Wald and later proven to be optimal by Wald
Sequential probability ratio test
Sequential_probability_ratio_test
Resource problem in machine learning
constructed convergent population selection strategies in "some aspects of the sequential design of experiments". A theorem, the Gittins index, first published
Multi-armed_bandit
Probabilistic problem-solving algorithm
and MCMC methodologies, these mean-field particle techniques rely on sequential interacting samples. The terminology mean field reflects the fact that
Monte_Carlo_method
Process by which software is developed
difference between methodologies is the degree to which the phases are sequential vs. iterative. Agile methodologies, such as XP and scrum, focus on lightweight
Software_development_process
Statistical theorem
statistics Blackwell, D. (1947). "Conditional expectation and unbiased sequential estimation". Annals of Mathematical Statistics. 18 (1): 105–110. doi:10.1214/aoms/1177730497
Rao–Blackwell_theorem
Sequential model-based optimization of expensive black-box functions
Bayesian optimization is a sequential model-based strategy for global optimization of black-box objective functions whose evaluations are costly. It is
Bayesian_optimization
Determining the position and orientation of a robot by analyzing associated camera images
odometry is the process of determining equivalent odometry information using sequential camera images to estimate the distance traveled. Visual odometry allows
Visual_odometry
Class of reinforcement learning algorithm
algorithms include Monte Carlo (MC) RL, SARSA, and Q-learning. Monte Carlo estimation is a central component of many model-free RL algorithms. The MC learning
Model-free (reinforcement learning)
Model-free_(reinforcement_learning)
partial knowledge of their state, as in statistical mechanics or sequential estimation. A great discovery of twentieth-century physics was the probabilistic
Glossary_of_engineering:_M–Z
Statistical technique correcting sampling bias
ISBN 0-674-00560-0. Cameron, A. Colin; Trivedi, Pravin K. (2005). "Sequential Two-Step m-Estimation". Microeconometrics: Methods and Applications. New York: Cambridge
Heckman_correction
Procedure to estimate standard deviation from a sample
In statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Hungarian mathematician
decision theory, geometry and econometrics, and founded the field of sequential analysis. One of his well-known statistical works was written during World
Abraham_Wald
Rule for estimating the mean of a dataset
{\displaystyle {\boldsymbol {Y}}:=(Y_{1},Y_{2},\dots Y_{m})} . It arose sequentially in two main published papers. The earlier version of the estimator was
James–Stein_estimator
Computational method in Bayesian statistics
wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years
Approximate Bayesian computation
Approximate_Bayesian_computation
Creation and maintenance of software
customized and emergent for the development effort. The process may be sequential, in which each major phase (i.e., design, implement, and test) is completed
Software_development
Problem in statistical estimation
In the statistical theory of estimation, the German tank problem consists of estimating the maximum of a discrete uniform distribution from sampling without
German_tank_problem
Reconstructing an historical ocean state
climatological monthly estimates. The second approach is that of the sequential data assimilation analyses, which move forward in time from a previous
Ocean_reanalysis
foundations of statistics. Included earlier results of Wald on sequential analysis and the sequential probability ratio test and on Wald's complete class theorem
List of publications in statistics
List_of_publications_in_statistics
Form of dyadic relationship
Serial monogamy is a mating practice in which individuals may engage in sequential monogamous pairings, or in terms of humans, when men or women can marry
Monogamy
Statistical method
intervals, prediction error, etc.) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling
Bootstrapping_(statistics)
Procedure for comparing multivariate sample means
life satisfactions scores measured at sequential time points and p job satisfaction scores measured at sequential time points. In this case there are k+p
Multivariate analysis of variance
Multivariate_analysis_of_variance
Perception concept
subsystem, or an elementary component of the system (e.g. a neuron). In sequential ideal observer analysis, the goal is to measure a real system's performance
Ideal_observer_analysis
Empirical law on the variance of species in a habitat
single-nucleotide polymorphisms (SNPs) gene structures in number theory with sequential values of the Mertens function and also with the distribution of prime
Taylor's_law
Statistical algorithm
Zili; Zhang, Peng; Qi, Wenjuan; Liu, Jinfang; Gao, Yuan (2012-04-15). "Sequential covariance intersection fusion Kalman filter". Information Sciences. 189:
Covariance_intersection
Concept in econometrics
from those that are predetermined (exogenous). Ignoring simultaneity in estimation leads to biased and inconsistent estimators, as it violates the exogeneity
Endogeneity_(econometrics)
Computer simulation of chemical systems
theorem. The phase estimation algorithm can be enhanced or altered in several ways, such as using a single ancilla qubit for sequential measurements, increasing
Quantum computational chemistry
Quantum_computational_chemistry
Sub-field of reinforcement learning
explored using classic matrix games such as prisoner's dilemma, more complex sequential social dilemmas, and recreational games such as Among Us, Diplomacy and
