A Simple Sequential Stopping Rule for Monte Carlo Simulation

In this paper, a sequential stopping rule for the estimation of a probability p by means of Monte Carlo simulation is analyzed. It is shown that the proposed estimator is almost unbiased, and guarantees a given relative precision irrespective of p. Under very mild conditions, the method also guarantees a certain confidence level for a given relative estimation error, provided that p does not exceed a maximum value. An extension to importance sampling is discussed

Improved Sequential Stopping Rule for Monte Carlo Simulation

This paper presents an improved result on the negative-binomial Monte Carlo technique analyzed in a previous paper for the estimation of an unknown probability p. Specifically, the confidence level associated to a relative interval [p/\mu_2, p\mu_1], with \mu_1, \mu_2 > 1, is proved to exceed its asymptotic value for a broader range of intervals than that given in the referred paper, and for any value of p. This extends the applicability of the estimator, relaxing the conditions that guarantee a given confidence level.Comment: 2 figures. Paper accepted in IEEE Transactions on Communication

Estimation of a Probability with Guaranteed Normalized Mean Absolute Error

The estimation of a probability p from repeated Bernoulli trials is considered in this letter. A sequential approach is followed, using a simple stopping rule. A closed-form expression and an upper bound are obtained for the mean absolute error of the unbiased estimator of p. The results given permit the estimation of an arbitrary probability with a prescribed level of normalized mean absolute error

Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\hat p$, its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters $a$ and $b$ for $\hat pp$ respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as $p$ tends to $0$, and which guarantee that, for any $p$ in $(0,1)$, the risk is lower than its asymptotic value. This allows selecting the required number of successes, $r$, to meet a prescribed quality irrespective of the unknown $p$. In addition, the proposed estimators are shown to be approximately minimax when $a/b$ does not deviate too much from $1$, and asymptotically minimax as $r$ tends to infinity when $a=b$.Comment: 4 figure

Minimum-Variance Importance-Sampling Bernoulli Estimator for Fast Simulation of Linear Block Codes over Binary Symmetric Channels

In this paper the choice of the Bernoulli distribution as biased distribution for importance sampling (IS) Monte-Carlo (MC) simulation of linear block codes over binary symmetric channels (BSCs) is studied. Based on the analytical derivation of the optimal IS Bernoulli distribution, with explicit calculation of the variance of the corresponding IS estimator, two novel algorithms for fast-simulation of linear block codes are proposed. For sufficiently high signal-to-noise ratios (SNRs) one of the proposed algorithm is SNR-invariant, i.e. the IS estimator does not depend on the cross-over probability of the channel. Also, the proposed algorithms are shown to be suitable for the estimation of the error-correcting capability of the code and the decoder. Finally, the effectiveness of the algorithms is confirmed through simulation results in comparison to standard Monte Carlo method

Optimisation of energy supply at off-grid healthcare facilities using Monte Carlo simulation

In this paper, we present a methodology for the optimisation of off-grid hybrid systems (photovoltaic-diesel-battery systems). A stochastic approach is developed by means of Monte Carlo simulation to consider the uncertainties of irradiation and load. The optimisation is economic; that is, we look for a system with a lower net present cost including installation, replacement of the components, operation and maintenance, etc. The most important variable that must be estimated is the batteries lifespan, which depends on the operating conditions (charge/discharge cycles, corrosion, state of charge, etc.). Previous works used classical methods for the estimation of batteries lifespan, which can be too optimistic in many cases, obtaining a net present cost of the system much lower than in reality. In this work, we include an advanced weighted Ah-throughput model for the lead-acid batteries, which is much more realistic. The optimisation methodology presented in this paper is applied in the optimisation of the electrical supply for an off-grid hospital located in Kalonge (Democratic Republic of the Congo). At the moment, the power supply relies on a diesel generator; batteries are used in order to ensure the basic supply of energy when the generator is unavailable (night hours). The optimisation includes the possibility of adding solar photovoltaic (PV) panels to improve the supply of electrical energy. The results show that optimal design could achieve a 28% reduction in the levelised cost of energy and a 54% reduction in the diesel fuel used in the generator, thereby reducing pollution. Furthermore, we discuss possible improvements to the telecommunications of the hospital

Estimation of a probability with optimum guaranteed confidence in inverse binomial sampling

Sequential estimation of a probability p by means of inverse binomial sampling is considered. For mu_1, mu_2 > 1 given, the accuracy of an estimator p^ is measured by the confidence level Pr[p/mu_2 = c_0 for all p in (0,1), are investigated. It is shown that, within the general class of randomized or nonrandomized estimators based on inverse binomial sampling, there is a maximum c_0 that can be guaranteed for p arbitrary. A nonrandomized estimator is given that achieves this maximum guaranteed confidence under mild conditions on mu_1, mu_2

Asymptotically optimum estimation of a probability in inverse binomial sampling under general loss functions

The optimum quality that can be asymptotically achieved in the estimation of a probability p using inverse binomial sampling is addressed. A general definition of quality is used in terms of the risk associated with a loss function that satisfies certain assumptions. It is shown that the limit superior of the risk for p asymptotically small has a minimum over all (possibly randomized) estimators. This minimum is achieved by certain non-randomized estimators. The model includes commonly used quality criteria as particular cases. Applications to the non-asymptotic regime are discussed considering specific loss functions, for which minimax estimators are derived.Comment: Journal of Statistical Planning and Inference. Published online 201