Multi-agent reinforcement learning
Multi-agent_reinforcement_learning
Statistical method of dividing data into equal-sized intervals for analysis
a random process. These are statistics derived methods, sequential nonparametric estimation algorithms in particular. There are a number of such algorithms
Quantile
Mathematical optimization algorithm
methods include: Successive linear programming (SLP) Sequential quadratic programming (SQP) Sequential linear-quadratic programming (SLQP) Reduced gradient
Active-set_method
Israeli-American academic
interplay between estimation theory and information theory, entropy, noise reduction (denoising), filtering, prediction, sequential decision making, learning
Tsachy_Weissman
Statistician and professor
research in nonparametric inference, sequential analysis, decision theory, Bayesian statistics and small-area estimation. As a recognition of his seminal
Malay_Ghosh
Function of the observed sample results
difference between the two meanings of "extreme" appear when we consider a sequential hypothesis testing, or optional stopping, for the fairness of the coin
P-value
Overview of and topical guide to statistics
(statistics) Survival analysis Density estimation Kernel density estimation Multivariate kernel density estimation Time series Time series analysis Box–Jenkins
Outline_of_statistics
Distribution estimation technique
to sample from a different distribution to lower the variance of the estimation of E P [ X ] {\displaystyle \mathbb {E} _{\mathbb {P} }[X]} , or when
Importance_sampling
Class of video frames processed in a distinct way by a compression algorithm
I-macroblocks Multi‑frame motion estimation (up to 16 reference frames or 32 reference fields) Multi‑frame motion estimation increases the quality of the
Video compression picture types
Video_compression_picture_types
Method of statistical inference
interesting information. Also, this technique can hardly be avoided in sequential analysis." "A useful fact is that any Bayes decision rule obtained by
Bayesian_inference
Design of tasks
experimenting, is within the scope of sequential analysis, a field that was pioneered by Abraham Wald in the context of sequential tests of statistical hypotheses
Design_of_experiments
Branch of statistics
situations. Inferential statistics are used to test hypotheses and make estimations using sample data. Whereas descriptive statistics describe a sample,
Mathematical_statistics
Time series statistical test
vectors is r = r* < k, vs. the alternative that r = k. Testing proceeds sequentially for r* = 1,2, etc. and the first non-rejection of the null is taken as
Johansen_test
Branch of statistics focusing on spatial data sets
random variable) theory to model the uncertainty associated with spatial estimation and simulation. A number of simpler interpolation methods/algorithms,
Geostatistics
rather than number, to refer to the concept that supports approximate estimation but does not support an exact representation of number quality. Number
Number_sense_in_animals
Proposition in statistics
strong likelihood principle applies this same criterion to cases such as sequential experiments where the sample of data that is available results from applying
Likelihood_principle
Theory in microeconomics
Jae Hyen; Chintagunta, Pradeep K.; Misra, Sanjog (2019-05-06). "Estimation of Sequential Search Model". SSRN. Rochester, NY. SSRN 3203973. Ursu, Raluca;
Search_theory
directions. The data interaction process can be well explained as a local sequential Bayesian updating process within a neighborhood. Because single-step transition
Markov_chain_geostatistics
Relationship between items in a set
an Internet search engine may rank the pages it finds according to an estimation of their relevance, making it possible for the user quickly to select
Ranking
Collection of statistical models
planned to satisfy the goals of the experiment. Experimentation is often sequential. Early experiments are often designed to provide mean-unbiased estimates
Analysis_of_variance
Statistical concept
clustering, under the name model-based clustering, and also for density estimation. Mixture models should not be confused with models for compositional data
Mixture_model
Business process modeling tool
and IDEF. A control-flow diagram can consist of a subdivision to show sequential steps, with if-then-else conditions, repetition, and/or case conditions
Control-flow_diagram
Algorithmically generated data that have a similar distribution as sampled data
synthetic data with missing data. Similarly, they developed the technique of Sequential Regression Multivariate Imputation. Researchers test the framework on
Synthetic_data
Class of statistical modeling methods
predictions. Other examples where CRFs are used are: labeling or parsing of sequential data for natural language processing or biological sequences, part-of-speech
Conditional_random_field
Statistical Markov model
0 {\displaystyle t=t_{0}} . Estimation of the parameters in an HMM can be performed using maximum likelihood estimation. For linear chain HMMs, the Baum–Welch
Hidden_Markov_model
Indian statistician
in 1995. Most notable areas of his research include, sequential analysis, statistical estimation in diffusion processes, the law of large numbers and
Arup_Bose
Statistical test
to calculate sums of squares. The three most common types are Type I (sequential), Type II (hierarchical), and Type III (marginal). Most statistical software
Two-way_analysis_of_variance
Metric used in probability and statistics
Q)={\sqrt {1-BC(P,Q)}}.} Hellinger distances are used in the theory of sequential and asymptotic statistics. The squared Hellinger distance between two
Hellinger_distance
Bayesian-optimal mechanism Bayesian-optimal pricing Bayesian optimization – Sequential model-based optimization of expensive black-box functions Bayesian poisoning –
List of things named after Thomas Bayes
List_of_things_named_after_Thomas_Bayes
American statistician
November 15, 1941) is an American statistician who has worked extensively on sequential analysis. Siegmund grew up in Webster Groves, Missouri. He received his
David_Siegmund
Order issued by a business or trader to a customer
allows the internal audit control of completeness to be monitored. A sequential sales order number may be used by the company for its sales order documents
Sales_order
Mathematical problem involving optimal stopping theory
ranked from best to worst unambiguously. The applicants are interviewed sequentially in random order, with each order being equally likely. Immediately after
Secretary_problem
Largest known fish species
(February 21, 2023). "A Devonian Fish Tale: A New Method of Body Length Estimation Suggests Much Smaller Sizes for Dunkleosteus terrelli (Placodermi: Arthrodira)"
List_of_largest_fish
Polynomial sequence
Herrmann, J. (1981). "Cross coupling and aliasing in modal wave-front estimation". J. Opt. Soc. Am. 71 (8): 989. Bibcode:1981JOSA...71..989H. doi:10.1364/JOSA
Zernike_polynomials
Progressive neurodegenerative disease
resulting in overall slowed movement with reduced amplitude that affects sequential and simultaneous tasks. Bradykinesia can also lead to hypomimia, reduced
Parkinson's_disease
Technique for setting initial values of trainable parameters in a neural network
modelling in LSTM. Orthogonal initialization has been generalized to layer-sequential unit-variance (LSUV) initialization. It is a data-dependent initialization
Weight_initialization
German academic working in photogrammetry and geodesy
studies and blunder detection in bundle systems Algorithms for sequential estimation in bundle systems (on-line triangulation) Geometrically constrained
Armin_Gruen
Continuous progression from past to future
or temporal existence, is broken or transcended. We are not stuck in sequential time. We are able to remember the past and project into the future; we
Time
American economist and econometrician (born 1971)
contributions to three fields: affirmative action in higher education, structural estimation of dynamic discrete choice models, and college major choice, having written
Peter_Arcidiacono
Method in the dynamics of blood flow
forward and backward waveforms follow from summing the magnitudes of the sequential wavelets P ± = Σ Δ P ± {\displaystyle P_{\pm }=\Sigma \Delta P_{\pm }}
Wave_intensity_analysis
Law of time perception
neither overestimated nor underestimated. The other major paradigm of time estimation methodology measures time prospectively as seen in the time measurement
Vierordt's_law
Model to simulate Li-ion cells electrical dynamics
real-time Battery Management System (BMS) tasks like State of Charge (SoC) estimation, State of Health (SoH) monitoring and battery thermal management. The
Equivalent circuit model for Li-ion cells
Equivalent_circuit_model_for_Li-ion_cells
Chinese American statistician (born 1960)
from 1997 to 2001. His wide research interests cover Survival Analysis, Sequential Analysis, Longitudinal Data Analysis, Stochastic Processes, Semiparametric
Zhiliang_Ying
Mathematical model for sequential decision making under uncertainty
A Markov decision process (MDP) is a mathematical model for sequential decision making when outcomes are uncertain. It is a type of stochastic decision
Markov_decision_process
transmitter, single receiver framework the Viterbi algorithm (or one of the sequential decoding algorithms) only has to proceed over a trellis in a single time
Space–time_trellis_code
AI's tendency to abruptly and drastically forget old info after learning new info
then the network readily learned all of the associations correctly. In sequential training the A-B list was trained first, followed by the A-C list. After
Catastrophic_interference
Theory and paradigm of statistics
includes a concept called 'influence of prior beliefs'. This approach uses sequential analysis techniques to include the outcome of earlier experiments in the
Bayesian_statistics
Experimental design that is optimal with respect to some statistical criterion
design of sequential experiments. Sequential analysis was pioneered by Abraham Wald. In 1972, Herman Chernoff wrote an overview of optimal sequential designs
Optimal_experimental_design
3D reconstruction technique
orientation, often through some combination of SLAM, GPS, or inertial estimation. Researchers often use synthetic data to evaluate NeRF and related techniques
Neural_radiance_field
Calculation of complex statistical distributions
expanded the MCMC toolkit, including particle filters (Sequential Monte Carlo) for sequential problems, Perfect sampling aiming for exact simulation (Jim
Markov_chain_Monte_Carlo
Random process independent of past history
types of models, that generalize Markov chains depending on whether every sequential state is observable or not, and whether the system is to be adjusted on
Markov_chain
the two-factor interaction BC has an effect on the response, then the estimation of factor A's effect on the response is contaminated because factor A's
Robust_parameter_design
Danish astronomer
generalisation of approval voting to multiple winner elections called sequential proportional approval voting, which was briefly used for party lists in
Thorvald_N._Thiele
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SEQUENTIAL ESTIMATION